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Kalman Filtering for Navigation and Target Tracking:

U.S. Navy Submarine applications related to Kalman filtering 

We have prior experience for over 40+ years in a variety of defense areas including Submarine Inertial Navigation (compare the prior hyperlink to our clearer discussion below) [and an understanding and a facility with the underlying navigation error models constituting a psi-angle analysis of an Inertial Navigation System (INS) consisting of accelerometers and gyroscopes in an integrated whole]; Air Force Aircraft Navigation and Radio Multi-lateration Relative Navigation (JTIDS RelNav) and communication (JTIDS/MUFBARS/ICNIA); Sonobuoy DIFAR/LOFAR target tracking; Search and Screening; Antenna Radar Cross-Section Detectability; NavSat (a.k.a. Transit), LORAN-C (both hyperbolic and phase-shift rho-rho circular), Bathymetry (bottom sounding sonar map-matching) and GPS analysis and usage on Submarines; and GPS analysis and usage in test aircraft (along with test plans and procedures for many of the above); and Early Warning Radar Target tracking considerations relating to the target tracking filters and estimation concerns (and the underlying mathematical models of all of the above and more). Thanks to John Rommelfanger (MITRE, retired), we have a copy of Modern Navigation Systems, a short course by (the late) Walter R. Fried (Hughes Aircraft Company), 10-12 June 1992. Of course, we at TeK Associates already had both editions of Walter R. Frieds book but having access to his slide-based concise summary is priceless. Thomas Kerr III knew Walter Fried personally and when Tom last saw him in 1994, based on Tom’s rather aggressive questions and comments from the audience, Walter Fried seemed pleased that Tom had evidently become a watchdog for navigation since they had first met back in 1980, when Tom made his first technical Navigation presentation at Position, Location, and Navigation Symposium (PLANS) in Atlantic City and Walter Fried was there as his session chairman. Tom received a written a accommodation certificate for his work and presentation there (not shown here), signed by Walter Fried himself.

Familiarity with historical application constraints and specs for many platforms (especially including C-3 Poseidon, C-4 Poseidon-back-fit [which, in those days, used multiple Univac CP-890/YUK computers in the Navigation Room], and similarly outfitted D-1 Trident SSBN\SSN submarine mission objectives, scenarios, and countermeasures). We have had first hand shipboard experience in San Diego in the 1980s and earlier weapons system and fire control training in the 1970s (regarding numbers and mixes of RVs) at Dam Neck, VA. We have also been aboard the Compass Island (sister ship of Cobra Judy used for strategic radar target tracking) in the 1970s, where components being planned for use within the SSBN Navigation Room are tested beforehand (in a Navigation Room that was identical to but bass-ackwards from how it is oriented within actual SSBNs). The U.S.S. Compass Island was replaced in this role in the late 1970s by the U.S.S. Vanguard (as obtained from NASA). We are aware of vintage 1970s vibration tests for submarine INS components using Big Bertha and the Little Chipperson the deck above it. Present day barge tests with submerged C-4 plastic explosives emulating depth charges and use of 300 pound swinging hammers, capable of impacting at up to 100 gs, now reveal weaknesses or non-compliance of electronics within the expected dangerous environments is just as important today (even if their names are no longer as colorful). We have also performed GPS testing, both dockside and at sea, onboard the SSN-701 LaJolla in the early 1980s at the San Diego, CA submarine base (for NADC and for NOSC).

We have participated in several Independent Verification and Validation (IV&V) programs for sonar\sonobuoy target tracking (PTA and LOFAR/DIFAR and LAMPS), and in analysis and development programs for integrated augmented INS navigation for Submarines (SSBNs) and in Joint Tactical Information and Distribution System (JTIDS) Relative Navigation (RelNav),  and in Development Testing and Evaluation for Operational Readiness [DT&E(OR)] for GPS navigation aboard submarines (SSNs). (To see a high level overview slide show on current status of GPS, please click here to obtain the main executable file stpete.exe. In order to view the slideshow, user must first download this associated .DLL file, then this .DLL file, then this VBX file, all to the same location in one folder on their local computer. Our Web Site host requires temporary conversion to exclusively lower case spellings. A constraint in running it is that a Windows host Operating System is required. Those typical OSs that allow this are Windows 9X/2000/NT/Millenium/XP and Vista and likely on Windows 7/10. It also runs on older OSs like Windows 3.1 and 3.11 For Workgroups.) 

“Escape Velocity” from a Linkedin discussion: I agree with what everyone said except for:
(1) when Hugo Jiménez-Pérez said that eccentricity e = 0 for a parabolic orbit (properly corrected by THK: e = 0 for a circular orbit, 0 < e < 1 for an elliptical orbit; e = 1 for a parabolic orbit; e > 1 for a hyperbolic orbit).
(2) when David Elm said that at 4 earth radii, the sun becomes a bigger factor (properly corrected by THK: the moon becomes a bigger factor first since it is nearer and has a greater effect on earth tides than the sun). Don't forget all the (i.e., 5) Libation points of three body problems (also called Lagrangian points): being L1, to L5. (these are totally unrelated to GPS frequencies of the same name designations)
(3) when Carlos Antonio Campos Nogueira said one needed to assume an idealized Earth (a perfectly homogeneous, uniform, and smooth sphere of mass M). Properly corrected by THK: one can assume a prolate ellipsoid with J2 accounted for but treat all the mass M as though it were all concentrated at the earths centroid or center of mass.
Escape velocity is aptly explained in: http://en.wikipedia.org/wiki/Escape_velocity 
Recall historical precedent: RPIs Murray R. Spiegel. Applied Differential Equations 1963 edition, with a fully worked out section: From Earth to Moon, which properly accounted for mass decrease as rocket fuel was consumed.

Other interesting precedents (to set the stage):

Lest we forget, Emeritus Prof. Ronald L. Klein (UWV) published many articles on estimation Theory using Gaussian Quadrature formulas [in order to improve the accuracy of the Propagate Step integration of the system dynamics within an EKF]. Here and in what follows below, Thomas H. Kerr III’s comments and annotations are in a different color font to make it easier for readers to distinguish (and, perhaps, to ignore).

Emeritus Prof. Thomas Kailath (Stanford Univ.) alerted the estimation community to a precedent by some Japanese researchers that posed linear estimation within a “Krein Space” instead of within a Hilbert Space and apparently obtained faster convergence as a consequence. While Matrix Positive definiteness plays a prominent role within all the analytic proofs supporting the usual Hilbert Space-based derivation of Kalman filters, the Krein Space approach frequently involves matrices that are indefinite (but, perhaps, the difference of two positive definite matrices). The tool in common is still  projections onto linear subspaces.
-Hassibi, B., Ali H. Sayed, A. H., and Kailath, T., “Linear Estimation in Krein Spaces-Part I: Theory,” IEEE Trans. on Automatic Control, Vol. 41, No. 1, pp. 18-33, Jan. 1996.

-Sayed, A. H., and Kailath, T., “A State Space Approach to Adaptive RLS Filtering,” IEEE Signal Processing Magazine, Vol. 11, No. 3, pp. 18-60, July 1994. (Here they demonstrate that most of the myriad of RLS filters are merely variants of a Linear Kalman filter.)

In the early 1970’s, many researchers from Washington University in St. Louis, MO (e.g., Alfred S. Gilman, K-P. Dunn, Prof. Ian B. Rhodes) investigated approximate nonlinear estimation in the presence of so-called “Cone-Bounded” nonlinearities so that the resulting mechanizations are still fairly tractable. Dunn and Gilman went to work at Lincoln Laboratory after obtaining their Ph.D.'s but, unfortunately, these nice results apparently were not deemed directly relevant to EWR target tracking at that time.

An additional caution by Dr. James L. Farrell (VIGIL, Inc.) in specialized topics related to Integrated Avionics in order to reach their fullest potential (as an update to the most recent version of his book on Integrated Avionics). 

For situations involving imaging and optics that have zero mean Poisson Process White noise (as the formal derivative of a Centered Poisson Process with independent increments just as Gaussian white noise is the formal derivative of a Brownian motion process [a.k.a., a Weiner process] with independent increments),  please see: (1) Donald L. Snyder, Random Point Processes in Time and Space, Springer Texts in Electrical Engineering, 2nd Ed. 1991 (1st Ed. from John Wiley and Sons, NY, 1975). Prof. Donald L. Snyder (Washington University in St. Louis, MO); (2) Fishman, P., Snyder, D. L., “The statistical analysis of space-time point processes,” IEEE Trans. on Information Theory, Vol. 22, No. 3, pp. 257-274, May 1976; (3) Snyder, D. L., and Fishman, P., “How to Track a Swarm of Fireflies by Observing Their Flashes,” IEEE Trans. on Information Theory, Vol. 21, No. 6, pp. 692-695, Nov. 1975; (4) Salimpour, Y., Soltanian-Zadeh, H., Abolhassani, M. D., “Extended Kalman Filtering of Point Process Observations,” Conf. Proc. IEEE Eng. Med. Biol. Soc., Buenos Aires, Argentina, 6670-3, Conference Dates: 31 Aug.-4 Sept. 2010. Alse see [233] to [240]. My speculations: The above technologies  could be of interest to SBIRS-high or SIBRS-low to detect and track Russia’s Avangard Hypersonic glide missiles, capable of traveling 20 times the speed of sound (i.e., 767 mph) and of performing maneuvers in taking an evasive zigzagged path as it speeds towards its designated target (and to, ostensibly, be deployed by Russia in 2019 and so far contained within a UR-100N UTTKh missile [designated in NATO terminology as the SS-19 Stiletto] first stage used to carry the glider up into the atmosphere but eventually to be replaced in this role by a new first stage missile that Russia is currently developing in 2019). It was test fired in 2018 from a silo in the Dombarovsky missile base in Orenburg Oblast, in the southern Ural Mountains and traveling more than 3,000 miles to Kura training ground in the Kamchatka region in Russia’s far northeast) and, perhaps, aim lasers toward them as potential targets of interest. [The U.S. and China are currently jointly working on a Hypersonic missile too, according to Jane’s Defense in late December 2018.]  https://www.flightglobal.com/news/articles/dod-keeps-eye-on-hypersonic-missiles-and-manoeuvring-425086/  https://news.usni.org/2019/02/01/40831?_lrsc=a801f315-b3d7-4987-b0c7-78717bd0b9e9  


Simulation of hypersonic aircraft radar and other characteristics, as seen by different sensors (click here to get this unclassified 5MB pdf on this subject): 

      Also see: https://journals.sagepub.com/doi/abs/10.1177/002072097401100415  
A Ball-Balancing System for Demonstration of Basic Concepts in the State-Space Control Theory
by V. Jørgensen First Published October 1, 1974 Research Article
The Ball-balancing Systems is intended to demonstrate the basic concepts in the state-space control theory for graduate education. The physical properties of the system are stated and the mathematical model is evaluated. Conditions of stability are discussed.

1.Jorgensen, Kjeld , The Multivariable approach in Theory and Practise (in Danish), M.Sc. Thesis, Technical University of Denmark (1971).
2.Elgard, Olle, I., Control Systems Theory, McGraw-Hill (1967).

      For a modern application of Elgard's theory above, please see: http://www.ijeei.org/docs-5184432705c6a43e405da8.pdf   
Pushpa Gaur1, Nirmala Soren1, and Debashish Bhowmik, Secondary Frequency Regulation of Multi-area Interconnected Hybrid Power System with Electric Vehicle, 
International Journal on Electrical Engineering and Informatics - Volume 10, Number 4, pp. 738-752, December 2018.
Reference list contains 25 references. The first five are:
[1]. O. I. Elgard, Electric energy systems theory, McGraw Hill, New York, 1982, pp. 299-362.
[2]. O. I. Elgerd, C. Fosha, “Optimum megawatt frequency control of multi-area electric energy systems”, IEEE Trans. Power Appl. Syst., Vol. PAS-89, No. 4, pp. 556-563, 1970.
[3]. P. Kundur, Power system stability and control, McGraw Hill, New York, 1994.
[4]. R.J. Abraham, D. Das, A. Patra, “Damping oscillations in tie power and area frequencies in a thermal power system with SMES-TCPS combination”, J Electr. Syst, Vol. 7, No. 1, pp. 71–80, 2011.
[5]. K. C. Divya, P. S. N. Rao, “A simulation model for AGC studies of hydro–hydro systems”, Int. J. Elec. Power and Energy Syst., Vol. 27, pp. 335–342, 2005.  



Bulut, Yalcin, "Applied kalman filter theory" (2011). Civil Engineering Ph.D. Dissertation:


Samra Harkat, Malika Boukharrouba, Douaoui Abdelkader, "Multi-site modeling and prediction of annual and monthly precipitation in the watershed of Cheliff (Algeria)," in Desalination and water treatment:


A fix for previous timing problems experienced by Patriot Missile:

Defeating Hypersonic Missile Threats:

Raytheon Hypersonic Contract:

U.S. X60A Hypersonic Test aircraft in 2019:

The Air Force Research Laboratory, Aerospace Systems Directorate, High Speed Systems Division, in partnership with Generation Orbit Launch Services, Inc., is developing the X-60A vehicle. It is an air-dropped liquid rocket specifically designed for hypersonic flight research. X-60A program completed its Critical Design Review, a major milestone in the program in 2019. The program now moves into the fabrication phase. The initial flight of the vehicle, scheduled in about a year, is based out of Cecil Spaceport in Jacksonville, Florida.

Hypersonics: DoD Wants ‘Hundreds of Weapons’ ASAP:



USAF Kicks Off Early Study For Hypersonic Cruise Missile:

After the shutdown of the ESA/CNES launch base in Kourou, French Guiana, and despite the initial statements by the US space industry, COVID-19 starts creating negative impacts on on-going programs.
It is a reality to face. Space programs, being long term, might suffer less (apart from delays and induced cost impacts) than other industrial sectors, but it is indubitable that 2020 will see an overall contraction of the space economy in terms of revenues, as compared to very optimistic forecasts of several hundreds of million in US dollars. This is the time when governments should keep their support to the space industry, resisting the temptation of short-sighted "savings". One example: we still want to go back to the Moon!
US Space Force Delays GPS III Launch in Response to COVID-19 - Via Satellite:

The Space Force recently launched its sixth and final Advanced EHF satellite from the Cape March 26. But other national security-related launches have already been delayed as the COVID-19 pandemic spreads across the globe: Rocket Lab announced in March that it has temporarily halted launch preparations for its “Don’t Stop Me Now” mission, which includes three National Reconnaissance Office (NRO) payloads and was scheduled to launch in late March from the company’s Launch Complex 1 in New Zealand.

GeekWire | Stratolaunch resurrects its hypersonic rocket vehicle under a new name: Talon-A:

The Future of Laser Missile Defense:
What can catch a missile moving many times the speed of sound? An interceptor that's as fast as light. See how we're hurtling toward lasers that can stop hypersonic missiles: https://rtn.co/2WMIscv 

What can catch a missile moving many times the speed of sound? An interceptor that’s as fast as light. See how we’re hurtling toward lasers that can stop hypersonic missiles: https://rtn.co/2WMIscv  :

Hypersonic missile tests: https://www.navy.mil/submit/display.asp?story_id=112406  

Raytheon, Lockheed Martin sign teaming agreement to pursue contract to modernize surveillance and air traffic control radar systems:

U.S. Army, Raytheon complete preliminary design review of DeepStrike missile:

Space Fence SST radar operational! A huge leap ahead in space surveillance!
Looking forward to seeing the increase in the number of objects monitored and in the orbital accuracies:


Missile Defense Agency Advances Laser-Blasting UAVs:

Lasers: Beyond The Power Problem:

Air Force Releases Video of New Combat Drone, the XQ-58A Valkyie in 2019:

U.S. Army to Buy $39.6 Million Worth of Pocket-Sized Drones:

NASA Dream Chaser:

There are a lot of advantages to attacking signals vice satellites:
-It is a lot easier to do
-It can be easily undone if you don't want to do it any more
-It probably isn't an act of war
-and (sic, consider) the power you would have available from a nuclear reactor...!

An interesting bit from the article:
"...the deployment of EW [electronic warfare] platforms in orbit would be in accordance with a policy for Russia’s electronic warfare program until 2020 approved by the Russian government in January 2012. A summary of this policy indeed mentions space-based electronic warfare as one of the objectives to be accomplished in the period before 2025. More specifically, it talks about the need to deploy “multifunctional space-based EW complexes for reconnaissance and suppression of radio-electronic systems used by radar, navigation and communications systems.”
Ekipazh: Russia’s top-secret nuclear-powered satellite:


Kazakhstan uses drones to patrol capital during COVID-19 lockdown:


Invisibility Technology Takes Big Leaps That Can Be Seen:

https://now.northropgrumman.com/invisibility-technology-takes-big-leaps-that-can-be-seen/    (Dr. Eli Brookner, Raytheon [retired] has published plenty in keeping track of the status of meta-materials for radar, optics, and acoustics.)

U.S. Air Force to transfer 23 units to the Space Force:


Remembering a bit of history pertaining to the Cold War and the U.S.’s successful race to the moon:

NASA’s Original Apollo Moon Landing Guidance Computer Is Being Restored:


Thousands of Hours of Newly Released Audio Tell the Backstage Story of Apollo 11 Moon Mission:


Apollo 12 in Pictures: Photos from NASA’s Pinpoint Moon Landing Mission:


Also in the 1980’s from the Air Force Institute of Technology (AFIT) and elsewhere: (1) Maybeck, Peter S., and Rogers, Steven K., “Adaptive Tracking of Multiple Hot-Spot Target IR Images,” IEEE Trans. on Automatic Control, Vol. 28, No. 10, pp. 937-943, May 1983; (2) Maybeck, Peter S., and Hentz, Karl P., “Investigations of Moving-Bank Multiple Model Adaptive Algorithms,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 10, No. 1, pp. 90-96, Jan. -Feb. 1987; (3) Tobin, David M., and Maybeck, Peter S., “Enhancements to a Multiple Model Adaptive Estimator/Adpative Image-Tracker,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 24, No. 4, pp. 417-426, July 1988. A hot time in the old town tonight!  Maybeck, P. S., Stochastic Models, Estimation and Control, Vol. 1, Academic Press, NY, 1979 (and Vols. 2 and 3 published in the 1980’s.)

Also see: Special Issue of IEEE Transactions of Automatic Control, Vol. 28, No. 3, 1983 devoted to nonstandard applications of Kalman Filters. For more standard applications of Kalman filters, please see 1982 NATO AGARDograph No. 256 and Feb. 1970, No. 139 (Noordhoff International Publishing, Lieden).

A good book by: Bruce P. Gibbs (and contributed to by many of Thomas H. Kerr III's  prior TASC cohorts from the 1970’s and by other illustrious contemporaries): Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook, John Wiley & Sons, 23 February 2011:  http://onlinelibrary.wiley.com/doi/10.1002/9780470890042.fmatter/pdf  [They joke in the introduction that they could show pictures of famous mathematicians of yesteryear too (My words: instead of pertinent content such as: What?, How?, and Why?) but they refrain from doing so in their book. However, they do so on the cover.]

Click here to obtain a detailed 128Kilobyte resume for Thomas H. Kerr III emphasizing only his Navigation experience.

Click here to download a 214KByte pdf file which conveys our view on the problems with Covariance Intersection

Click here to obtain a detailed 266Kilobyte resume for Thomas H. Kerr III emphasizing only Target Tracking for strategic Updated Early Warning Radar (UEWR).

Also see or click on http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADP011192 or please click on http://www.dtic.mil/dtic/tr/fulltext/u2/p011192.pdf 

Click here to view our abstract for GNC Challenges for Miniature Autonomous Systems Workshop, 26-28 October 2009 to occur at Fort Walton Beach,.FL.

Click here to download a 1.56MByte pdf file that demonstrates our Navigation familiarity by our pioneering new developments in using Inertial Navigation Systems and GPS in support of airborne platforms performing terrain mapping, which is a slide presentation corresponding to: Kerr, T. H., Use of GPS\INS in the Design of Airborne Multisensor Data Collection Missions (for Tuning NN-based ATR algorithms),Institute of Navigation Proceedings of GPS-94, pp. 1173-1188, 20-23 Sept. 1994.  Click here to download a 4.40MByte pdf file that conveys the entire report. (Thomas H. Kerr III became a senior member of AIAA via the required endorsements by running this specific report by Richard Battin [Draper Laboratory and MIT Aero. & Astro.] and by Wally Vander Velde [MIT Aero. & Astro.].)

Click here to see a 160 KByte quantitative analyses of the relative pointing accuracy associated with each of several alternative candidate INS platforms of varying gyro drift-rate quality (and cost) by using high quality GPS external position and velocity fix alternatives: (1) P(Y)-code, (2) differential mode, or (3) kinematic mode at  higher rates to enhance the INS with frequent updates to compensate for gyro drift degradations that otherwise adversely increase in magnitude and severity to the system as time elapses.  Click here to obtain the corresponding 1.40 MByte PowerPoint presentation.

Click here to view our recent short comment submitted to the Institute of Navigation for publication in their Journal and already published.

Please click here for information on jamming vulnerability of STAP.

Key Benefits:

·       On a more positive note, the late Prof. Itzhack Bar-Itzhack proved the observability and controllability of the linear error models that represent navigation systems:

1. Drora Goshen, I.Y. Bar-Itzhack, "Observability Analysis of Piece-Wise Constant Systems-Part 1: Theory," IEEE Transactions on Aerospace and Electronic Systems, Vol.28, No.4, pp. 1056-67, Oct. 1992.

2. Drora Goshen, I. Y. Bar-Itzhack, "Observability analysis of piece-wise constant systems II: Application to inertial navigation in-flight alignment (military applications)," IEEE Transactions on Aerospace and Electronic Systems, Vol. 28, No. 4, pp. 1068-1075, Oct. 1992.

3. Drora Goshen, I. Y. Bar-Itzhack, "On the Connection Between Estimability and Observability," IEEE Transactions on Automatic Control, Vol. 37, No. 8, pp. 1225-1226, Aug. 1992. 
It is shown that when a linear dynamic system is stochastically autonomous (that is, when the system is not excited by a random signal), its estimability property as defined by Y. Baram and T. Kailath (ibid., vol.33, p.1116-21, Dec. 1988) reduces to the classical observability property.

4. Itzhack Y. Bar-Itzhack, Drora Goshen, "Unified approach to inertial navigation system error modeling," AIAA Journal of Guidance, Control, and Dynamics, Vol. 15, No. 3, pp. 648-654, May-June 1992. 
Several inertial navigation system error models have been developed and used in the literature. Most of the models are ad hoc models which were needed to solve certain particular problems and were developed for that purpose only. Consequently, the relationship, correspondence, and equivalence between the various models is not evident. This paper provides...

5. I. Y. Bar-Itzhack, Y. Vitek, "The enigma of false bias detection in a strapdown system during transfer alignment," AIAA Journal of Guidance, Control, and Dynamics, Vol. 8, No. 2, pp. 175-180, March-April 1985.
This work describes a phenomenon discovered during in-flight transfer alignment of a strapdown inertial navigation system. The phenomenon, which has not been reported in the literature before, is that of false longitudinal accelerometer bias estimation by the Kalman filter employed in the transfer alignment. Reference data timing error is suggested...

6. Itzhack Y. Bar-Itzhack, "Modeling of certain strapdown heading-sensitive errors in INS error models," AIAA Journal of Guidance, Control, and Dynamics, Vol. 8, No. 1, p. 142 ff, Jan.-Feb. 1985.
Self-alignment of a gimbaled inertial navigation system (INS) results in a platform tilt which cancels the effect of the level accelerometer biases. The same cancellation takes place in strapdown INS too; however, unlike gimbaled INS, in a strapdown system, this cancellation is perturbed once the INS changes heading. This note shows that the standalone...
so Kalman filtering may be rigorously applied in this application domain. (It had already been successfully applied to navigation for more than 10 years without these analytical niceties having been supplied to shore up the hole in the analysis that everyone recognized was present but just had not bothered to clean up since they were busy actually implementing Navigation solutions using Kalman filtering in a somewhat cavalier fashion without this rigorous analytical stepping stone yet officially being in place.) Others worked on this aspect too: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5375725/  

Also see:

-William S. Widnall, Stability of Alternate Designs for Rate-Aiding of Non-Coherent Mode of a GPS Receiver, Intermetrics Report No. IR-302, 25 Sept. 1978.
-Boris Danik, "A Low-Cost Velocity Reference System for Rapid Alignment of Aircraft Inertial Platforms on a Moving Base," Proceedings of the IEEE 1980 National Aerospace and Electronics Conference (NAECON), pp. 608-615, 1980.
-Gelb, A., Course Notes Marine Inertial Navigation, The Analytic Sciences Corporation (TASC), TASC TR-119-1, Reading, MA, January 1967. (Handles Monitor Gyro in alignment procedure for SINS/ESGM)
-John E. Bortz, Micron Analysis, Vol. 1. MESGA Attitude Readout Error, The Analytic Sciences Corporation (TASC), Technical Report AFAL-TR-72-228, Air Force Avionics Laboratory, Air Force Systems Command, Wright-Patterson Air Force Base, Ohio 45433, August 1972.

We are knowledgeable about various historical approaches, their assumptions, their derivation, and their evolution [such as the INS analysis conventions of Peter Grundy and William Widnall (Intermetrics, Inc.) vs. that of the late Kenneth Brittings (Northrop) and the missing minus sign in that of (the late) Prof. Itzhack Bar-Itzhacks (Technion Univ.)  vs. Don Bensons (Delco AC Electronics, TASC, Dynamics Research Corporation (DRC), and now at MITRE): Benson, D. O., `The Psi-Angle Error Equation in Strapdown Inertial Navigation Systems’, IEEE Trans. on Aerospace and Electronic Systems, Vol. 15, No. 1, pp. 168-170, Jan. 1979., where Donald Benson was correct all along; or on issues of intentionally and actively maintaining the small angle approximation for INS analysis to ensure (or enforce) the validity of the associated analysis that relies on this assumption being correct]. A sad commentary is that in one of Prof. Bar-Itzacks later publications, he notices that the underlying navigation coordinate systems appear to move in a direction opposite from what he previously expects but he still fails to recognize this quirk as merely a consequence of his prior failure to recognize and adhere to the sign convention that Don Benson tried unsuccessfully to alert him to 20 years earlier as being in error. It was rather sad and disappointing that no one from a recognized navigation analysis house (like C. S. Draper Laboratory [James Potter?], Rockwell International-Autonetics [James Lowery III?, J. S. Stambaugh?], Rockwell Collins, Singer-Kerfott [Dr. Bernard Friedland?], Honeywell, Northrop Grumman, Sperry Systems Management at Sperry Univac - Unisys [e.g., Dr. Hy Strell or the late Norman Zabb or the many other navigation analysts there], Magnavox, Motorola, TASC, General Dynamics, Teledyne Brown, JHU/APL, JPL, Air Force Institute of Technology (AFIT) [Peter S. Maybeck?], MIT Aeronautics & Astronautics [Prof. Wally VanderVelde or Prof. Richard Battin], Stanford Univ. [Prof. Arthur Bryson or Prof. Charles Hutchinson, who received his Ph.D. from Stanford Univ. and was a TASC navigation consultant at that time], Stanford Telecommunications, or anyone else from Dynamics Research Corporation [DRC] like Al Dushman? Al Kleinman? Herb Sanberg?) entered into the fray to back up Don Bensons view. At the ION 57th Annual Meeting & CIGTF 20th Biennial Guidance Test Symposium, 11-13 June  2001, Albuquerque, NM, Tom found out that Don faults Tom for not doing so back then since Tom described how he recognized the problem but did not say anything at the time (but Tom has always had to pick his battles carefully and wait his turn since Tom is frequently critical and does not want to be labeled as just another Nay Sayer) and, moreover, Tom was not yet a recognized authority in this particular area of specifying navigation error models from first principles even though Tom had seen it done and understood it, including its underlying principles and assumptions. Besides, at the time, Tom worked for TASC, which was a direct competitor of DRC (where Don Benson then worked), so it would have been extremely politically incorrect for Tom to have entered the fray back then and endorse our competition (especially since Itzhack Bar-Ithzach was working at TASC at the time). As the Happy Warrior, Tom certainly has not shied away from controversial technical battles. However, he can disagree without being disagreeable (most times, unless he has to return fire in like kind).
We are somewhat familiar with the historical HAD/HAP procedure, developed by the late William Zimmerman in the 1960s while he was at DRC, for computationally calibrating biases within the SSBN submarine Ships Inertial Navigation System (SINS), in those days consisting of only single-degree-of-freedom conventional gyros (but with two SINS present with one as a warm standby system with the other one being in the path of primary navigation reliance) with mechanical spinning rotator gyros. We also know about the Carousel navigation system INS that is constantly rotated to average out the adverse effect of the biases that are present (where William Zimmerman and Robert Ship [along with several others] hold a patent on this important concept). 
We have gone through the rigorous supporting mathematics, yet we summarize the results in a clear straightforward manner, expressed as simply as possible.
We are familiar with the application constraints associated with utilizing these algorithms and are aware of what application constraints are usually actively in force.

TeK Associates Capabilities:

Knowledge of operational principles and behavior of INS gyros and accelerometers and likewise for GPS: Familiar with their underlying state variable error models and INS calibration procedures and typical failure modes and interactions. 

A clear simple overview (that appeared on the Internet on 1 January 2019) that offers an understanding of INS concerns is available here by clicking on it.  

The future of GPS and  GNSS that appeared on the Internet is provided here by clicking on it. 



--The first satellite in the new GPS III constellation blasted off in late December 2018 on a SpaceX Falcon 9 rocket at Cape Canaveral – Harris technology is on board, as it has been on every launch for the last 40 years. 

--Lockheed Martin provides the satellite, and Harris navigation technology generates the GPS signal that billions of people depend on everyday. Harris technology has been on more than 70 GPS satellite payloads, including the 31 GPS satellites moving through space today. Harris says that they are looking forward to a continued partnership on future GPS III satellite launches. 

--Harris congratulates the United States Air Force, Lockheed Martin, and SpaceX on the successful GPS III launch. “Special thanks go to the dedicated Harris employees at their Clifton, NJ facility who develop this amazing technology. Learn more about Harris’ role in the GPS mission here:



Map of GPS Control Segment: https://www.gps.gov/multimedia/images/GPS-control-segment-map.pdf                                                     

Satellites being reported in view, as seen from the GPS Project Office, at a fixed location within CONUS (as the earth rotates and as the satellites move in their respective 6 orbital planes).

Realistically, the GPS receiver can move and the platform upon which it is based can move also (like a person with a GPS-equipped cell phone on a ferry boat sailing from Manhattan, NY to Staten Island). 

GPS interference:


Space Command Calls Out Russia for Anti-Satellite Test:

Air Force’s Joint Forces Space Component Command Missions to Move to U.S. Space Command.

GPS interference Solutions:


Sophisticated Spoofing of GPS: 








New GPS ‘circle spoofing’ moves ship locations thousands of miles:




GPS jamming on agenda as Russian defence delegation sat down for talks in Oslo:


Size of GPS Jammer markets: https://www.transparencymarketresearch.com/signal-jammer-market.html 


Power of THOR ready to down enemy drones - GPS World:
The Air Force Research Laboratory (AFRL) developed a counter-swarm high-power weapon to deter enemy drones — THOR

Learn more about the weapon, which provides non-kinetic defeat of multiple targets. (Photo: AFRL) #AFRL weapon  #drone 


Please click on the link to see: 7 Deadly Sins of Innovation in the Age of AI: 

Public-private partnership to launch eLORAN technology to back-up and accompany GPS - Intelligent Aerospace:


International Civil Aviation Org Issues Advisory on GNSS Disruption (Finally!)
In September, 2019, it was reported how airline and pilot groups had raised the issue of GNSS disruption to the UN's International Civil Aviation Organization (ICAO).

The body decided it was an urgent issue (since airplanes have almost crashed because of GNSS disruption, after all) and they decided to act promptly.

The result was a letter to member states published today:
A few thoughts before you get too discouraged about why it took so long for ICAO to act:

ICAO is an international body and they can't do anything quickly. The only real power ICAO has is to bring nations together to talk and provide them information. It can't do much more than merely inform. For things to happen, nations have to start changing the way they do business.
Most all the member states had all the information already. This is just nudging them to act in ways they already know that they should. The list of things ICAO recommends nations do is a pretty good one. If any nations pay attention and do some or all they will be better off than before.
When we do have a major air crash because of GNSS disruption this will be a list of good practices for people to look at and adopt to help prevent it happening again.

Editorial Advisory Board PNT Q&A: Opportunities with GNSS correction services - GPS World:

New players are offering GNSS correction services — pushing prices down and offering new business models. What opportunities does this open up?


GPS Disruptions Varied, Widespread - Reports to the US Government:

RNTF Report:

Very few people know how to report problems with GPS reception. And few of those take the trouble to do it. So the listing that the US government maintains of GPS disruption reports really represents the tip of the iceberg. Likely only the most sophisticated and diligent users, often with the most persnickety problems, appear on the website.

We like to check in on the listing periodically and see what kinds of things have shown up. The reports so far in 2020 have been a varied collection.

There are always a number of problems that the government says are due to "user equipment." Interestingly, problems due to week rollover are still being reported, along with the usual number of receivers that needed updating or had another sort of problem.

In February and July of this year there were problems with the GPS ground control system that caused the information broadcast to contain minor errors. These was detected and reported by some sophisticated users and acknowledged by the Air Force's GPS Operations Center. The web page, which goes back as far as 2017, shows similar events in February and November of 2018, and in May of 2017.

The most interesting by far, though, are the ones the government categorizes as "unknown interference" or "insufficient information." Reading the information that is posted, it is not hard to imagine either a sloppy technician allowing their equipment to emit interference, or some sort of malicious actor with a jammer.

The site includes a number of reports from the Mediterranean and Middle East, which are never any surprise. US military commanders have called the area the most contested electronic warfare environment in the world.

A significant number of reports suggest persistent interference due to a device fixed in one place.

A persistent problem in Edmonton, Canada, that has been going on for quite some time.

In Lancaster, CA a ... permanent disruption of GPS reception noticed over 6 months, driving daily in early evening and late evening, and is detected by 2 separate models of Garmin automotive GPS units. There is no overhead signage that could cause a drop out. The drop out and loss of reception covers a span of approximately 200-300 yards centered on the Ave J overpass.

Boulder, CO reported ...Noticed irregular signal multiple times near the same block during weekdays.

From New Hampshire ...I have had a number of intermittent GPS issues within 1 mile of this location over the past year. GPS drops almost exactly 10 mph and the location plots diverge for approximately 1km parallel to the actual track. I took a picture of the GPS track showing the deviation. Contact me (Dana) if you would like a copy of the track picture. I had previous similar incidents in the same vicinity.

In Puerto Rico ...My GPS position is changing. Beginning on 1-14-2020 almost every day, why is that? I measure from the same point at my home.
There are also quite a few that could well be due to a mobile source, possibly someone with a "personal jammer":

Driving in San Francisco and across the Golden Gate bridge with ...a 1,000 foot offset to the west.
A US Coast Guard vessel in Atlantic Beach, FL reported ...losing both of the ship's GPS receivers during their mooring evolution. Unit verified with another USCG vessel, at the pier, who was experiencing the same issue. Unit restarted both GPS displays with no resolve. After waiting approximately 20 minutes GPS signal regained and seems to be working properly.

In Warrenville, IL I used GPS for a trip immediately prior to this anomaly, without issue. When I attempted to enter my next trip leg, I noted an anomaly. My GPS apps could not locate my vehicle correctly and could not plot a course to my destination. The map display spun around multiple times, and at times placed my vehicle at the end of nearby dead end roads and even in the middle of a nearby field. I restarted the apps, to no avail. I restarted my phone and the bizarre behavior continued. About fifteen minutes after first noting the problem, I restarted my phone again and my GPS apps began working correctly. I do not know if it was a device issue or a GPS system issue. As of this date, I have used GPS twice on this device, without issue.

A user in Medford, OR lost their whole network for a while. We use GPS timing servers across our network within the CONUS. Across our network at approximately the same time, the timing servers went into holdover. As this issue was seen in multiple places, we do not think there were any issues with the hardware or software. We are trying to understand if something impacted the GPS satellite systems ability to provide timing on March 16th, 2020. (there wasn't)

Near Dulles Airport in VA I was on Rt. 50 heading East near Avion Pkwy close to Dulles Airport. The GPS navigation in my vehicle stopped working. When I looked for more information in the GPS it displayed no bars for a GPS satellite signal. This outage continued until the end of my trip in Reston, VA. I made two attempts to turn off my vehicle and restart the navigation during the trip, but this did not work to restart my GPS navigation. It was when I stopped the vehicle, stopped the engine, and got out of my car for 10-15 minutes that the GPS system resumed activity. 

Rehoboth, MA - Position shown on maps was off by approximately .5 mile to the west. Also had same occurrence last night while in the same general area. When I noticed the issue on my Nav radio, I checked location on my iPhone and it was consistent with the radio in showing the wrong location.

Gibsonton, FL - I was driving following my GPS when all of sudden it lost GPS signal on the highway. I checked my vehicles GPS also and it could not lock onto me. It finally returned after about 20 mins but something must have knocked it out.
Quite the collection of reports!

If you would like to check them out yourself, feel free to visit the US Coast Guard Navigation Center website at:

Applanix introduces OEM solution for direct georeferencing of airborne sensor data - GPS World

Applanix Corporation, a Trimble Inc. company, introduced the Trimble AP+ Air OEM solution for direct georeferencing of airborne sensor data. Learn more about the solution, which enables users to produce maps and 3D models without using ground control points.


Teardown: Mini GPS Jammer:

Read, meditate and do not imitate.
It is scaring to realize how easy is to jam GNSS signals.
This is the reason why we need a resilient, worldwide, integrated PNT infrastructure.


GPS World 30th Anniversary Timeline - GPS World:

GPS World’s 30th anniversary GNSS timeline provides highlights in both system and policy development and industry over the past three decades. Check it out now.

Downloads available for free for these wonderful historical posters.

Yup, we added the question mark to the headline. The Army's Mounted Alternative PNT System (MAPS) is certainly helping soldiers in challenging GPS environments, but it doesn't come close to what most would call an "alternative."


In the words of the Army program manager, MAPS 1 is helping with jamming and MAPS 2 is helping with spoofing. Lots of interesting capability in the package, including the eventual ability to use M-Code. There are IMUs involved and some other tech as you will see in the article, but not really what most folks would call an "alternative."

We also take issue with the quote "... will ensue soldiers know where they are even if GPS isn't working." We are going to bet that most soldiers would have a fair idea where they are regardless. This sounds like a power point sound bite in a budget brief (don't get us wrong - these kinds of programs should be much better funded).

The most interesting thing, with MAPS, in our opinion, is the C4ISR/EW Modular Open Suite of Standards, or CMOSS. This seems to be one realization of the DOD PNT Strategy's "Modular Open Architecture System" CMOS (everyone has to have their own name and acronym). The high level concept (which we have long espoused) is:

The best way to ensure you have PNT is to use a lot of diverse sources
This means you need to have a robust architecture
There are lots of diverse sources around right now and more could be brought on line with existing mature technology
When new sources become available, sophisticated users ought to be able to access them fairly easily
So a part of the critical path is figuring out a way for users to be able to access as many diverse sources (existing and future) as they can. Hence the modular, open architecture approach. This is not a trivial problem (authentication, fusion of diverse senors, prioritizing and 'voting,' to name a few) but it is an essential one..

Note - we also link to a second, related C4ISRNet article below.




Jens Hoxmark:
Solutionprovider for Mission Critical PNT, IoT and 5G Telecom Ctrl Cmd and Trusted Precise Wireless Timing, TPWiT.
Dana, yes, I read "army" and thought of people in close contact with Terra Firma. Doing 500kts makes it lot more challenging to shop at the local bakery, for sure.

But I came to think of the presentation by Dr. Aaron Canciani at the US Space Based Advisory Board meeting back in December 2018, where he presented the very interesting concept of "Magnetic Navigation" 


This has also been published in Inside GNSS 15th June 2020 https://insidegnss.com/183615-2/ 

It's a very promising concept in combination with inertial and compact atomic clocks to be an alternative for a system that can be applied for military application by looking at the presented results, either in relative or absolute mode.

Jens Hoxmark:
Solutionprovider for Mission Critical PNT, IoT and 5G Telecom Ctrl Cmd and Trusted Precise Wireless Timing, TPWiT.
The detection of natural variation of the magnetic field is also applied for seismic interpretation. Please check the information on the homepage of "Electromagnetic Geoservices" EMGS.


"The MT signal is measured using the same seafloor receivers as used for a conventional controlled source electromagnetic (CSEM) survey.

However, the MT (MagneTotelluric) signal strength depends on solar activity interacting with Earth’s magnetosphere. To ensure good data quality, the receivers are kept on the seafloor for several days, continuously measuring the natural variation of the electromagnetic fields.

Resistivity models from MT inversion images deep structures such as basement and delineates complex salt and volcanic structures."

So they actually make constructive use of the Solar Magnetospheric alterations, in close cooperation with various observatories like the one in Tromsoe that is continuously measuring the magnetic flux /field http://flux.phys.uit.no/Last24/Last24_tro2a.gif 

So there is definitely a magnetic "landscape" out there, that can be applied for navigation, even at 500 knots with present technology in pattern-recognition and fuzzy logic.

Tom Kerr:
In the 1970's and perhaps even before, (under Project: LINEAR CHAIR) the U.S. Navy was investigating just that above topic for external position fixes to compensate for deleterious gyro drift over time for U.S. submarines to avoid any "observables" exposure (of antennas or sonar bathymetric map-matching to any potential enemy surveillance). Such an endeavor was progressing back then and needed to utilize onboard Fluxgate magnetometers, which have recently greatly improved and reduced in size, as I learned at a recent 2018 series of IEEE Boston lectures on Optics-related topics. In the mid 1970's, there was a Kalman filter design planned for magnetic position fix "navaid" update to a submarine-borne INS that was called a "Schmidt Filter". (Not corresponding to Stanley Schmidt nor to George Schmidt at Draper Laboratory at that time, who were involved with novel use of Kalman filters of their own for navigation applications; but to another person named Schmidt.) For this approach to be useful, it was necessary for an accurate Earth's magnetic map to be available. People had speculated on trying to marry magnetic navigation with Gravity-based maps of the Earth since there are unique features of each that may be complementary. Specialized surface ship fleets would be needed to compile such maps of magnetic and gravity fields experienced at various depths.

Y. Jade Morton received the Johannes Kepler Award from the Institute of Navigation (ION). 

Read about the advances she's made in receiver technology, automated data collection, robust carrier phase tracking and remote sensing.:



GPS World celebrates 30 Years of leadership (7 Oct. 2020):


What would the world do without GPS?


GPS Program Updates and its role in the SMC Space Enterprise Architecture: as of 8 October 2020

GPS tracking devices industry to grow 12.2% CAGR by 2026:

According to a report by InForGrowth, the global GPS tracking devices market was valued at $1,567 million in 2018 and is expected to grow at a CAGR of 12.2% during the forecast period 2026. Find out what factors are driving that growth.


Justyna Redelkiewicz on how GSA is using Galileo to enable innovation:

This week, our colleague Justyna Redelkiewicz (Head of Section Consumer Solutions at the GSA) sat down with Ronan Leonard from the Irish Tech News Podcast to talk about #Galileo, #IoT, and #EUSpace��️ enabling innovation and entrepreneurship.
You can listen to the podcast here: https://lnkd.in/dBGy75p 


L5-only receiver designed for mobile phones:

GNSS receivers first reached the commercial domain in the early 1980s. Here's how receiver technology has advanced since then.


Safran Optics 1 Mission:

Delighted to be a part of the Safran Optics 1 team! See how our electro-optic and navigation systems solutions are making a difference in surveillance and reconnaissance missions for dismounted soldier, airborne, naval, and land vehicle operations.

https://lnkd.in/dqTaxTt                          https://lnkd.in/deebVXG 

GPS Dual Use:



ESA seeks proposals to demo 5G positioning, timing - GPS World:


We're launching the world's latest Earth-observing satellite to monitor sea levels & provide data for weather forecasting and climate models:

5 things to know about Sentinel-6/Michael Freilich, a historic U.S.-European partnership: https://lnkd.in/dX4cKEG 

Our Buyers Guide has a dedicated site that we’re continuously updating to ensure that you have the most accurate and complete resource available. With 100+ product categories and new ones added regularly, the GPS World Buyers Guide (gpsworldbuyersguide.com) is the No. 1 resource when making purchasing decisions for your company. For more information on our guide or getting your company listed, please contact Emily Adkins at eadkins@northcoastmedia.net

OneWeb LEO PNT: Progress or Risky Gamble? - Inside GNSS:



Under Attack – Receiver Response to Spoofing: Robustness vs. Resilience - Inside GNSS:




China expanding Loran as GNSS backup - GPS World:



What is mobile mapping?


Learn about how #GNSS antennas and receivers are combined with Inertial Navigation Systems to provide highly accurate data on the positioning, velocity and attitude of moving objects, and how engineers use these devices to document landscapes and more >> https://hxgn.biz/2Vkj7aM 

Science: Death by Spaghettification: Scientists Record Last Moments of Star Devoured by a Black Hole:

The phenomenon, known as a tidal disruption event, is the closest flare of its kind yet recorded, occurring just 215 million light-years from Earth.


The phenomenon, known as a tidal disruption event, is the closest flare of its kind yet recorded, occurring just 215 million light-years from Earth. It is caused when a star passes too close to a black hole and the extreme gravitational pull from the black hole shreds the star into thin streams of material – a process called ‘spaghettification’. During this process some of the material falls into the black hole, releasing a bright flare of energy which astronomers can detect.


Search and Rescue beacons developed at Goddard have helped locate more than 46,000 people through Cospas-Sarsat, an international cooperative system for search and rescue.

Now Maryland-based Concentric Real Time LLC has licensed a 2nd generation of this technology to be used by individuals who carry personal locator beacons in case of emergency. The 2nd generation technology allows for higher-resolution signaling that produces highly accurate location results. Learn more about NASA technology available for licensing at: https://lnkd.in/eUDZCWY 

Learn more about the new licensed technology at: https://lnkd.in/eJ9WQMK 

Aerospace Corporation:

Massive THANK YOU to the firefighting crews who saved the historic Mt. Wilson Observatory when it was threatened by the #BobcatFire. Our MAFIOT Project is among the major space observation programs being housed at the site.

Read: https://lnkd.in/gMtXhsH 

“We are grateful to the firefighters who put their lives on the line to battle the fire around the facility,” said Dave Cardoza, the Principal Director of Aerospace's Electronics and Photonics Laboratory. “The fact that the structures are still standing is a testament to the dedication that they put into their jobs. This will allow us to continue our important work on the mountain.”

Collins Aerospace wins contract to improve anti-jamming for warfighters:

The United States Army awarded Collins Aerospace a Phase III contract to build the second generation of its Mounted Assured Position Navigation and Timing System (MAPS). Learn more about the MAPS program.


The future of the U.S. Coast Guard is in outer space:

The #USCG and outer space? CAPT Michael Sinclair at Brookings explores the possibilities of leveraging advances in space technology to facilitate the execution of the Coast Guard’s 11 statutory missions here on earth.


APN-086 Datum Transformations & Plate Tectonics Compensation:

For information on the above, please click this link here

NASA Science: 

Particles smaller than an atom hurtle through the universe nearly at the speed of light, blasted into space from something, somewhere, in the cosmos. A scientific collaboration of the Pierre Auger Observatory, including researchers from the University of Delaware, has measured the most powerful of these particles — ultra-high-energy cosmic rays — with unprecedented precision. In doing so, they have found a “kink” in the energy spectrum that is shining more light on the possible origins of these subatomic space travelers. The team’s findings are based on the analysis of 215,030 cosmic ray events with energies above 2.5 quintillion electron volts (eV), recorded over the past decade by the Pierre Auger Observatory in Argentina. It is the largest observatory in the world for studying cosmic rays.


WTO: EU can impose tariffs on $4 billion of U.S. goods:


Featured Innovator: Kaitlin Moore:

Meet Kaitlin Moore, an atomic physicist in the field of #quantum science and #engineering at our Applied Sciences division. There, she and the team she’s part of are spearheading advancements in the potentially world-changing realm of #quantumsensing and #quantumcommunications.
Read more about our latest featured innovator: https://bit.ly/2HPxv7R 

On October 5th, the Real-Time Working Group of the International GNSS Service (IGS) will release the first version of the new IGS-SSR standard! It will be accessible at: https://lnkd.in/dY3EVry.

The IGS SSR format is an open standard for dissemination of real-time products to support the IGS Real-Time Service and the wider community. The messages support multi-GNSS and include corrections for orbits, clocks, DCB's, phase-biases and ionospheric delays. Extensions to also cover satellite attitude, phase center offsets and variations and group delay variations are planned in the near future. The goal is to create a self-contained and scalable standard for a wide range of real-time applications.
International GNSS Service.

On 9 December 2020, this new (incoming) website will be moved from its temporary home on igscb.org to our main website, IGS.org. The content in the current (outgoing) IGS.org website will be archived.

Also on 9 December 2020, ALL FTP access to ftp://ftp.igs.org  will be permanently terminated and replaced with a secured https://files.igs.org/ . Data, content, and directory hierarchy will remain unchanged.

Precise time for all: Paper calls for resilient national timing - GPS World:



GNSS simulator companies help pilots find their way:

Find out how GNSS is playing a role in enhancing safety and training when using flight simulators


How many Global Navigation Satellite System do you know? Only GPS? GPS and GLONASS?:

Check the right answer in the book "An Introduction to GNSS..." from NovAtel Inc.


P.S.: Don't forget to pay attention to two regional systems!

GPS/GNSS industry recollections and predictions from the GPS World Editorial Advisory Board - GPS World:

Members of the GPS World Editorial Advisory Board share their memories and thoughts about the GPS industry over the past 30 years. Find out what they had to say.


New algorithm could unleash the power of quantum computers:

A new algorithm that fast forwards simulations could bring greater use ability to current and near-term quantum computers, opening the way for applications to run past strict time limits that hamper many quantum calculations. “Quantum computers have a limited time to perform calculations before their useful quantum nature, which we call coherence, breaks down,” said Andrew Sornborger of the Computer, Computational, and Statistical Sciences division at Los Alamos National Laboratory, and senior author on a paper announcing the research. “With a new algorithm that we have developed and tested, we will be able to fast forward quantum simulations to solve problems that were previously out of reach.”


Schools Weren't Prepared for a Crisis Like COVID-19:

How did schools' planning *before* the pandemic affect their transitions to remote learning when COVID-19 hit? Results from our new national survey provide some insights.


Ada Lovelace Day is a worldwide celebration of the achievements that women have made in STEM industries, which stands for science, technology, engineering, and math.

The day is about increasing the profile of females in STEM. The hope is that by doing this we will help to create new role models for women all across the globe and encourage more females to take roles within STEM sectors.

WOMEN IN TECH - Global Movement Nadia Mannell Carine de Meyere Candyce Costa A IDM Lindalia Sofia Junqueira Reis Isabel Velarde, Founder, CEO Innovation Hub Consulting® Dr. Cara Antoine Claudia Mendes Silva Elina Valeeva Jenyfer Maisonneuve Joanna Carson Mandi Gunsberger, GAICD Polina Vasilenko Monika Rizovska Katerina Trajchevska Melissa Slaymaker

Tactical Airborne Laser Weapon System (TALWS):


Hexagon launches autonomy kits for agriculture with demo tractor - GPS World:

Hexagon’s Autonomy and Positioning division has launched its first autonomy positioning and sensing kits for the agriculture market. Learn more about the kits, which the company validated in its new autonomous research and development tractor.

The evolution of GPS satellites and their use today - GPS World: 

From Cold War origins of a chirping beach ball traveling through space 63 years ago, now more than 2,600 satellites enhance our terrestrial lives. Here's how satellite technology has gotten to this point. (Photo: U.S. Army/DARPA) #satellite #technology


Norway Govt Wants GPS Backup - Offering $910K To Develop for Maritime Pilots
Blog Editor's Notes:

Less than a million dollars (US) doesn't seem like much to develop a navigation system.

Also, there are existing systems already developed (or nearly there) that could be implemented. But they certainly cannot be had for such a small sum.

Perhaps the Norwegian government just wants to fund a study.

But why is a study needed? The problem of GNSS disruption in maritime has already been addressed by the European Space Agency (ESA), of which Norway is a member in good standing.

Last year ESA's NAVISP program sponsored a very comprehensive, year-long study of requirements and solutions for resilient maritime navigation. The 1,100 pages of reports of the MarRINav project outline process, findings, results and recommendations in great detail. True, it was written with a focus on the UK, but the methodology and results can be applied anywhere. 

We hope that this announcement isn't just a way for government leaders to give the appearance of action so it doesn't have to actually do anything. 

No alt text provided for this image

(Technical Weekly)

Most of the pilots have experienced GPS failure. Now they want to develop a safer alternative
Over the next few months, the Norwegian Coastal Administration will announce NOK 8.5 million to those who can develop a secure backup for satellite navigation.
The senses, local knowledge and radar are the most important tools the pilots use for unloading ships safely in port, but they have increasingly become dependent on satellite navigation such as GPS. These signals can be lost, either by accident or as a result of deliberate hacking.

- It can lead to dangerous situations and unwanted incidents, says Odd Sveinung Hareide, advisor and project manager in the pilot service.

The pilotage service will therefore in November announce a contract of NOK 8.55 million for someone who can develop a backup solution for satellite navigation. The new sensor technology will be able to compensate for the unreliability of satellite navigation and warn when the signals are affected. 

Basically, it should be a mobile solution that can be used by the pilotage service, but the goal is that the solution can also be used in shipping in general. 

The goal is to sign the development contract in early 2021. The finished prototype is scheduled to be ready in 2023.

READ MORE Site has a header button for version in English (but TeK Associates could not find it!)

Very Long Baseline Array (VLBA) Makes First Direct Distance Measurement to Magnetar:

Fenton Heirtzler, Organic materials chemistry and nonlinear optics:

"Very cool! Thanks for the enlightenment on magnetars (I had never heard of them). Maybe you could amend your posting to include the distance which was measured? 
Would it be reasonable to assume that there are no other heavenly bodies anywhere nearby to this? 
Can this thing be considered a massive ferromagnetic object, and is there any way to learn what its atomic composition would be?
There are other speculative questions, but I assume that at this point in time, there are no answers for them...."

RL Poole, Author, The Leedskalnin Codex: Breakthroughs in Understanding the Coral Castle - #1 Best Seller in the Physics of Gravity (Amazon Kindle):

"I read the Wikipedia reference. It says in the same place, that these magnetic fields are a hundred million times stronger than any man-made magnet."

Fenton Heirtzler:

" Is there any pop science magazine article on this...? I am afraid I wouldn't know. I think that is a question better directed at Google. I watched a science program about magnetars years ago, and found them fascinating. 

"Classical magnetism occurs when the nuclear spins of atoms are spatially aligned (I think). So is a magneton one big unidirectional nuclear spin ?" Says, who?

Magnetars are FASCINATING."

Free navigation tutorials (from China and Andover, MA): (THK: Danger)

Precise Navigation Made Simple:
ACEINNA’s inertial solutions deliver high precision in an easy-to-use open source development environment. Our fully temperature calibrated solutions deliver the performance needed to sense the real-world motion of today’s intelligent systems. (THK: Danger)


Vulnerabilities of GPS is a big concern: Dana Goward - Geospatial World:

Satellite systems have become an integral part of our businesses for precise navigation and timing services. Yet GPS/GNSS jamming, spoofing, and other forms of interference appear to be growing in frequency and severity. Recently, the Senate Armed Services Committee (SASC) asked Pentagon to provide Combatant Commander’s alternate position, navigation and timing (PNT) systems to GPS within two years.

We caught up with Dana Goward, a member of the National PNT Advisory Board, and President & Director of RNT Foundation, an independent, member-supported non-profit that works in the area building awareness about the importance and vulnerabilities of navigation and timing systems, encourages development and implementation of resilient terrestrial systems, and advocates for policies to deter spoofing and jamming. Goward is retired from the federal Senior Executive Service having served as the maritime navigation authority for the United States. He has represented the US at IMO, IALA, the UN anti-piracy working group, and other international forums. He is also a Senior Adviser to Space Command’s Purposeful Interference Response Team.

Why is there so much concern around vulnerabilities of GPS?
It’s not just about GPS; all GNSS signals are weak. They are 20,000 km above the Earth, powered by solar panels, and are transmitting all the time, after all. Just as a matter of physics, it’s very easy to block a relatively weak signal. That is what GPS jamming is. Also, because the different global navigation satellites systems want to increase their user base, they release all the information about their signals so they can be integrated into other systems. But if you know exactly what the signals look like, you know how to imitate them. This makes the signals open to spoofing as well. That is another significant challenge, because, in many ways spoofing is worse than jamming — instead of no information, spoofing can give you hazardously misleading information.

ALSO READ: Why Resilient PNT Infrastructure is Imperative to Global Economic Growth

All GNSS are relatively the same signal strength and in same general frequency band, and they are all in space. Naturally, they are subjected to same kind of vulnerabilities — severe solar activity, malicious high-power electro-magnetic pulses, local jamming, spoofing, etc. Even urban canyons and downtown cities are a challenge as the signals tend to bounce off buildings and can cause problems for receivers. Using multiple GNSS systems at the same time does protect users a bit if one of the systems suffers a cyberattack or an equipment failure. So, it does offer some measure of additional resilience. But, generally, they all have similar vulnerabilities and are subject to the same threats, so the added resilience and security is marginal.

These shared vulnerabilities have been a concern for some time. There are all kinds of incentives for individuals and organizations to interfere with GPS signals — from delivery drivers taking long breaks, to criminal organizations wanting to divert a shipment, to nations looking to counter the armed forces of another. For example, American generals have said that Syria and the Middle East have the highest intensity of electronic warfare anywhere on the face of the planet. A lot of that is GPS/GNSS jamming and spoofing.

Interestingly, a recent sampling by the European Union found 500,000 instances of transmissions on GNSS frequency that should not have been there. About 10% of them were determined to be malicious and intentional, while the others were just apparently accidental. So, there are a lot of vulnerabilities in the system, and a lot of real-world threats

From cellular networks to power grids to transport systems, GNSS is the source of accurate, synchronized time for almost everything. A 2012 Boston Consulting Group study found that the geospatial services fueled by GPS resulted in $1.4 trillion a year in savings to the US economy and another $1.6 trillion in added revenues. A London Economics study found that if GPS/GNSS went away for five days, the UK economy would suffer losses of £5.2 billion, which translates to $482 billion per year.

We are fortunate that nothing really bad has happened so far. At the RNT Foundation we encourage responsible governments to try to get ahead of things and prevent mishaps, rather than waiting for them to happen before swinging into action.

Tell us about the details of the FCC-Ligado controversy?
Ligado is really an interesting case. Ligado Networks, an American satellite communications company, claims they want to establish a low-power nationwide 5G network. And it has been allotted space in the L-band spectrum which is the same band as that of GPS and other GNSS. US government tests have shown that these transmissions will interfere with GPS reception for many users. Naturally, a lot of organizations and individuals, including the Executive branch of the government, are concerned about its possible impact on GPS and are of the opinion that we shouldn’t go ahead with this. However, the Federal Communications Commission, which is an independent agency and works on its own under a congressional mandate, is convinced that this isn’t going to be that much of a problem, approved the request, and is refusing to budge.

Ever since, the opposition to the proposal has been growing. The entire executive branch of the government, including the Department of Defense and Department of Transportation, have amplified their protest and a number of organizations including the RNT Foundation, have formerly requested that the FCC reconsider their decision. Now, there is some legislation in Congress to examine the decision. The end of that story is yet to be written.

One of my thoughts here is that the FCC is the ‘communications’ commission, not the ‘navigation’ or ‘geospatial’ commission. Radio communications are different from radio navigation in a lot of ways. In fact, they are almost opposites — in radio communications you are blasting the 1s and 0s through the surrounding noise to get the message through, while in radio navigation you look down within the background noise for the 1s and 0s. And rather than identifying the 1s and 0s as the message in communications, radio navigation precisely measures the time of the change from a 1 to a 0 so the receiver can figure out its location. There are a bunch of other differences as well.

It could well be that the radio and communications engineers at FCC didn’t have the right context to evaluate the Ligado proposal as it would affect navigation. As an example — I was on a panel with the head of Ligado who is a communications engineer. I said there were tests that found Ligado transmissions violated the government safety buffer for GPS failures. I said that, rather than using the safety buffer in its tests, Ligado had tested the GPS receivers to the point of failure. Ligado’s CEO replied that they hadn’t done that. They had just tested the receivers to where they started “giving bad information.” OK, so that’s worse. Bad information is worse than no information at all.

But it shows the difference between the way communications engineers and navigation engineers view things. In communications, a little bit of interference might not be so bad. You could probably understand the overall message. Or, if it is two-way communications, you could ask for a repeat. Not so for navigation. One of the first signs of interference with GPS/GNSS signals in many receivers is bad, potentially hazardous, information. A safety report to NASA last year detailed how a passenger aircraft nearly crashed into a mountain because of this kind of interference with its GPS receiver.


FAA gives go-ahead for Amazon drone-delivery tests - GPS World:

Amazon received Federal Aviation Administration approval to use drones to deliver packages. Find out what this could mean for package delivery times.


Collaboration aimed at GNSS solution for IoT modems - GPS World

Synopsys Inc and Nestwave are collaborating to combine Nestwave’s geolocation software with the Synopsys DesignWare ARC IoT Communications Subsystem for a complete low-power GNSS solution for integration into IoT modems. Get more details. (Image: metamorworks/iStock/Getty Images Plus/Getty Images) #GNSS  #IoT  #communications 


Impact of UK Jamming Trials - More Details
And here is the notice:

2nd September 2020 SW2020/187

Jamming trial impacting electronic situational awareness devices, UAS command systems and GNSS receivers: 8 Sep – 4 Dec, Luce Bay
Jamming activity will take place 8 September – 4 December 2020 in and around Luce Bay. The activity may affect GNSS receivers along with UAS and cockpit devices operating on 433, 868, 915, 2400, 5800 MHz operating up to 40,000FT AMSL within 55NM of 545020N 045548W (West Freugh).

During the trials impacted systems may suffer intermittent or total failure. Individual events will not exceed 2 minutes in duration with no more than 5 events per hour. Activity will take place in daytime hours between 0830 and 1600.

For further information contact spectrum@caa.co.uk 

Emergency cease jamming contact 01776 888932 or 01776 888930 

Aviation Policy News: Airline Bailouts and Revenue Sources for Air Traffic Control During Pandemic:


SAE International EDGE Report: Air Traffic Management:


Building a better aerial imagery program beyond UAVs:


New Photon-Counting Camera Captures 3D Images with Record Speed and Resolution:


Researchers have developed the first megapixel photon-counting camera based on new-generation image sensor technology that uses single-photon avalanche diodes (SPADs). The new camera can detect single photons of light at unprecedented speeds, a capability that could advance applications that require fast acquisition of 3D images such as augmented reality and LiDAR systems for autonomous vehicles.


Distributing high-precision time over optical networks in the 5G world - GPS World:
Mobile operators are investing heavily in the deployment of LTE-Advanced and 5G networks that will transform cellular communications and connectivity. Check out some challenges they face. 


No silver bullet for US PNT: Many sources needed - GPS World:

At the moment, the U.S. GPS provides the vast majority of PNT services in the U.S. and around the world. Yet, like all space-based systems, its signals are weak and very vulnerable to interference. (Image: DOT) #GPS #PNT #space


Enemy jammer takes first test flight aboard EA-18G Growler:


Securing PNT Workshop Looks at GNSS Back-up Options - Inside GNSS:






Friday 04/17/2020 Ligado / FCC Roundup - What might really happen:






FCC Chairman Moves Forward on Ligado Approval - Inside GNSS:


Attorney General William P. Barr’s Statement on FCC Chairman Pai’s Draft Order to Approve Ligado’s Application to Facilitate 5G and Internet of Things Services:


FCC Chairman Moves Forward on Ligado Approval Interfering with GPS:
The Federal Communications Commission announced April 16 that Chairman Ajit Pai is circulating a draft proposal within the Commission that would approve a plan by Ligado Networks to use frequencies neighboring those used by GPS for a 5G terrestrial service.


NATO’s new tool shows the impact of GPS jammers:


NATO’s new tool shows the impact of GPS jammers - C4ISRNet (More):




Now Operational, BeiDou Could Conceal Cybersecurity Threat:


Defense Secretary Fires on FCC about Ligado - What else to remember:

It is clear that Defense Secretary Esper is upset with the FCC for dismissing his concerns about national security and Ligado out of hand. The below article documents some of his frustration. This article is a pretty good opening salvo for tomorrow's hearing by the Senate Armed Services Committee.

As we go into tomorrow's hearing, though, there are a couple things to keep in mind that we have not heard about at all in the media to date,

First, the FCC giving away (no charge to Ligado other than application fees) this satellite spectrum for terrestrial use means it won't be available for space assets. We understand the L-Band is ideal for space-based PNT. So if we want any more of it (like the LEO systems Chinese are building and the US Air Force is experimenting with) our options are going to be that much more limited. Spectrum is a finite resource.

Second, we didn't need to be here. The executive branch has long said that we need to take better care of our GPS and PNT with: 1) a system to detect and identify disruption sources; 2) far wider use of receivers that reject many forms of interference; and 3) signals from a terrestrial system that would stabilize GPS signals in receivers making them very resistant to interference, and provide PNT when GPS isn't available at all.

The Pentagon made its case against Ligado. What now? - C4ISRNet:




Pai to Congress "You're Wrong"​ - FCC fires back on Ligado Decision:
Blog Editor's Note: The more we read materials from each side of this issue, the more the opponents seem to be talking past each other. They might as well be speaking different languages. Everyone sees themselves as doing the right thing and is puzzled by why the other side sees them as in error at best and a force for evil at the worst.

We are sure that everyone is trying to do the right thing, but there are clearly some fundamental disconnects as to how folks see the world, interpret data, from testing, etc. 

That is why we have called for an independent expert evaluation of the testing results and a cost-benefit analysis so as to better inform public policy decisions.

Chairman Pai Letter to House Armed Services Committee Chair Adam Smith
In a letter to Congressman Adam Smith, Chair of the House Armed Services Committee, last week, FCC Chairman Ajit Pai refuted claims that he and the unanimous, bipartisan vote of the Commission had erred in their decision on Ligado Networks.

Over the course of four pages he said that:

- National security and the safety of the public was a critical concern for him and the commission

- He would never do anything to compromise safety and security

- There is a fundamental misconception that the FCC has authorized "sharing" spectrum. GPS has not (sic) right to operate in the spectrum allocated to Ligado.

- Regarding consultation with the Department of Defense

"... the Department of Defense was provided with numerous opportunities over nearly a decade to provide the
Commission with any relevant evidence it wished to submit."

The commission considers all comments provided for the docket and formally sought comments six separate times over the course of nine years.

The commission provided DoD, via NTIA, a draft order to consider in October 2019.

He (Chairman Pai) personally spoke to the Secretary of Defense and other senior DoD officials on the matter

- The FCC's process and decisions are not impugned just because another agency doesn't like the outcome

- FCC's excellent career staff worked for years on technical analysis supporting the decision.

- FCC did not violate the law regarding the need to "resolve concerns." Paragraphs 129 and 130 of the order did that.

- DoD never offered a classified briefing (if they had, he would have taken it), nor did they enter into the record any testing results.

All five FCC Commissioners responded to Chairman Smith's letter. Here are copies of all the letters:

FCC’s Ligado decision broadens, deepens opposition - GPS World

Last week, 27 members of the U.S. House Agriculture Committee sent a letter to Federal Communications Commission Chairman (FCC) Ajit Pai. In it, they urged him to reconsider the FCC’s decision to allow Ligado Networks to operate a terrestrial nationwide network that the executive branch says will cause harmful interference to GPS signals for many users. This concern and opposition from a sector not traditionally engaged in GPS or positioning, navigation and timing (PNT) issues is just one example of how the FCC’s decision — rather than putting the issue to rest — has instead recruited a whole new set of actors from across multiple sectors for the opposition. Many observers don’t see this as surprising.

According to one observer, previously it was easy for many to assume the FCC would reject Ligado’s proposal. The entire executive branch had been vehemently opposed for years. So had aviation groups, the weather community, geospatial interests and some satellite communications concerns. With such opposition from so many important quarters, it was reasonable for many to assume they need not become involved. Now that the FCC has acted to the contrary, these interests have become well energized. The FCC decision also empowered opponents to educate and recruit others who don’t normally think or worry about GPS and PNT issues, folks like farmers and agricultural interests. As one insider said, “The existing opposition can now go to just about anyone in any sector and say, ‘This is going to happen and it will harm your operation. There are no ifs, ands, or buts. The FCC has decided’.”

Agriculture’s reliance on GPS
Agriculture is a good example. While not the sector that first springs to mind when most people think about GPS, farming has become dependent on augmented GPS for precisely and automatically driving machinery, minimizing fertilizer and pesticide use, and a wide variety of other productivity gains over pre-GPS operations. “GPS is critically important to the commercial agriculture, mining, forestry and rural manufacturing industries. In fact, GPS has become the single most significant technological advancement for American farm equipment in the past two decades… [A 2019 RTI study] found that during planting season, if GPS were interrupted, the economic impact to the agriculture sector could amount to losses of $15 billion due to lower crop yields. Moreover, an earlier study suggested GPS-enabled precision agriculture could save farmers an estimated 10 to 15 percent in operating costs and purchased inputs. This same study estimated the benefits of GPS to precision agriculture between $10 and $17 billion.”

Department of Transportation studies have shown that high-precision GPS receivers, such as those used in agriculture, could be impacted within 3,000 meters of a Ligado transmitters. With tens of thousands of transmitters deployed in a nationwide network, this could pose a real problem for American farming. Other sectors have also become involved in the opposition. The recently formed Keep GPS Working Coalition has members representing aviation, surface transportation, maritime, agriculture and equipment manufacturing. This formal and public coalition, though, seems to be just the tip of the opposition iceberg.

Almost 100 dissenting organizations:
According to some involved with protesting the FCC’s decision, there are nearly a hundred organizations and companies that are working in some way to have it overturned. These include multiple aviation, delivery service, agriculture, surface transportation, geospatial, weather, maritime, space and technology interests. One sign of the influence they are having is an increase in concerns being expressed by members of Congress.

There’s a growing need for positioning solutions for Advanced Driver-Assistance Systems (#ADAS) in #autonomous vehicles. #GNSS-reliant vehicles require lane-level resolution in order to navigate safely and reliably. Additional sensors are used to enhance this accuracy, but what role does GNSS play in these sensor suites?

Hexagon | NovAtel technical sales rep Kevin Doherty explains how GNSS is integrated into R&D through series production to deliver #autonomy and #positioning - assured.

Watch now >> https://hxgn.biz/2C4LGmq 

The #UAE has taken an exciting leap in the #spaceeconomy with its recent successful launch of the Hope spacecraft to #Mars.

By sometime in Feb of next year (2021) it will enter a Martian orbit and begin collecting, analyzing and transmitting Mars atmospheric, climate and weather data. The launch used #Japan H-IIA rockets from Japan’s Tanegashima Space Center and with contract support from Mitsubishi Heavy Industries. The UAE used a unique approach to build the spacecraft themselves deploying strong academic coordination.

Given the UAE success already from the project by both staying on its $200M budget and short timetables it is likely to serve as a new model for other nations #Space �� ambitions.


U.S. Department of Transportation announces drone Remote ID partners - GPS World:


A new, more secure GPS signal could be ready by 2020:


How Vulnerable Is G.P.S.?
An engineering professor has proved—and exploited—its vulnerabilities. by Greg Milner August 6, 2020

The proliferation of G.P.S. interference is a major reckoning for the country’s military and defense systems.

In the cool, dark hours after midnight on June 20, 2012, Todd Humphreys made the final preparations for his attack on the Global Positioning System. He stood alone in the middle of White Sands Missile Range, in southern New Mexico, sixty miles north of Juárez. All around him were the glowing gypsum dunes of the Chihuahuan Desert. In the distance, the snow-capped San Andres Mountains loomed.

On a hill about a kilometre away, his team was gathered around a flat metal box the size of a carry-on suitcase. The electronic machinery inside the box was called a spoofer—a weapon by another name. Soon, a Hornet Mini, a drone-operated helicopter popular with law-enforcement and rescue agencies, was scheduled to appear forty feet above them. Then the spoofer would be put to the test.




Technology establishes your Position, Navigation, and Time (PNT) in the environment -- but we have to protect it.

Defend your #PNT in challenging environments through Hexagon | NovAtel anti-jam antennas, interference mitigation, and GNSS+INS combined systems.

Read more about how to protect the integrity of your PNT solution >> https://hxgn.biz/2RM4zg9 


Feds outline all the ways they can get you for messing with drones:
The Advisory on the Application of Federal Laws to the Acquisition and Use of Technology to Detect and Mitigate Unmanned Aircraft Systems was jointly issued by the Justice Department, Federal Communications Commission, Department of Homeland Security, and Transportation Department. It starts out noting that Congress has only given the authority to those four departments plus the Department of Energy to do such things. No other entities, including state, local, and tribal law enforcement, are allowed - and presumably could be sanctioned if they did so.

When talking about measures that involve jamming or spoofing GPS, the advisory cites 18 U.S.C. § 1367, Interference with the Operation of a Satellite that "...generally prohibits “obstruct[ing] or hinder[ing] any satellite transmission.”

We will try to avoid any snarky comments about the FCC's decision on Ligado Networks at this point...

The National Geodetic Survey (NGS) recently announced two new items related to the modernized National Spatial Reference System. Check out the updates.



ESA project calls for terrestrial navigation systems to reduce risk


Webinar to discuss MarRINav project results:

In 2018 the first-ever European Radionavigation Plan said “It is recognized that GNSS should not be the sole source of PNT information. Alternative PNT systems, not necessarily using radio frequencies, should thus be put in place where the criticality of the application requires it.”Graphic from MarRINav report showing system of systems approach to PNT resilience and reliability. In 2019 the European Space Agency (ESA) published a permanent open call for proposals for positioning, navigation, and timing studies and systems, including those that had nothing to do with space.

One of the first fruits of this is the ESA-funded Maritime Resilience and Integrity of Navigation project, or MarRINav, recently completed by researchers in the United Kingdom. “Maritime navigation and port operations are critical for almost every nation,” said Jonathan Turner, one of the MarRINav project team. “As an island nation with a strong maritime heritage, we in the United Kingdom perhaps have an even greater appreciation of this.” Turner is co-founder of the blue economy solutions company NLA International, which led a team of eight organizations cooperating on the project. While MarRINav focused its analysis on the United Kingdom, the intent was to provide information, and an analysis framework, that could also be used by other nations.

Maritime is one of sectors most dependent upon Global Navigation Satellite Systems, according to the project reports, and one of the ones with the greatest awareness of GNSS vulnerabilities and their consequences. MarRINav concludes that integrity and resilience are two of the most important parameters for maritime navigation. Maritime is also one of the sectors most ready to integrate space and terrestrial navigation systems, according to the report’s authors. The International Maritime Organization has already introduced a performance standard for a Multi-System Receiver, or MSR, that will incorporate a wide variety of navigation signals.

Despite the distractions of Brexit over the last four years, the United Kingdom has been particularly focused on its vulnerability to GNSS outages.

Eyeing Russia, Army fields jam-resistant GPS in Europe:


U.S. Space Command blasts Russia for anti-satellite missile test - SpaceNews (Why, because they did not use an F-15 double thruster?):


US Air Force selects Raytheon Missiles & Defense to develop Long-Range Standoff weapon:


What we know about Iran’s counter-space weapons:


Norway says Russia jammed GPS signal during NATO drill:










Norway Powerless Against GPS Interference - NRK:



Russia’s new navigation plan reveals a fear of jamming - C4ISRNet:


In addition to jamming NATO exercises and spoofing GPS receivers to protect VIPs, Moscow also claims it added GPS jammers to over 250,000 domestic cell towers to help defeat U.S. cruise missiles should they attack.

Letter to Karen Van Dyke (DOT):  http://rntfnd.org/wp-content/uploads/Alliance_for_Telecommunications_Industry_Solutions_ATIS_Copper_Optical_Access_Synchronization_and_Transport_Committee_COAST-2.pdf 




Communication and Navigation Satellite Signal Broadcast Histories and Interruptions:
Please click menu items scattered around the top for a more detailed view.
I just ran across this overview summary:

https://www.gpsworld.com/survey-accuracy-the-future-of-precision-with-5-gnss-constellations/         My Speculation on the cause of Boeing 737 MAX 8 Failure

FCC to approve spectrum plan that Pentagon claims will harm GPS - C4ISRNet



Congressmen demand answers after Pentagon issues GPS warning - C4ISRNet:


https://rntfnd.org/wp-content/uploads/2020-04-10-DeFazio-Garamendi-Letter-to-DOT-GPS.pdf  (Chao's letter)

In response to this filed by Ligado:


Resolution scheduled here:


Multi-agency Report Opposing Ligado Request Could Be Last Element in Controversy - Inside GNSS:



Senate Armed Services, Former FCC Commissioner Slam Ligado:


It’s Time for the FCC to Terminate the ‘LightSquared’ Proceeding:


New Executive Order regarding PNT:



Industry perspective: Next-gen PNT needs careful assessment:


Three obstacles are slowing space sensors for hypersonic threats:



Four Challenges to Hypersonics:


Pentagon's Top R&D Chief Throws Cold Water On Laser Missile Defense Aspirations:

"Turn out the lights - the Party is over" Marketing flacks can go find something else to do for a few years instead of hawking concepts from movies based on comic books. Directed Energy lost its key advocate. 



Six months of reported GPS issues:


Analysis and Overview:



Lockheed’s Skunk Works Team to Help Update Air Force Reconnaissance Aircraft Avionics:


DHS S&T Invites Critical Infrastructure Owners and Operators to GPS Spoofing Test Event - HS Today:


New GPS 'circle spoofing' moves ship locations thousands of miles - GPS World:

New research by Bjorn Bergman of the environmental non-profit SkyTruth has found ships in various parts of the world reporting locations thousands of miles away and circling at precisely 20 knots. 


COSMIC-1 mission for GPS reflectometry comes to an end - GPS World
The COSMIC-1 program ended last month, when the last of six tiny satellites were decommissioned. Find out how long the satellites were in space. 


The Department of Homeland Security (DHS), Science and Technology Directorate (S&T) announced today an opportunity for critical infrastructure owners & operators and Global Positioning System (GPS) equipment manufacturers to test their equipment against GPS spoofing. The 2020 GPS Testing for Critical Infrastructure (GET-CI) event will be held later this year and is the third in this series of test opportunities.


Modernizing SIGINT—Technology Adapts to Serve Multiple Missions and Masters:
In this month’s Journal of Electromagnetic Dominance, I have a discussion with John Haystead about the evolving relationship between Signals Intelligence and electronic support measures, and the blurring of the lines between SIGINT, communications intelligence, and electronic intelligence. Spectrum dominance is the key for our DoD customers, and BAE Systems is poised at the forefront of innovation in this discriminator. At the end of the day, situational awareness across a variety of missions in as compact, efficient and upgradeable a package as possible is the goal. To read more on this important technology, check out May’s feature article in JED.


More Jamming and Spoofing of GPS:



Click here to see some other aspects of GPS evolution.               Brad Parkinson’s 2017 wish list: https://rntfnd.org/wp-content/uploads/Three-Wishes-v11s.pdf  

Click  here to see MORE aspects of GPS evolution.        https://www.septentrio.com/en/applications/referencestations  

USDOT seeks university to help secure automated navigation:                                                    


Raytheon, to replace OCX hardware by 2022 for $378 million:


The War perpetrated by Others on GPS (Part II) and other updates:






GPS III - Misleading Sound Bites Harm Nation - National Defense:



PCCW Global and UniStrong to link GNSS tech with telecoms, airports - GPS World:
PCCW GLOBAL Limited and UniStrong APAC Pte Ltd will collaborate on developing GNSS technologies and services for the telecommunications and aviation industries. Read more on the partnership and their goals.


Second GPS III Satellite Declared Ready for Military Use:


GPS Backup Analysis Stays on Track:



If your GPS position, navigation and time are under threat from jamming, then you need to consider NovAtel® Anti-Jam antennas. These are designed to defend against sources of interference -- that's assured positioning.

Read more about  NovAtel®'s GPS Anti-Jam Technology
>> https://hxgn.biz/2zl1vEp 

A new system, called WarLoc, makes it possible to locate warfighters and first responders in GPS-denied environments. 

Read more about the system, created by Robotic Research, LLC. (Photo: Robotic Research) #GPS:


CHC Navigation introduces Apache3 marine drone - GPS World:
The 2020 Apache3 Marine Drone provides a series of new features and additional enhancements to make lake, river and coastal hydrographic surveys more productive, according to maker CHC Navigation. Learn more about the drone. (Photo: CHC Navigation) #drone  #marine  #survey:


TeK Associates follows novel INS developments and relative INS accuracies: Familiar with Electro-statically supported Gyro (ESG) such as the airborne Micro, the SSBN ESG, as well as that in the Gravity-Probe satellite), Laser Gyros, Fiber Optics Gyros, Wine glass\tuning fork gyros, Microelectromechanical systems (MEMS) Gyroscopes. Prof. Christopher Jekelis (Ohio University, Columbus, OH) published mathematical model for Cold-Atom Gyros, as well as conventional mechanical spinning rotor gyros and their analysis.

We follow evolving procedures for moving platform shipborne and  in-air alignment gyro-compassing and alternative mechanizations: Local Level, Space-Stable, Wander-Azimuth, Strapdown and associated transformations (and typical frequency of re-calculation sample rates).  Surprisingly, new insights have recently been offered that much of the technology harkens back to analog gyro behavior more than is currently necessary in this digital age of extremely high processing speeds which can now support relatively high external GPS updates within strapdown gyroscope implementations. Previous notions of coning, sculling, the dynamics of Schuler loop oscillations being activated, or 24 hour diurnal oscillations are no longer necessary in Navigation systems mechanized with MEMS throughout and with GPS or differential GPS updates on the order of seconds or minutes because the gyros no longer need to go open loop without a compensating and ameliorating external  navaid fix for anything that approaches a significant fraction of the ~hour and a half Schuler period [30].

We are familiar with typical operational constraints and weapon system accuracies of several military platforms as well: e.g., Ships Submersible Ballistic Nuclear (SSBNs) submarines (a.k.a. Boomers), Ships Submersible Nuclear (SSN) submarines (a.k.a., attack subs), which allied countrys submarines use degaussing coils and which use flash, deperm procedures,  etc. We are also familiar with the tenets, details, and history of Search and Screening: e.g., detection range, worse case detection threats, observables-in-the-military-sense, countermeasures and counter-countermeasures for various sensors, etc. See [1] to [7] for perspectives on our early experience in this area. We are also knowledgeable in the associated terminology such as that of U.S. submarine alertness levels: 1SQ, 2SQ,..., Operation Sanguine [before the name change in thr 1970s to evade the scrutiny of protesters ], TACAMO, long trailing wire antenna (BCA), pig tail antenna, whip antenna, Blue-green laser, Counter Value vs. Counter Force, Mid-course star fix, firing keys (where located and who has access, and orderly sequence of events, and expected synchronizations and chain-of-command), etc.

Our SSBN submarines can launch while submerged; while those of many other countries must surface first before they can launch.

We are cognizant of the Society of Old Crows, of the Countermeasures Handbook (we possess several back issues), and Paladin Press publications over the years (that should never have been allowed to appear). CV motion models, Lamps helicopters and ships, use of  ship-borne winch and cables dropped from helicopters seeking to land onboard in rough seas (where cable is secured to winch and helicopter pulls cable taught and is reeled in slowly so that Helicopter motion automatically matches that of the deck of the ship as both pitch, roll, and yaw together (to avoid damaging the helicopter with a nasty unexpected impact with the deck of the much more massive ship capable of preserving inertia by inflicting a severe impulse force as a big crushing blow over the short period of time-BANG!) We know about historical pipe dreams that failed miserably as well as alternative more robust approaches (using older technology) that was good enough without being vulnerable to a myriad of difficulties associated with other things going wrong (one example being trying to use a laser-based reflection system to guide the helicopter to land on the deck in rough seas-obvious vulnerabilities being: fog, battle smoke, electronic failures at an extremely critical time ala Murphys law, laser orientation capability for interacting with surface ships deck-in-motion possibly falling out of sufficient calibration [as needed to retrieve the necessary reflection close to perpendicular to the moving deck for instantaneous round trip timing-so you cant solve the problem until you have already solved the problem] and needing additional INS components with their additional costs and vulnerabilities and operational procedures). Thank Michael Athans and AlphaTech for the less practical approach, described above. Example 2: What about the attempt to align several (two or more) surface ships at sea in tandem to create an effective landing strip for those super-sized carrier air craft to take-off and land for re-supply at sea. Although some of their numerous computer studies demonstrated feasibility, please just think about being in the North Atlantic with typical winter weather conditions involving very high sea states and then try to pull off this stunt. We have Raman Mehra and Scientific Systems to thank for this second one. Both examples were funded by the U.S. Navy and further reported in an open unclassified forum but my critical ear hears all and I dont soon forget these apparent technical boondoggles but do continue to wonder how they ever got pass other watchdogs. I guess it pays to be well connected. Its not my cup of tea though. I have to say what I see and what I smell. We Kerrs (curs) are well known watchdogs too. We try to avoid stepping in it as our predecessors did! Sometimes we mark our territory as a good alpha dog. Arrrooooo! Better to lead than to follow since the scenery is much better and more interesting (as every sled dog knows).

Rodriguez, J. J., Aggarwal, J. K., “Matching Aerial Images to 3D Terrain Maps,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 12, No. 12, pp. 1138-1149, Dec. 1990: Sparse terrain profile data are stored onboard and direct measurement of relative shifts between images are used to estimate position and velocity; however, an EKF is deemed superior here to use of merely a Kalman filter that uses altitude estimates in order to estimate aircraft position and velocity. 

Heeger, D. J., Jepson, A. D., “Subspace Methods for Recovering Rigid Motion I: Algorithm and Implementation,” International Journal of Computer Vision, Vol. 7, No. 2, pp. 95-117, Jan. 1992: Terrain matching methods are also used to estimate platform position and orientation via comparisons to an on-board digital elevation map. 

Soatto, S., Frezza, R., Perona, P., “Motion Estimation via Dynamic Vision,” IEEE Trans. on Automatic Control, Vol. 41, No. 3, pp. 95-117, Mar. 1996: A least squares formulation is used to recover user's 3D motion (3 translation variables and 6 rotation variables or 4 if quaternions are utilized). 

Goyurfil, P., Rotstein, H., “Partial Aircraft State Estimation from Visual Motion Using the Substate Constraint Approach,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 24, No. 5, pp. 1016-1025, Sep.-Oct. 2001: What is called an implicit EKF is used here to estimate aircraft states-aircraft velocities, angular rates, angle of attack, and angle of sideslip but not aircraft Euler angles nor inertial location. Measurements available are the image points of N featured objects, which are tracked from one frame to another. 

Craig Lawson, John F. Raquet, Michael J. Veth, “The Impact of Attitude on Image-Based Integrity,” Navigation: Journal of the Institute of Navigation, Vol. 57, No. 4, pp. 249-292, Winter 2010: Being aware of the historical importance of having good satellite geometry when seeking to utilize GPS for positioning and for timing (characterized by HDOP, VDOP, TDOP, and GDOP), they analogously extrapolate these ideas to the geometry of their airborne image collecting and refer to this as image integrity (similar to how researchers endeavor to associate sufficient Integrity to GPS measurements). Also see: Dennis Milbert, “Dilution of Precision Revisited,” Navigation: Journal of The Institute of Navigation (ION), Vol. 55, No. 1, pp. 67-81, Spring 2008.

Hoshizaki, T., Andrisani, D., Braun, A. W., Mulyana, A. K., and Bethel, J. S., Performance of Integrated Electro-Optical Navigation Systems,” Navigation: Journal of the Institute of Navigation, Vol. 51, No. 2, pp. 101-122, Summer 2004: Contains good modeling and they have a “tightly coupled system consisting of INS, GPS, and EO” all working together to simultaneously benefit both navigation and photogrammetry (estimates platform states, sensor biases, and unknown ground object coordinates using a single Kalman filter).

Kyungsuk Lee, Jason M. Kriesel, Nahum Gat, Autonomous Airborne Video-Aided Navigation,” Navigation: Journal of the Institute of Navigation, Vol. 57, No. 3, pp. 163-173, Fall 2010: ONR-funded discussion utilizes (1) “digitally stored georeferenced landmark images” (altimeter/DTED), (2) video from an onboard camera, and (3) data from an IMU. Relative position and motion are tracked by comparing simple mathematical representations of consecutive video frames. A single image frame is periodically compared to a landmark image to determine absolute position and to correct for possible drift or bias in calculating the relative motion.

Crassidis, J. L., Markley, F. L., Cheng, Y., “Survey of Nonlinear Attitude Estimation Methods,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 30, No. 1, pp. 12-28, Jan. 2007: An excellent survey on the subject of attitude estimation. It provides insights into what is important in estimation algorithms. It is a more practical and rigorous addendum to their many earlier NASA surveys, concerned with utilizing alternative EKF's or Nonlinear Luenberger Observers (as alternatives to Extended Kalman filter-based approaches). Compare to [152] below. (Thomas H. Kerr III comment: This version is more concise.)

Maji, M., Junkins, J. L., Turner, J. D., Jth Moment Extended Kalman Filtering for Estimation of Nonlinear Dynamic Systems,” AIAA Guidance, Navigation, and Control Conference and Exhibit, Honolulu, HI, Paper No. AIAA 2008-7386, pp. 1-18, 18-21 Aug. 2008: Explores two variations on JMEKF formulations that properly handle higher order moments (that lurk in the background while trying to get good estimates and covariances from EKF’s). Approximations utilized are acknowledged and properly handled (rather than ignored, as is usually the case). 

Scorse, W. T., Crassidis, A. L., Robust Longitudinal and transverse Rate Gyro Bias Estimation for Precise Pitch and Roll Attitude Estimation in Highly Dynamic Operating Environments Utilizing a Two Dimensional Accelerometer Array,” AIAA Atmospheric Flight Mechanics Conference, Paper No. AIAA 2011-6447, Portland, OR, pp. 1-28, 8-11 Aug. 2011: Using the latest in rigorous real-time estimation algorithms (neither a particle filter nor an unscented/Oxford/Sigma-Point filter) for enabling accurate pointing (precise pitch and roll) within an aircraft within a high dynamics operating environment is reported. While it does utilize rate integrating gyros, as does SYERS-2C, it also utilizes 2D accelerometer arrays and compares to an onboard gravity map to achieve its accuracy. 

Discussing Gyroscopes (the heart of an INS)

The classical mechanical  gyroscope has a relatively massive rotor suspended within a framework of light supporting rings called gimbals which have nearly frictionless bearings (as the ideal that is sought) that are used to help isolate the central spinning rotor from all outside influences (i.e., torques). At high rotation speeds of the rotor, the gyroscope exhibits extraordinary stability of its balance and maintains the orientation of the direction of the high speed rotation axis of its central rotor in where it points in 3-dimensional space. The implication or consequence of the physical law known as the conservation of angular momentum is that the angular momentum of the rotor is constant and it maintains not only its magnitude or speed of spin, but also its direction in space of the spin axis in the absence of any external torques. The classical gyroscope finds application in gyro-compasses (as an alternative to using a magnetic compass) and in more sophisticated Inertial Navigation Systems (that reveal location and orientation of vehicles on the earth; and under and over the sea, respectively, in submarines and ships; and in space in aircraft, in rockets, and in missiles). However, there are many more common examples of gyroscopic motion and its associated stability: spinning tops  and their associated almost mysterious precession behavior, the spinning wheels of bicycles and motorcycles keeping them from falling over even in a severe leaning angle, the spin of the Earth in space as it orbits the sun, even the behavior of a boomerang as it is being hurled are all examples of gyroscopic motion.

Classical Inertial Navigation Systems:


The typical mechanical spinning-rotor gyroscope found within classical Inertial Navigation Systems (INS) is constructed by suspending a relatively massive spinning rotor inside three orthogonally mounted support rings called gimbals. Mounting each of these rotors on axes with high quality bearing surfaces with low friction insures that very little resisting torque is  exerted on the inside rotor as the rotor continues to spin. Electrical torquers (not shown here) are utilized to initially spin up the inner-most rotor to its nominal speed and to maintain its angular velocity, as continuously monitored by electrical or mechanical pick-offs (also not shown here). Modern day INS gyros take many different forms based on whatever other particular inherent physical principle is being exploited, such as that for wine glass acoustic frequency vibrating gyros, for electro-statically supported spherical gyros, for electro-magnetically supported spherical gyros, for ring laser gyros (RLG), for fiber optic gyros, for atomic quantum spin gyros, for Cold Atom gyros, etc. Other important aspects are in exactly how the two or more gyros are implemented or bound together within an Inertial Navigation System (INS) such as in a Space Stable configuration, in a  Local-Level  configuration (as either Wander Azimuth, Free Inertial, or North Pointing), or in a Strap-Down configuration, and in its corresponding Navigation filter formulation, which can be implemented in three different alternative ways but with the differential feedback form being somewhat of a standard now. New insights have been recently revealed into how modern MEMS gyros may now be implemented in Strap Down configurations without the same hassles or operational constraints being present that were historically associated with handling the classical spinning rotor gyros depicted here. A Charles Stark Draper Laboratory study and report in the late 1960s had concluded that a preferred optimal configuration for redundant gyros (with a one-degree-of-freedom input axis) was being located in a certain prescribed way as placed along all the faces of a regular dodecahedron. It is indeed a pity that Draper seems to have forgotten this 40 year old conclusion of theirs as they now work with MEMS gyros for which  Draper should again appropriately invoke the very same solution (but they dont),

Gyroscopic Precession:

If a gyroscope is tipped away from its original orientation, the gimbals will try to reorient to keep the spin axis of the rotor aligned in the same original direction as conservation of momentum. If released after being tipped over in this new  orientation, the gyroscope will precess in the indicated direction depicted here due to the external torque exerted  on the gyroscope by gravity.



Euler angle representations of 3D rotations can be problematic at singularities; Direction Cosine Matrices (DCM) are 3 by 3 and include much redundancy and achieve a rotation goal in 3 space via 3 separate constituent rotations; Quarterions get the job done concisely by picking a particular direction in space as the axis of rotation and then performing merely a single rotation about that axis: four numbers suffice (but for practical reasons, there is a need to normalize within a software implementation otherwise nice theoretical structural results are jeopardized by ever present computer round-off). Please see: Bernard Friedland, Analysis of Strapdown Navigation Using Quaternions, IEEE Transactions on Aerospace and Electronic Systems, Vol. 14 , No. 5, pp. 764-768, Sept. 1978. 

While 3 by 3 matrix rotations are well known to enable rotations in 3D Euclidean space, less well known is that a 4 by 4 matrix multiply can enact both a rotation and an offset (as first deduced by people in computer graphics as a neat insight beyond what physicists and other engineers had realized). I frequently saw engineers in shock with their jaws dropped when they could work it out and prove it to themselves but had never studied it in school. My first encounter with this new aspect just mentioned was in: 
-Kerr, T. H., Comments on `Determining if Two Solid Ellipsoids Intersect’, AIAA Journal of Guidance, Control, and Dynamics, Vol. 28, No. 1, pp. 189-190, Jan.-Feb. 2005. (I found a way to simplify their earlier result) 
-Kerr, T. H., Integral Evaluation Enabling Performance Trade-offs for Two Confidence Region-Based Failure Detection, AIAA Journal of Guidance, Control, and Dynamics, Vol. 29, No. 3, pp. 757-762, May-Jun. 2006. (I summarized the above described simplification in a single line in this paper.) http://www.tekassociates.biz/tkerrcr2roc.pdf  

From James Farrell in May 2020: "Of potential interest to you: an IMU interface standard under development, with SAE International involved, requiring raw uncorrected increments from gyros and accelerometers plus coefficients for purposes of compensation. In addition to the usual well-known error sources, there is a wide variety of (less familiar) motion-sensitive degradations. A tip-of-the-iceberg is shown at https://jlfblog.com/gyro-mounting-misalignment".

New Gyroscope technology: https://www.linkedin.com/pulse/new-gyroscope-borrows-best-from-mems-optical-devices-lieberman-/?trackingId=0rPjqUMjUM0sa%2B%2BDuQWyzQ%3D%3D  


Quantum Antenna Solution Makes Resilient PNT Receivers Easier/Better:

https://www.linkedin.com/pulse/quantum-antenna-solution-makes-resilient-pnt-receivers-dana-a-goward/?trackingId=qu2IE9Qv6WCuZA5OUBZUbA%3D%3D https://phys.org/news/2020-03-scientists-quantum-sensor-entire-radio.html


University of Michigan gyroscope could reduce dependence on GPS in electronics:
Researchers powered the University of Michigan have developed a small but powerful gyroscope that could reduce the GPS-dependency of drones and autonomous cars. According to U-M’s Schlumberger Professor of Engineering, Khalil Najafi, the gyroscope -- a device used to measure and maintain navigation found in smartphones and other technologies -- is 10,000 times more accurate than a typical smartphone gyroscope but at only 10 times the cost.

Optical Gyro + MEMS Fab: A Match Made in INS Heaven?:
Gyroscope designs used in inertial navigation systems (INS) fall into three basic groups: the classic spinning-rotor mechanical gyro (still in use in specialized situations due to its superior performance capabilities); the optical-based laser gyro using either a mirrored, close-loop path or a lengthy, coiled optical fiber (capable of very high performance, but with substantial weight and size); and the MEMS device (small, light, and low power, with lesser—yet still very good—performance). Now, a team based at the California Institute of Technology (Caltech) has devised, analyzed, built, and tested a laser-based gyro that also leverages the unique capabilities of microelectromechanical-systems (MEMS) technology (but not a MEMS-gyro core) for some of its internal components.

Deep Learning for Inertial Navigation:
A short review of cutting edge deep learning-based solutions for inertial navigation.

We are cognizant of the necessary interaction between the architectures associated with various alternative approaches to multi-target tracking and Kalman filter-based target tracking algorithms in use (alternative tracking algorithms hypothesized as possible modern replacements).

Our primary strength is having an in depth awareness of all the Kalman filter estimation-based approaches used to date for handling failure\fault detection in an INS or in GPS RAIM, or in a GPS/INS hybrid. We are analytic algorithm specialists. This is our area of greatest familiarity.

Even more usefull information is availed here following the 305 references provided immediately below (click this link to automatically move pass these citations).

Historical Account of our experience therein:

[1] Kerr, T. H., “Poseidon Improvement Studies: Real-Time Failure Detection in the SINS\ESGM (U),” TASC Report TR-418-20, Reading, MA, June 1974 (Confidential) for Navy, SP-2413 (Jerome “Jerry” Katz).
[2] Kerr, T. H., “Failure Detection in the SINS\ESGM System (U),” TASC Report TR-528-3-1, Reading, MA, July 1975 (Confidential) for Navy, SP-2413 (Jerome “Jerry” Katz).
[3] Kerr, T. H., “Improving ESGM Failure Detection in the SINS\ESGM System (U),” TASC Report TR-678-3-1, Reading, MA, October 1976 (Confidential) for Navy, SP-2413 (Jerome “Jerry” Katz).
[4] Kerr, T. H., “Preliminary Quantitative Evaluation of Accuracy\Observables Trade-off in Selecting Loran\NAVSAT Fix Strategies (U),” TASC Technical Information Memorandum TIM-889-3-1, Reading, MA, December 1977 (Confidential) for Navy, SP-2413 (Jerome “Jerry” Katz).
[5] Kerr, T. H., “Improving C-3 SSBN Navaid Utilization (U),” TASC Technical Information Memorandum TIM-1390-3-1, Reading, MA, August 1979 (Secret) for Navy, SP-2413 (Jerome Jerry Katz).

[6] Kerr, T. H., “Modeling and Evaluating an Empirical INS Difference Monitoring Procedure Used to Sequence SSBN Navaid Fixes,” Proceedings of the Annual Meeting of the Institute of Navigation, U.S. Naval Academy, Annapolis, Md., 9-11 June 1981. (Selected for reprinting in Navigation: Journal of the Institute of Navigation, Vol. 28, No. 4, pp. 263-285, Winter 1981-82). 

[7] Kerr, T. H., “Impact of Navigation Accuracy in Optimized Straight-Line Surveillance\Detection of Undersea Buried Pipe Valves,” Proceedings of National Marine Meeting of the Institute of Navigation (ION), Cambridge, MA, 27-29 October 1982.

[8]  Kerr, T. H., “Stability Conditions for the RelNav Community as a Decentralized Estimator-Final Report,” Intermetrics, Inc. Report No. IR-480, Cambridge, MA, 10 August 1980, for NADC (Warminster, PA).

[9] Kerr, T. H., and Chin, L., “A Stable Decentralized Filtering Implementation for JTIDS RelNav,” Proceedings of IEEE Position, Location, and Navigation Symposium (PLANS), Atlantic City, NJ, 8-11 December 1980.   ( Kerr, T. H., and Chin, L., “A Stable Decentralized Filtering Implementation for JTIDS RelNav,” Proceedings of IEEE Position, Location, and Navigation Symposium (PLANS), Atlantic City, NJ, 8-11 December 1980.  )

[10] Kerr, T. H., and Chin, L., “The Theory and Techniques of Discrete-Time Decentralized Filters,” in Advances in the Techniques and Technology in the Application of Nonlinear Filters and Kalman Filters, edited by C. T. Leondes, NATO Advisory Group for Aerospace Research and Development, AGARDograph No. 256, Noordhoff International Publishing, Lieden, 1981.

[11] Kerr, T. H., and Rogers, R., Report on PINS Filter Design Review (of Magnavox), Intermetrics Memo, Cambridge, MA, 11 August 1983, for NOSC (San Diego, CA). (Minesweeper Navigation)

[12] Kerr, T. H., “GPS\SSN Antenna Detectability,” Intermetrics Report No. IR-MA-199, Cambridge, MA, 15 March 1983, for NADC (George Lowenstein).

[13] Kerr, T. H., “Functional and Mathematical Structural Analysis of the Passive Tracking Algorithm (PTA),” Intermetrics Report No. IR-MA-208, Cambridge, MA, 25 May 1983, for NADC. (LAMPS Sonobuoy algorithms.)

[14] Kerr, T. H., “Navy GPS\SSN Phase II User Equipment DT&E Magnavox Modification Center (Mod Center) Test Report,” 1 June 1985, for NADC Code 4022 (George Lowenstein).

[15] Kerr, T. H., “Navy GPS\SSN Phase II User Equipment DT&E Rockwell-Collins Modification Center (Mod Center) Test Report,” 1 June 1985, for NADC Code 4022 (George Lowenstein).

[16] Kerr, T. H., “Navy GPS\SSN Phase II User Equipment DT&E Rockwell-Collins Developmental Test and Evaluation (Operational Readiness) [DT&E (OR)] Test Report,” 10 June 1985, for NADC Code 4022 (George Lowenstein).

[17] Kerr, T. H., “Magnavox Military Utility Test Report,” 10 June 1985, for NADC Code 4022 (for George Lowenstein).

[18] Kerr, T. H., “Phase III GPS Integration; Volume 1: GPS U.E. Characteristics,” Intermetrics Report IR-MA-177, Cambridge, MA, January 1983, for Navair and for NOSC (Richard Akita).

[19] Kerr, T. H., Decentralized Filtering and Redundancy Management Failure Detection for Multi-Sensor Integrated Navigation Systems, Proceedings of the National Technical Meeting of the Institute of Navigation (ION), San Diego, CA, 15-17 January 1985.

[20] Kerr, T. H., “Use of GPS\INS in the Design of Airborne Multisensor Data Collection Missions (for Tuning NN-based ATR algorithms),” the Institute of Navigation Proceedings of GPS-94, Salt Lake City, UT, pp. 1173-1188, 20-23 Sept. 1994.

[21] Kerr, T. H., “Further Comments on ‘Optimal Sensor Selection Strategy for Discrete-Time Estimators’,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 31, No. 3, pp. 1159-1166, June 1995.

[22] Kerr, T. H., “Sensor Scheduling in Kalman Filters: Evaluating a Procedure for Varying Submarine Navaids,” Proceedings of 57th Annual Meeting of the Institute of Navigation, pp. 310-324, Albuquerque, NM, 9-13 June 2001.  

[23] Kerr, T. H., Sensor Scheduling in Kalman Filters: varying navaid fixes for trading-off submarine NAV accuracy vs. ASW exposure,” Proceedings of The Workshop on Estimation, Tracking, and Fusion: A Tribute to Yaakov Bar-Shalom (on the occasion of his 60th Birthday) following the Fourth ONR/GTRI Workshop on Target Tracking and Sensor Fusion, Naval Postgraduate School, Monterey, CA, pp. 104-122, 17 May 2001.

[24] Kerr, T. H., Further Critical Perspectives on Certain Aspects of GPS Development and Use,” Proceedings of 57th Annual Meeting of the Institute of Navigation, 9-13 June 2001.

(To see a high level overview slide show associated with the topics of the preceding paper, please click here to obtain the main executable file stpete.exe. In order to view the slideshow, user must first also download these auxiliary files: this associated .DLL file, then this .DLL file, then this VBX file, all to the same folder location on their local computer, where stpete.exe resides. Our Web Site host required temporary conversion to exclusively lower case spellings. Once this is done, merely click on stpete.exe to start the show and click on screen to move to the next screen in the sequence until the end [when it closes and stops].)

[25] Biezad, D. J., Integrated Navigation and Guidance Systems, AIAA Education Series, Reston, VA, 1999.

[26] Sofir, I., “Improved Method for Calculating Exact Geodetic Latitude and Attitude-Revisited, AIAA Journal of Guidance, Control, and Dynamics, Vol. 23, No. 2, ff. 369, 2000.

[27] Siouris, G. M., “Navigation: Inertial,” Encyclopedia of Physical Science and Technology, 2nd Edition, V. 10, pp. 595-647, Academic Press, NY, 1992.

[28] Jordan, J. F., Wood, L. J., “Navigation: Space Missions,” Encyclopedia of Physical Science and Technology, 2nd Edition, Vol. 10, pp. 649-673, Academic Press, NY, 1992.

[29] Ward, P., “Navigation: Satellites,” Encyclopedia of Physical Science and Technology, 2nd Edition, Vol. 10, pp. 675-702, Academic Press, NY, 1992.

[30] Farrell, J. L., “Strapdown at the Crossroads, Navigation, Journal of the Institute of Navigation, Vol. 51, No. 4, pp. 249-257, Winter 2004. (A good modern perspective! Correction in Vol. 52, No. 1, page iii, Spring 2005. Strong conclusions in this paper should be viewed  as being somewhat controversial.)

[31] Kerr, T. H., “Comment on `Precision Free-Inertial Navigation with Gravity Compensation by an Onboard Gradiometer’, AIAA Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4, July-Aug. 2007.

[32] Felter, S. C., Wu, N. E., “A Relative Navigation System for Formation Flight,IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 7, pp. 958-967, July 1997.

[33] Juang, J.-C., Huang, G.-S., “Development of GPS-Based Altitude Determination Algorithms,IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 7, pp. 968-976, July 1997.

[34] Chatterji, G. B., Menon, P. K., Sridhar, B., “GPS/Machine Vision Navigation System for Aircraft,IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 7, pp. 1012-1095, July 1997.

[35] Xiong, P., “Spacial and Temporal Processing for Global Navigation Satellite Systems: GPS receiver paradigm,IEEE Trans. on Aerospace and Electronic Systems, Vol. 39, No. 7, pp. 936-948, July 2003.

[36] Madhani, P. H., “Application of Successive Interference Cancellation to GPS Pseudolite Near-Far Problem,IEEE Trans. on Aerospace and Electronic Systems, Vol. 39, No. 4, pp. 481-488, April 2003.

[37] Luo, N., “Multiple Moving Platform, GPS, Relative Positioning,IEEE Trans. on Aerospace and Electronic Systems, Vol. 39, No. 7, pp. 936-948, July 2003.

[38] Fante, R. L., “Multipath-induced bias, GPS time-of-arrival, Evaluation and Reduction,IEEE Trans. on Aerospace and Electronic Systems, Vol. 39, No. 7, pp. 911-920, July 2003.

[39] Qi, H., “GPS/INS Integration: Direct Kalman Filtering Approach,IEEE Trans. on Aerospace and Electronic Systems, Vol. 38, No. 1, pp. 687-693, Jan. 2002.

[40] Shin, D.-H., “TOA and TDOA Positioning Error,IEEE Trans. on Aerospace and Electronic Systems, Vol. 38, No. 1, pp. 307-308, Jan. 2002.

[41] Pervan, B., “Sigma Inflation for Local Area Augmentation of GPS,IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 10, pp. 1301-1311, Out. 2001.

[42] Praasch, M. S., “SS-Ranging Multipath Model Validation for DGPS,IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 1, pp. 298-304, Jan. 2001.

[43] Ray, J. K., “Carrier Multipath Mitigation, Multiantenna System,IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 1, pp. 183-195, Jan. 2001.

[44] Kim, K. H., Lee, J. G., Park, C. G., “Adaptive Two Stage Extended Kalman Filter for a Fault-Tolerant INS-GPS Loosely Coupled System,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 45, No. 1, pp. 125-137, Jan. 2009.

[45] Jardak, N., Samama, N., “Indoor Positioning Based on GPS-Repeators: Performance Enhancement using an Open Code Loop Architecture,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 45, No. 1, pp. 347-359, Jan. 2009.

[46] “Noncoherrent Integrations for GNSS Detection: Analysis and Comparisons,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 45, No. 1, pp. 360-375, Jan. 2009.

[47] Chiang, K.-W., Noureldin, A., El-Sheimy, N., “Constructive Neural-Networks-Based MEMS/GPS Integration Scheme,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 582-594, April 2008.

[48] Farrell, W. J., “Interacting Multiple Model Filter for Tactical Ballistic Missile Tracking,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 418-426, April 2008.

[49] Borio, D., Camoriano, L., Lo Presti, L., Fantino, M., “DTFT-Based Frequency Lock Loop for GNSS Applications,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 595-612, April 2008.

[50] Kaplan, L. M., “Assignment Costs for Multiple Sensor Track-to-Track Association,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 655-675, April 2008.

[51] Bon, N., Khenchaf, A., Garello, R., “GLRT Subspace Detection for Range and Doppler Distributed Targets,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 678-695, April 2008.

[52] Juang, J.-C., “Multi-Objective Approach to GNSS Code Discrimination Design,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 481-492, April 2008.

[53] Geren, W. P., Murphy, T., Pankaskif, T. A., “Analysis of Airborne GPS Multipath Effects using High-Fidelity EM Models,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 711-723, April 2008.

[54] Jan, S.-S., Gebre-Egziabher, D., Walter, T., Enge, P., “Improving GPS-Based Landing System Performance using an Empirical Barometric Altimeter Confidence Bound,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 1, pp. 127-146, Jan. 2008.

[55] Lambert, H. C., “Tracking Filter for the Mitigation of the Ionospheric Range Bias,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 1, pp. 339-348, Jan. 2008.

[56] Tudoroiu, N., Khorasani, K., “Satellite Fault Diagnosis using a Bank of Interacting Kalman Filters,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 43, No. 4, pp. 1334-1350, Oct. 2007.

[57] Musicki, D., La Scala, B., “Multi-Target Tracking in Clutter Without Measurement Assignment,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 877-896, July 2008.

[58] Blanch, J., Walter, T., Enge, P., “Position Error Bound Calculation for GNSS Using Measurement Residuals,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 977-984, July 2008.

[59] Musicki, D., “Multi-Target Tracking using Multiple Passive Bearings-Only Asynchronous Sensors,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 1151-1160, July 2008.  Also see: http://www.gallup.unm.edu/~smarandache/NATOASI_ATJDTSPK.pdf 

[60] Foster, C. C., Elkaim, G. H., “Extension of a Two-Step Calibration Methodology to Include Nonorthogonal Sensor Axes,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 1070-1078, July 2008.

[61] Borio, D., Camoriano, L., Lo Presti, L., “Impact of GPS Acquisition Strategy on Decision Probabilities,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 996-1011, July 2008.

[62] Lee, J., Pullen, S., Enge, P., “Sigma-Mean Monitoring for the Local Area Augmentation of GPS,IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 2, pp. 625-635, Apr. 2006.

[63] Bednarz, S., Misra, P., “Receiver Clock-Based Integrity Monitoring for GPS Precision Approaches,IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 2, pp. 636-643, Apr. 2006.

[64] Heo, M.-B., Pervan, B., “Carrier Phase Navigation Architecture for Shipboard Relative GPS,IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 2, pp. 670-679, Apr. 2006.

[65] Pacher, M., Porter, A., Polat, M., INS-Aiding Using Bearings-Only Measurements of an Unknown Ground Object,Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 1-20, Spring 2006.

[66] Wendel, J., Metzger, J., Moenikes, R., Maier, A., Trommer, G. F., A Performance Comparison of Tightly Coupled GPS/INS Navigation Systems Based on Extended and Sigma Point Kalman Filters,Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 21-31, Spring 2006.

[67] Farrell, J. L., Full Integrity Testing for GPS/INS,Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 33-40, Spring 2006.

[68] Hwang, P. Y., Brown, R. G., RAIM-FDE Revisited: A New Breakthrough in Availability Performance with nioRAIM (Novel Integrity-Optimized RAIM),Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 41-51, Spring 2006.

[69] Alves, D. B. M., Monico, J. F. G., Mitigating Systematic Errors for Single Frequency GPS Receivers Employing A Penalized Least Squares Methodology,Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 53-60, Spring 2006.

[70] Fante, R. L., Vaccaro, J. J., “Cancellation of Jammers and Jammer Multipath in a GPS Receiver,IEEE AES Systems Magazine, Vol. 13, No. 11, pp. 25-28, Nov. 1998.

[71] Fante, R. L., Vaccaro, J. J., “Wideband Cancellation of Interference in a GPS Receive Array,IEEE Trans. on Aerospace and Electronic Systems, Vol. 36, No. 2, pp. 549-564, April 2000.

[72] Counselman, C. C., “Array Antennas for DGPS,IEEE Systems Magazine, Vol. 13, No. 12, pp. 15-19, Dec. 1998.

[73] Rabideau, D. J., “Clutter and Jammer Multipath Cancellation in Airborne Adaptive Radar,IEEE Trans. on Aerospace and Electronic Systems, Vol. 36, No. 2, pp. 565-583, April 2000.

[74] Myers, L., Improved Radio Jamming Techniques: Electronic Guerilla Warfare, ISBN 0873645200, Paladin Press, Boulder, CO, 1989.

[75] Daher, J. K., Harris, J. M., Wheeler, M. L., “An Evaluation of the Radio Frequency Susceptibility of Commercial GPS Receivers,IEEE AES Systems Magazine, Vol. 9, No. 10, pp. 21-25, October 1994.

[76] White, N. A., “Detection of Interference/Jamming and Spoofing in DGPS-aided Inertial Systems,IEEE Trans. on Aerospace and Electronic Systems, Vol. 34, No. 5, pp. 1208-1217, Oct. 1998.

[77] White, N. A., Maybeck, P. S., DeVilbiss, S. L., “Detection of Interference/Jamming and Spoofing in a DGPS-Aided Inertial System,IEEE Trans. on Aerospace and Electronic Systems, Vol. 34, No. 4 pp. 1208-1217, Oct. 1998.

[78] Pinker, A., Smith, D., Walker, D., “Jamming the GPS Signal,Proceedings of the 55th Annual Meeting of the ION, Cambridge, MA, 28-30 June 1999.

[79] Littlepage, R. S., “The Impact of Interference on Civil GPS,Proceedings of the 55th Annual Meeting of the ION, Cambridge, MA, 28-30 June 1999. (He warned us early on! His presentation was more explicit than his paper. He was truly concerned.)

[80] Goldstein, J. S., “Multistage partially adaptive STAP CFAR detection algorithm,IEEE Trans. on Aerospace and Electronic Systems, Vol. 35, No. 2, pp. 645-669,  April 1999.

[81] Saha, R. K., “Effect of Common Process Noise on Two-Sensor Track Fusion,AIAA Journal of Guidance, Control, and Dynamics, Vol. 19, No. 4, pp. 829-835, July-August 1996.

[82] Fitzgerald, R. J., “Effects of Range-Doppler Coupling on Chirp Radar Tracking  Accuracy,IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-10, No. 4, pp. 528-532, July 1974.

[83] Brennan, L. E., Reed, I. S., “Theory of Adaptive Radar,IEEE Trans. on Aerospace and Electronic Systems, Vol. 9, No., pp. 237-252, March 1973.

[84] Brennan, L. E., Mallett, J. D., Reed, I. S., “Adaptive Arrays in Airborne MTI Radar,IEEE Trans. on Antennas and Propagation, Vol. 24, No. 5, pp. 607-615, September 1978.

[85] Arregui, F. J. (ed.), Sensors Based on Nanostructured Materials, Springer Science & Business Media LLC, 2009.

[86] Righini, G. C., Tajani, A., Cutolo, A., An Introduction to Optoelectronic Sensors, World Scientific, NY, 2009.

[87] Vladimir Cherkassky and Filip Mulier, Learning from Data: Concepts, Theory, and Methods, John Wiley & Sons, Inc., NY, 1998.

[88] Gupta, S. N., “An Extension of Closed-Form Solutions of Target-Tracking Filters with Discrete Measurements,IEEE Trans. on Aerospace and Electronic Systems, Vol. 20, No. 6, pp. 839-840, Nov. 1984.

[89] Junichiro Toriwaki, Hiroyuki Yoshida, Fundamentals of Three-Dimensional Digital Processing, Springer-Verlag, London, 2009.

[90] Julien Bourgeois, Wolfgang Minker, Time-Domain Beamforming and Blind Source Separation: Speech Input in the Car Environment, Springer Science + Business Media, NY, 2009.

[91] Jekeli, C., “Navigation Error Analysis of Atom Interferometer Inertial Sensing, Navigation: Journal of the Institute of Navigation, Vol. 52, No. 1, pp. 1-14, Spring 2005.

[92] Another intriguing wrinkle is conveyed in Fernandez-Alcada, R., Navarro-Moreno, Ruiz-Molina, J. C., Oya, A., “Recursive Linear Estimation for Doubly Stochastic Poisson Processes,” Proceedings of the World Congress on Engineering (WCE), Vol. II, London, UK, pp. 2-6, 2-4 July 2007.

[93] Huddle, J.R., “Inertial Navigation System Error Model Considerations in Kalman Filter Applications,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 20, Academic Press, NY, pp. 294-340, Part 2 of 3, 1983.

[94] Lechner, W., “Application of Model Switching and Adaptive Kalman Filtering for Aided Strapdown Navigation Systems,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 20, Academic Press, NY, pp. 155-185, Part 2 of 3, 1983.

[95] Chien, T. T., “An Adaptive Technique for a Redundant-Sensor Navigation System,” Report No. T-560, C. S. Draper Laboratory, Cambridge, MA, 1972.

[96] Salazar, M. R., “State Estimation of Ballistic Trajectories with Angle-Only Measurements,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 21, Academic Press, NY, pp. 117-175, Part 3 of 3, 1984.

[97] Hsiao, C.- Y., “Computational Techniques in Angle-Only Tracking Filtering,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 29, Academic Press, NY, pp. 101-134, Part 2 of 3, 1988.

[98] Liang, D. F., “Comparisons of Nonlinear Recursive Filters for Systems with Non-negligible Nonlinearities,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 20, Academic Press, NY, pp. 341-402, Part 2 of 3, 1983.

[99] Yannis A. Phillis, “Algorithms for Systems with Multiplicative Noise,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 30, Academic Press, NY, pp. 65-83, Part 3 of 3, 1989.

[100] Yannis A. Phillis and Vassilis S. Kouikoglou, “Minimax Estimation and Control of Multiplicative Systems,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 31, Academic Press, NY, pp. 93-124, Part 1 of 3, 1989.

[101] Ahn, B.-H., Regan, R., et al, “Inertial Technology for the Future,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 20, No. 4, pp. 414-444, Jul. 1984.

[102] Jayawardhana, B., Logemann, H., and Ryan, E. P., “The Circle Criterion and Input-to-State Stability: new perspectives on a classical result,” IEEE Control System Magazine, pp. 32-67, Vol. 31, No. 4, August 2011.

[103] Yan, J., Hoag, J. B., Hindman, R. E., Bernstein, D. S.,  “Longitudinal Aircraft Dynamics and the Instantaneous Acceleration Center of Rotation: the case of the vanishing zeros,” IEEE Control System Magazine, pp. 68-92, Vol. 31, No. 4, August 2011.

[104] Bergin, J., Guerci, J. R., MIMO Radar: Theory and Practice, Artech House, Boston, 2018.

[105] Son, J. S., Thomas, G., Flores, B. C., Range-Doppler Radar Imaging and Motion Compensation, Artech House, Boston, 2001.

[106] Guerci, J. R., Space-Time Adaptive Processing for Radar, Artech House, Boston, 2003.

[107] Hudson, J. E., Adaptive Array Principles, Peter Peregrinus, Ltd., London, U. K., 1981, reprinted 1989, 1991. 

[108] Copps, E. M., “An aspect of the role of the clock in a GPS receiver,” Navigation, Journal of The (U.S.) Institute of Navigation, Vol. 31, No. 3, pp. 233-242, 1986. Also in Global Positioning System, papers published in Navigation, reprinted by The (U.S.) Institute of Navigation, Vol. III,  pp. 44-53, 1986. 

[109] Copps, E. M.,  Geier, G. J.,  Fidler, W. C. and Grundy, P. A. , “Optimal processing of GPS signals,” Proceedings of the Thirty-Sixth Annual Meeting of The (U.S.) Institute of Navigation, Monterey, CA, 23- 26 June, pp. 17-24, 1980. Also in Navigation, Journal of The (U.S.) Institute of Navigation, Vol. 27, No. 3, pp. 171-182, 1984. Also in Global Positioning System, papers published in Navigation, reprinted by The Institute of Navigation, Vol. II, pp. 13-24, 1984. (cf., [178])

[110] Kashyap, S. K., Naidu, V. P. S., Singh, J., Girija, G., Rao, J. R., “Tracking of Multiple Targets Using Interactive Multiple Model and Data Association Filter,” Journal of Aerospace Science and Technologies, Vol. 58, No. 1, pp. 66-74, 2006.

NAVIGATION via Visual Cues Using Only Imaging Sensors:
[111] Rodriguez, J. J., Aggarwal, J. K., “Matching Aerial Images to 3D Terrain Maps,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 12, No. 12, pp. 1138-1149, Dec. 1990: Sparse terrain profile data are stored onboard and direct measurement of relative shifts between images are used to estimate position and velocity; however, an EKF is deemed superior here to use of merely a Kalman filter that uses altitude estimates in order to estimate aircraft position and velocity. 
[112] Heeger, D. J., Jepson, A. D., “Subspace Methods for Recovering Rigid Motion I: Algorithm and Implementation,” International Journal of Computer Vision, Vol. 7, No. 2, pp. 95-117, Jan. 1992: Terrain matching methods are also used to estimate platform position and orientation via comparisons to an on-board digital elevation map. 
[113] Soatto, S., Frezza, R., Perona, P., “Motion Estimation via Dynamic Vision,” IEEE Trans. on Automatic Control, Vol. 41, No. 3, pp. 95-117, Mar. 1996: A least squares formulation is used to recover user's 3D motion (3 translation variables and 6 rotation variables or 4 if quaternions are utilized). 
[114] Goyurfil, P., Rotstein, H., “Partial Aircraft State Estimation from Visual Motion Using the Substate Constraint Approach,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 24, No. 5, pp. 1016-1025, Sep.-Oct. 2001: What is called an implicit EKF is used here to estimate aircraft states-aircraft velocities, angular rates, angle of attack, and angle of sideslip but not aircraft Euler angles nor inertial location. Measurements available are the image points of N featured objects, which are tracked from one frame to another. 
[115] Hoshizaki, T., Andrisani, D., Braun, A. W., Mulyana, A. K., and Bethel, J. S., “Performance of Integrated Electro-Optical Navigation Systems,” Navigation: Journal of the Institute of Navigation, Vol. 51, No. 2, pp. 101-122, Summer 2004: Contains good modeling and they have a “tightly coupled system consisting of INS, GPS, and EO” all working together to simultaneously benefit both navigation and photogrammetry (estimates platform states, sensor biases, and unknown ground object coordinates using a single Kalman filter).Use of control points avoided pre-stored terrain. 
[116] Kyungsuk Lee, Jason M. Kriesel, Nahum Gat, “Autonomous Airborne Video-Aided Navigation,” Navigation: Journal of the Institute of Navigation, Vol. 57, No. 3, pp. 163-173, Fall 2010: ONR-funded discussion utilizes (1) “digitally stored georeferenced landmark images” (altimeter/DTED), (2) video from an onboard camera, and (3) data from an IMU. Relative position and motion are tracked by comparing simple mathematical representations of consecutive video frames. A single image frame is periodically compared to a landmark image to determine absolute position and to correct for possible drift or bias in calculating the relative motion. 
[117] Craig Lawson, John F. Raquet, Michael J. Veth, “The Impact of Attitude on Image-Based Integrity,” Navigation: Journal of the Institute of Navigation, Vol. 57, No. 4, pp. 249-292, Winter 2010: Being aware of the historical importance of having good satellite geometry when seeking to utilize GPS for positioning and for timing (characterized by HDOP, VDOP, TDOP, and GDOP), they analogously extrapolate these ideas to the geometry of their airborne image collecting and refer to this as image integrity (similar to how researchers endeavor to associate sufficient Integrity to GPS measurements). Known a/c attitude significantly beats unknown attitude (altitude-indexed). Also see: [159] by Dennis Milbert further below. 
Likely comparable Classified DoD Pointing Improvements: Cobra Ball/Cobra Eye & other airborne Laser developments.
Rigorous updates in airborne estimation for attitude determination:
[118] Crassidis, J. L., Markley, F. L., Cheng, Y., “Survey of Nonlinear Attitude Estimation Methods,” Journal of Guidance, Control, and Dynamics, Vol. 30, No. 1, pp. 12-28, Jan. 2007: An excellent survey on the subject of attitude estimation. It provides insights into what is important in estimation algorithms. It is a more practical and rigorous addendum to their many earlier surveys, concerned with utilizing alternative EKF's or Nonlinear Luenberger Observers (as alternatives to Extended Kalman filter-based approaches). They admonish to “stick with EKF”.
[119] Majji, M., Junkins, J. L., Turner, J. D., “Jth Moment Extended Kalman Filtering for Estimation of Nonlinear Dynamic Systems,” AIAA Guidance, Navigation, and Control Conference and Exhibit, Honolulu, HI, Paper No. AIAA 2008-7386, pp. 1-18, 18-21 Aug. 2008: Explores two variations on JMEKF formulations that properly handle higher order moments (that lurk in the background while trying to get good estimates and covariances from EKF’s). Approximations utilized are acknowledged and properly handled (rather than ignored, as is usually the case). Errors reduced by several orders of magnitude within 5 sec., but results in normalized units (for comparisons to ordinary EKF approach, which it beat by a wide margin). Down side is its larger CPU burden yet to be completely quantified.
[120] Scorse, W. T., Crassidis, A. L., “Robust Longitudinal and transverse Rate Gyro Bias Estimation for Precise Pitch and Roll Attitude Estimation in Highly Dynamic Operating Environments Utilizing a Two Dimensional Accelerometer Array,” AIAA Atmospheric Flight Mechanics Conference, Paper No. AIAA 2011-6447, Portland, OR, pp. 1-28, 8-11 Aug. 2011: Using the latest in rigorous real-time estimation algorithms (neither a particle filter nor an unscented/Oxford /Sigma-Point filter) for enabling accurate pointing (precise pitch and roll) within an aircraft within a high dynamics operating environment is reported. While it does utilize rate integrating gyros. It also utilizes 2D accelerometer arrays and compares to an onboard gravity map to achieve its accuracy. Following reasonably large offsets, got back to within 0.1 degree pointing error within 10 seconds but results much worse with turbulence present. 
[121] Jensen, Kenneth J., “Generalized Nonlinear Complementary Attitude Filter,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 34, No. 5, pp. 1588-1593 , Sept.-Oct. 2011: Achieves a big breakthrough by providing a proof of this particular EKF’s global stability as a consequence and now states that it possesses “almost” global asymptotic stability; however, the term “almost” is required terminology to keep probability theorists and purists happy with the wording of his claim. Author Jensen attains his results by utilizing appropriate stochastic Lyapunov functions (proper handling of such is due to Prof. Emeritus Harold J. Kushner, Brown Univ.). I don’t know whether Jensen was the first to achieve this new result?
[122] La Scala, B. F., Bitmead, R. R., James, M. R., “Conditions for stability of the Extended Kalman Filter and their application to the frequency tracking problem,” Math. Control, Signals Syst. (MCSS), vol. 8, No. 1, pp. 1-26, Mar. 1995: Proof of Stability for yet another EKF. Now worries about EFK divergence evaporate for this application.
[123] Reif, K., Gunther, S., Yaz, E., Unbehauen, R., “Stochastic stability of the continuous-time extended Kalman filter,” Proc. Inst. Elect. Eng., Vol. 147, p. 45, 2000: Proof of Stability for yet another EKF. Now worries about EFK divergence evaporate for this application
[124] Salcudean, S., “A globally convergent angular velocity observer for rigid body motion,” IEEE Trans. on Autom. Control, Vol. 36, No. 12, pp.1493-1497, Dec. 1991: Proof of Stability for Luenberger Observer use too (~EKF). 
Rigorous Matrix Kalman Filter (MKF) updates in airborne estimation for attitude determination (Cont.’d):

In anticipation of later success, I have explored some possibilities offered by the following novel Kalman filter variants that use matrix sensor (allowing simultaneous angle) measurements in lieu of the more familiar version of a Kalman filter involving only vector sensor (one-direction-at-a-time) measurements. 
(JTIDS RelNav used multilateration and only ordinary Kalman filters with vector sensors on each platform but had many participants in the net who automatically responded at regular short intervals!)
[125] Choukroun, D., Weiss, H., Bar-Itzhack, I. Y., Oshman, “Kalman Filtering for Matrix Estimation,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 1, pp. 147-159, Jan. 2006: A linear Matrix Kalman filter for DCM. DCM Refinement #1 
[126] Choukroun, D., Weiss, H., Bar-Itzhack, I. Y., Oshman, “Direction Cosine Matrix Estimation from Vector Observations Using a Matrix Kalman Filter,” AIAA Guidance, Navigation, and Control Conference and Exhibit, pp. 1-11, Aug. 2003: A linear Matrix Kalman Filter for DMC using either vector or matrix measurement updates. DCM Refinement #2 . 
[127] Choukroun, D., “A Novel Quaternion Kalman Filter using GPS Measurements,” Proceedings of ION GPS, Portland, OR, pp. 1117-1128, 24-27 Sep. 2002: An alternative viewpoint: Quaternion Refinement #1.
[128] Choukroun, D., Weiss, H., Bar-Itzhack, I. Y., Oshman, “Kalman Filtering for Matrix Estimation,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 1, pp. 147-159, Jan. 2006: Quaternion Refinement #2.
[129] Choukroun, D., Bar-Itzhack, I. Y., Oshman, “Novel Quaternion Kalman Filter,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 1, pp. 174-190, Jan. 2006: Quaternion Refinement #3.
[130] Choukroun, D., Weiss, H., Bar-Itzhack, I. Y., Oshman, “Direction Cosine Matrix Estimation From Vector Observations Using A Matrix Kalman Filter,” Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, TX, pp. 1-11, 11-14 August 2003: DCM Refinement #3 
[131] Choukroun, D., “Ito Stochastic Modeling for Attitude Quarternion Filtering,”
Proceedings of Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, P. R. China, pp. 733-738, 16-18 Dec. 2009: Quaternion Refinement #4.

In the above,  DCM = Direction Cosine Matrix; and for the Quaterion Matrices, the quaterions are to be normalized. One can convert from quaternions to DCM and vice versa. For the Matrix KF material, above, a major contributor was Daniel Choukroun, B. S. (Summa cum Laude), M.S., Ph.D. (1997, 2000, 2003), post-doc (UCLA), currently an Assistant Professor at Delft University of Technology, Netherlands.

In Thomas H. Kerr III's humble opinion, Angle Only Tracking (AOT) can also be accommodated within the above structure by updating from two (or more) different time-synchronized (via sorted time-tags) noncolocated sensors (with lever arms appropriately accounted for) simultaneously (thus used as a matrix measurement). The optimal estimator retains a linear syructure and is finite dimensional. This is the benefit of this novel approach. 
NASA updates in Spaceborne estimation for attitude determination:
[132] Cheng, Y., Landis Markley, F., Crassidis, J. L. Oshman, Y., “Averaging Quaternions,” Advances in the Astronautical Sciences series, Vol. 127, American Astronautical Society, AAS paper No. 07-213, 2007: Will eventually Summarize!
[133] Landis Markley, F., “Attitude Filtering on SO(3),” Advances in the Astronautical Sciences series, Vol. 122, American Astronautical Society, AAS paper No. 06-460, 2006: Will eventually Summarize!
[134] Cheng, Y., Crassidis, J. L., and Landis Markley, F., “Attitude Estimation for Large Field-of-View Sensors,” Advances in the Astronautical Sciences series, Vol. 122, American Astronautical Society, AAS paper No. 06-462, 2006: Will eventually Summarize!
[135] Landis Markley, F., “Attitude Estimation or Quaternion Estimation?,” Advances in the Astronautical Sciences series, Vol. 115, American Astronautical Society, AAS paper No. 03-264, 2003: Critical and thorough Analysis of 3 different EKF’s vs. Technion MKF. MKF was ultimately improved by this investigation.
[136] Reynolds, R., Landis Markley, F., Crassidis, J. L., “Asymptotically Optimal Attitude and Rate Bias Estimation with Guaranteed Convergence,” Advances in the Astronautical Sciences series, Vol. 132, American Astronautical Society, AAS paper No. 08-286, 2008: Will eventually Summarize!
Estimation Results for Bilinear Systems (to tie into the MKF results above):
[137] Halawani, T. U., Mohler, R. R., and Kolodziej, W. J., “A two-step bilinear filtering algorithm,” IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 32, 344-352, 1984: Will eventually Summarize! 
[138] Glielmo, L., Marino, P., Setola, R., Vasca, F., “Parallel Kalman Filter Algorithm for State Estimation in Bilinear Systems,” Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL, pp. 1228-1229, Dec. 1994: Will eventually Summarize!
[139] Wang, Z., Qiao, H., “Robust Filtering for Bilinear Uncertain Stochastic Discrete-Time Systems,” IEEE Trans. on Signal Processing, Vol. 50, No. 3, pp. 560-567, Mar. 2002: In general, “Robust” approaches usually have a sluggish response time.
[140]] Lopes dos Santos, P., Ramos, J. A., Frias, R., “Derivation of a Bilinear Kalman Filter with Autocorrelated Inputs,” Proceedings of the 46th Conference on Decision and Control, New Orleans, LA, pp, 6196-6202, 12-14 Dec. 2007: Structure similar to what above Technion MKF exhibits.

While linear systems are very tractable, general nonlinear systems are less so. Bilinear systems are close to being linear systems and so are somewhat more tractable, and likewise for their associated Optimal estimators.
Prof. Roger W. Brockett (Harvard-Emeritus) discusses how to handle bilinear systems in:
[141] Brockett, R. W., "Finite Dimensional Linear Systems," SIAM Classics in Applied Mathematics, 2015 (original in 1970).

We can provide 17 more examples of practical estimators for bilinear systems, as have been reported in the technical literature by others over the last 40+ years, (some involving Lie Algebras and Lie Brackets such as those provided by A. S. Willsky and J. T.-H. Lo for SO(2) and by many others later).


[143] S. Blackman and R. Popoli, Design and Analysis of Modern Tracking Systems, Artech House, Boston, MA, 1999.

[144] B. D. Tapley, M. M. Watkins, J. C. Ries, G. W. Davis, R. J. Eanes, S. R. Poole, H. J. Rim, B. E. Schutz, and C. K. Shum, “The joint gravity model 3,” Journal of Geophysical Research, Vol. 101, No. B12, pp. 28 029–28 049, Dec. 1996.

[145] N. Bergman, “Recursive Bayesian estimation: Navigation and tracking applications,” Ph.D. dissertation, Linkoping University, SE-581 83 Linkoping, Sweden, April 1999.

[146] N. Bergman, Sequential Monte Carlo Methods in Practice, New York: Springer, New York, 2001 (Chapter: Posterior Cramér-Rao Bounds for Sequential Estimation, pp. 321–338).

[147] Vytas B. Gylys, Kalman Filters and Nonlinear Filters, Texas Instruments Inc.

[148] Wasim Huleihel, Joseph Tabrikian, and Reuven Shavit, “Optimal Adaptive Waveform Design for Cognitive MIMO Radar,”
IEEE Transactions on Signal Processing, Vol., 61, No. 20, pp. 5075-, Oct. 2013. [Assumes fixed, known target range and Doppler information and only in the conclusion do they sketch how it may, perhaps, be successfully extended to a more realistic situation where the target is actually moving with respect to the radar. Did anyone actually follow-up to see whether it actually resolves as they speculated? No wonder Dr. Eli Brookner is “up in arms” about MIMO practitioners either doing what can already be done conventionally or about overstepping or overstating what MIMO can actually do! Perhaps benefits of MIMO in communications applications are better justified.]

[149] M. Morf, J.R. Dobbins, B. Friedlander, T. Kailath, “Square-root algorithms for parallel processing in optimal estimation,” Automatica, Vol. 15, No. 3, pp. 299-306, 1979.

[150] H. H. Afshari, S. A. Gadsden, S. Habbi, “Gaussian Filters for parameter and state estimation: a general review of the theory and recent trends,” Signal Processing, Vol. 135, pp. 218-238, 2017.

[151] http://www.gallup.unm.edu/~smarandache/NATOASI_ATJDTSPK.pdf 

[152] F. Landis Markley, John L. Crassidis, Yang Cheng, “Nonlinear Attitude Filtering Methods,” American Institute of Aeronautics and Astronautics, pp. 1-32,  2007. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050212421.pdf    Landis.Markley@nasa.gov   AIAA Fellow
I. Introduction (from the above [152], and copied verbatim, as follows next)
The extended Kalman (EKF) is the workhorse of real-time spacecraft attitude estimation. Since the group SO(3) of rotation matrices has dimension three, most attitude determination EKFs use lower-dimensional attitude parameterizations than the nine-parameter attitude matrix itself. The fact that all three-parameter representations of SO(3) are singular or discontinuous for certain attitudes has led to extended discussions of constraints and attitude representations in EKF & 719-11 These issues are now well understood, however, and the EKF, especially in the form known as the multiplicative extended Kalman filter5-7 (MEKF), has performed admirably in the vast majority of attitude determination applications. Nevertheless, poor performance or even divergence arising from the linearization implicit in the EKF has led to the development of other filters. Several of these approaches retain the basic structure of the EKF, such as additive EKF a backwards-smoothing EKF,l8 and deterministic EKF-like estimators. ”-” In particular, the backwards-smoothing EKF solves a nonlinear smoothing problem for the current and past sample intervals using iterative numerical techniques. The numerical iteration retains all of the nonlinearities of a fixed number of stages that precede the terminal stage of interest, and it processes information from earlier stages in an approximate manner. l5 Deterministic EKF-like estimators are closely related to H_infinity control design.” Usually an upper bound is derived first, and then the bound is minimized based on approaches such as Riccati equations and linear matrix inequalities. The nonlinear problem is much more difficult; which requires the solution of the Hamilton-Jacobi-Isaacs partial differential inequality. For attitude estimation, small-error approximations are used to developed a filter. 19i20 Other designs use various assumptions to derive simplified filters. These generally provide suboptimal performance characteristics in relation to the EKF, but involve linear or pseudo-linear equations that are used to estimate the states of a nonlinear dynamical system. Therefore, linear design and analysis tools can be used to construct the filter and to assess its overall performance. Some of these use a deterministic solution of the attitude] e.g. methods that are based on the QUEST attitude determination solution.23 Simple filter designs based on QUEST include filter QUEST24 and recursive QUEST.25 A more complicated but far more robust approach] called extended uses a full nonlinear propagation along with a novel measurement update. This approach can be used to estimate attitude and additional parameters as well. Interlaced filters that replace a nonlinear filter with two or more linear filters have been used for rate estimation] but not for attitude e~timation.~~-~’ Several new alternatives to the standard EKF have been recently introduced] such as sigma point or unscented filter^^'-^^ and particle filter^.^^-^^ Unscented filters (UFs) have been shown to exhibit several advantages over the EKF, including: 1) the expected error is lower than the EKF, 2) they can be applied to non-differentiable functions, 3) no Jacobian matrix calculations are required] and 4) they provide higher- order expansions than the standard EKF. Unscented filters work on the premise that with a fixed number of parameters it should be easier to approximate a Gaussian distribution than to approximate an arbitrary nonlinear function. They typically use the standard Kalman form in the post-update, but use a different propagation of the covariance and pre-measurement update with no local iterations. The attitude estimation UF derived in Ref. 33 is based on a quaternion representation of the attitude kinematics. However, straightforward implementation of the standard UF equations derives a predicted quaternion mean from an averaged sum of quaternions. Therefore, no guarantees can be made that the resulting quaternion will have unit norm. This was overcome by using a generalized unconstrained three-component vector to represent the attitude error-quaternion] leading to an unconstrained formulation in the UF design. Unscented filters are essentially based on second or higher order approximations of nonlinear functions, which are used to estimate the mean and covariance of the state vector. Though the mean and covariance are the sufficient statistics of a Gaussian distribution, they are not sufficient to represent a general probability distribution. When UF methods are applied to strongly nonlinear and non-Gaussian estimation problems] where the a posteriori distribution of the state vector may be multi-peaked, heavily-tailed, or skewed, desired performance characteristics may not be obtained. This may be overcome by using particle filter^^^-^^ (PFs). Like other approximate approaches to optimal filtering] the ultimate objective of PFs is to construct the a posteriori probability density function (PDF) of the state vector, or the PDF of the state vector conditional on all the available measurements. However, the approximation of PFs is vastly different from that of conventional nonlinear filters. The central idea of a PF approximation is to represent a continuous distribution of interest by a finite (but large) number of weighted random samples of the state vector, or particles. A PF does not assume the a posteriori distribution of the state vector to be a Gaussian distribution or any other distribution of known form. In principle,it can estimate probability distributions of arbitrary form and solve any nonlinear and/or non-Gaussian system. Reference 36 presents a PF for attitude estimation based on the bootstrap filter.35 The optimal solution of the nonlinear estimation problem requires the propagation of the conditional PDF of the state given the observation history.37 All practical nonlinear filters are approximations to this ideal. Exact finite dimensional filters38 can be found that solve some nonlinear problems by using the Fokker-Planck equation2l3’ to propagate a non-Gaussian PDF between measurements and Bayes’ formula‘? to incorporate measurement information. A recently proposed filter4’ follows this pattern, but does not solve the nonlinear attitude filtering problem exactly. We refer to it as an orthogonal filter, because it represents the attitude by an orthogonal rotation matrix, rather than by some parameterization of the rotation matrix. The PDF is a non-Gaussian function defined on the Cartesian product of S0(3), the group of rotation matrices, and the Euclidean space Rn of bias parameters. This filter entirely avoids questions about singularities of representations or covariance matrices arising in EKFS~-~~ and UFS,~~ and has the additional advantage of providing a consistent initialization for a completely unknown initial attitude, owing to the fact that SO(3) is a compact space. Nonlinear observers often exhibit global convergence, which is to say that they can converge from any initial guess.41 Several applications of observers for attitude control have been proposed Refs. 42-48. A nonlinear observer and controller using only measurements of roll, pitch and yaw has been developed in Ref. 43. Local asymptotic stability is ensured under mild hypotheses. A globally convergent, nonlinear full- order observer using quaternions and Euler’s equations for the dynamics has been derived in Ref. 44. The observer structure contains a discontinuous term, which is often associated with “sliding mode” observers. The error-quaternion is defined using a multiplicative approach and stability is proven using a Lyapunov function. A simpler, robust smoothed sliding mode observer that avoids quaternion error differentiation noise and eliminates the necessity of measuring angular rate is derived in Ref. 45. Although an additive approach is used to define the quaternion error, global stability is still provided through a Lyapunov function. Algrain and Lee develop a nonlinear observer to estimate angular rates along the third axis of a spinning spacecraft using only two-axis measurement^.^^ A pseudo-linear model is developed by decomposing the nonlinear system into linear and nonlinear parts. BoSkoviC, Li and Mehra use angular rate measurements with quaternion kinematics to derive a nonlinear bias observer, which is coupled with an adaptive sliding mode ~ontroller.~~ Stability is proven as long as the attitude never passes through f180 rotations. Thienel and Sanner develop an exponentially convergent nonlinear observer given a constant gyro bias with identification of the bias proven through a persistency of excitation argument.48 An analysis is also shown that includes gyro noise. Adaptive approaches generally fall into two categories. One category encompasses approaches that adap- tively tune the Kalman filter through the identification of either the process noise covariance or measurement noise covariance, or both simultaneously. In practice “tuning” a Kalman filter can be arduous and very time- consuming. Usually, the measurement-error covariance is fairly well known, derived from statistical inferences of the hardware sensing device. However, the process noise covariance is usually not well known and is of- ten derived from experiences gained by the design engineer based on intimate knowledge of the particular system. The approach is based on “residual whitening.” 49 Unfortunately, most noise adaptive techniques are applicable only for linear systems,’ which creates problems for attitude estimation due to the nonlinear equations involved. Still, it is possible to use these techniques with linearized equations, as demonstrated in Ref. 50. Lam and Wu further develop adaptive filters that address both colored and white noise ~tatistics.~~ The former noise is identified using a non-parametric neural network approach, while the latter noise is identified using an a-P filter. An adaptive filter is also proposed in Ref. 17 to account for inaccuracy in the knowledge of the process noise statistical model, which uses a linear pseudo-measurement model. Other adaptive approaches use adaptive methods for fault tolerant estimation 53 The other category includes approaches that adaptively estimate unknown system parameters, such as the inertia matrix. These generally fall into two basic categories: 1) parameter estimation or filter-based methods, and 2) nonlinear adaptive techniques. Least squares methods to determine the inertia matrix and other constant parameters, such as disturbance model parameters and biases, are shown in Refs. 54-56. A disturbance accommodation technique that models the unknown disturbance angular rate using a power set of time as basis functions is shown in Ref. 57. Nonlinear adaptive techniques are similar to nonlinear observers in that they usually provide global stability proofs that guarantee convergence of the estimated parameter^.^^-^' This paper will review the basic assumptions of these filters, presenting enough mathematical detail to give a general orientation. First, reviews of the quaternion parameterization and gyro model equations are given. Then, attitude estimation methods based on the EKF are shown, followed by QUEST-based approaches. Next, the two-step estimator is shown. The UF and PF approaches are then shown, followed by the orthogonal filter. Then, the predictive filter, as well as nonlinear observers and adaptive approaches are reviewed. The paper concludes with a discussion of the strengths and weaknesses of the various filters. (Thomas H. Kerr comment: Also see item [168] below for a 1971 precedent for handling estimation on a circle, SO(2),  and on a sphere, SO(3).)

Other topics that I routinely follow:

[153] Niu, X., Nassar, S., El-Sheimy, N., “An Accurate Land-Vehicle MEMS IMU/GPS Navigation System Using 2D Auxiliary Velocity Updates,” Navigation: Journal of the Institute of Navigation, Vol. 54, No. 3, pp. 177-188, Fall 2007.

[154] Soloviev, A., van Graas, F., “Batch-Processing of Inertial Measurements for Mitigation of Sculling and Commutation Errors,” Navigation: Journal of the Institute of Navigation, Vol. 54, No. 4, pp. 265-276, Winter 2007.

[155] Soloviev, A., van Graas, F., “Enhancement of Integrated GPS/INS Performance Utilizing Frequency Domain Implementation of INS Calibration,” Navigation: Journal of the Institute of Navigation, Vol. 54, No. 2, pp. 87-98, Summer 2007.

[156] Lee, Y. C., “Two New RAIM Methods Based on the Optimally Weighted Average Solution (OWAS) Concept,” Navigation: Journal of the Institute of Navigation, Vol. 54, No. 4, ff. 333, Winter 2007.

[157] Farrell, J. L., “Inertial Instrument Error Characterization,” Navigation: Journal of the Institute of Navigation, Vol. 54, No. 3, pp. 169-176, Fall 2007.

[158] Farrell, J. L., “Full Integrity Testing for GPS/INS,” Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 33-40, Spring 2006.

[159] Milbert, D., “Dilution of Precision Revisited,” Navigation: Journal of the Institute of Navigation, Vol. 55, No. 1, pp. 67-81, Spring 2008.

[160] Pulford, G. W., “A Proof of the Spherically Symmetric Overbounding Theorem for Linear Systems,” Navigation: Journal of the Institute of Navigation, Vol. 55, No. 4, pp. 283-292, Winter 2008.

[161] Li, Y., Rizos, C., Wang, J., Mumford, P., Ding, W., “Sigma-Point Kalman Filtering for Tightly Coupled GPS/INS Integration,” Navigation: Journal of the Institute of Navigation, Vol. 55, No. 3, pp. 167-177, Fall 2008.

[162] “Algorithm Aligns Gyrocompass in Twisting and Swaying Vehicle,” NASA Tech Briefs MFS-28671, George C. Marshall Space Flight Center, Alabama 35812, Gyrocompass FDR Version 6.0.6/MO (from Specification CP-830100A, Appendix 1, Rev. A, 28 July 1989 for TOS on Titan), pp. 1-87, 18 June 1991.

[163] Shively, C. A., Hsio, T. T., “Error and Availability Analysis of CAT IIIb LAAS Augmented by Radar Altimetry,” Navigation: Journal of the Institute of Navigation, Vol. 52, No. 3, pp. 155-162, Fall 2005.

[164] Mason, J., “Algebraic Two-Satellite TOA/FOA Position Solution on an Ellipsoidal Earth,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 40, No. 7, pp. 1087-1092, July 2004. 

[165] Mason, J., Romero, L., “TOA/FOA Geolocation Solutions Using Multivariate Resultants,” Navigation: Journal of the Institute of Navigation, Vol. 52, No. 3, pp. 163-177, Fall 2005.

[166] Jekeli, C., “Navigation Error Analysis of Atom Interferometer Inertial Sensing,” Navigation: Journal of the Institute of Navigation, Vol. 52, No. 1, pp. 1-14, Spring 2005.

[167] Ristic, B., Arulampalam, S., Gordon, N., Beyond the Kalman Filter: Particle Filters for Tracking Applications, Artech House, Boston, MA, 2004. [One of the clearest discussions of both historical and recent estimation algorithms (including EKF, UKF, MMM, IMM, and Particle Filters), their underlying assumptions/mechanization equations and that also provides extremely useful insight into important aspects and distinctions in their implementations is offered in Chapters 1-3.]

[168] Li, J. T.-H. Lo and A. S. Willsky, “Estimation for Rotational Processes with One Degree of Freedom-Part 1,” IEEE Trans. on  Automatic Control, Vol. 20, No. 1, pp. 10-21, Feb. 1975. [They explicitly handle estimation on a circle, SO(2), rather than estimation on a sphere, SO(3), as NASA's F. Landis Markley, et al deal with above in their extensive survey and comparison between approaches and techniques in [152]. However, Willsky and Lo are particularly lucid in their development and exposition and, moreover, within the last sentence of their conclusion, provide specifics of their suggested generalization to estimation results on arbitrary Abelian Lie groups, such as SO(3).] 5_pub_IEEE.pdf  

[169] Lo, J. T.-H. and Willsky, A. S., “Stochastic Control of Rotational Processes with One Degree of Freedom,” SIAM Journal on Control, Vol. 13, No. 4, 886ff, July 1975.

[170] Patrick K. Simpson (Ed.), Neural Networks Theory, Technology, and Applications, Selected Conference Papers, IEEE Technology Update Series, NY, 1996.

[171] Jekeli, C., Inertial Navigation Systems with Geodetic Applications, Walter deGruyter GmbH \& Co. KG, Berlin, Ger., 2001.

For the following navigation textbooks:
[172] Rogers, R. M., Applied Mathematics in Integrated Navigation Systems, AIAA Education Series, AIAA, pp. 99-108, Reston, VA., 2000.
[173] Titterton, D. H., and J.L. Weston, Strapdown Inertial Navigation Technology, Peter Peregrinus Ltd., Stevenage, Herts, England, UK, 2004.
[174 ] Farrell, J. A., Aided Navigation: GPS with High Rate Sensors, McGraw-Hill, NY, 2008 (very well written but uses lower case Greek epsilon in a role that was NOT gyro drift-rates, contrary to the standard convention of the last 3 decades)
all three of these textbooks are not totally self-contained but, instead, defer to the following textbook at  exactly the same point in their discussions for completion of the proper handling of components of gyro drift-rate to be used in mathematical model to be eventually used in the corresponding navigation Kalman filter, as discussed in detail in:
[175] Kenneth R. Britting, Inertial Navigation Systems Analysis, Wiley-Interscience, NY, 1971. [Surprisingly, a new edition of this book and its 2010 sequel are now available from Artech, Boston, MA. The reason that it is surprising to me is that Kenneth R. Britting died from M.S. in the 1980's while he was with Nortronics at Northrop in Norwood, MA. A burning question is whether Fred J. Marcus is helping Kenneth R. Britting to publish from the grave AGAIN?]

[176] Chatfield, A. B. (Ed.), Fundamentals of High Accuracy Inertial Navigation, Paul Zarchan, Editor-in-Chief, AIAA Progress in Astronautics and Aeronautics Series, AIAA, 1997.

[177] Savage, P. G., “Strapdown Sculling Algorithm Design for Sensor Dynamic Amplitude and Phase-Shift Error,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 35, No. 6, pp. 1718-1729, Nov.-Dec. 2012.

[178] Jaewon Seo, Jang Gyu Lee, Chan Gook Park, “A New Error Compensation Scheme for INS Vertical Channel,” IFAC Proceedings, Vol. 37, No. 6, pp. 1119-1124, 2004.

[179] Viterbi algorithm being equivalent to Dynamic Programming: https://scholar.google.com/scholar?q=viterbi+algorithm+dynamic+programming&hl=en&as_sdt=0&as_vis=1&oi=scholart&sa=X&ved=0ahUKEwiwhOicsejaAhVGc98KHScLD1UQgQMIJTAA 

[180] Uwe D. Hanbeck, “Recursive Nonlinear Set-Theoretic Estimation Based on Pseudo-Ellipsoids,” Proceedings of the IEEE Conference on Multisensor Fusion and Integration for Intelligent Systems, pp. 159–164 (MFI2001), Baden–Baden
Their patent abandoned by Siemens AG (perhaps because of prior art: me): https://patents.google.com/patent/US20060234722A1/en 

[181] Fuqiang You, Hualu Zhang, Fuli Wang, “A new set-membership estimation method based on zonotopes and ellipsoids,” Transactions of the Institute of Measurement and Control, Vol. 40, issue 7, pp. 2091-2099, Article first published online: 27 July 2016; Issue published: 1 April 2018

[182] Grocholsky B., Stump E., Shiroma P.M., Kumar V., “Control for Localization of Targets Using Range-Only Sensors,” in Khatib, O., Kumar, V., Rus, D. (eds), Experimental Robotics, Springer Tracts in Advanced Robotics Series, Vol 39. Springer, Berlin, Heidelberg, pp. 191-200, 2008. 

[183] Ashok K. Rao, Yih-Fang Huang,  and Soura Dasgupta, “ARMA Parameter Estimation Using a Novel Recursive Estimation Algorithm with Selective Updating,” IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 38, No. 3, Mar. 1990.

[184] Set Estimation: https://en.wikipedia.org/wiki/Set_estimation 

[185] Donald Cooke, Fun with GPS, ESRI Press, 380 New York St., Redlands, CA, 2005.

[186] Quantum Navigation using magnetic sensing of gravity anomalies to match known maps of such: https://www.wired.com/story/quantum-physicists-found-a-new-safer-way-to-navigate/  

[187] Walking Robot uses the sun to navigate (and nothing else): https://gizmodo.com/this-walking-robot-navigates-using-the-sun-no-gps-requ-1832599931 

[188] Jeffrey E. Hilland, F. B. Stuhr, A. Freeman, D. Imel, R. L. Jordan, E. R. Caro, “Future NASA Spaceborne SAR Missions,” Systems Magazine, IEEE Aerospace and Electronic Systems, Vol. 13, No. 11, pp. 9-16, Nov. 1998.

[189] Yaakov Bar-Shalom, and Xiao-Rong Li, “Multitarget-Multisensor Tracking: Principles and Techniques,”
Systems Magazine, IEEE Aerospace and Electronic Systems, Vol. 11, No. 2, pp. 41-44, Feb. 1996.

[190] B. Wu, P. Nicolaides, and T.N. Upadhyay,T.R. Jenkins, IONOSPHERIC ERROR COMPENSATION FOR GPS RECEIVERS USING REAL-TIME IONOSPHERIC MODEL,” Proceedings of the 9th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1996), Kansas City, MO, pp. 575-583,

[191] Grewal, M. S., Weill, L. R., and Andrews, A. P., Global Positioning Systems, Inertial Navigation and Integration, John Wiley & Sons, Hoboken, NJ, 2007.

[192] Abbott, A. S., Lillo, W. E., Global Positioning Systems and Inertial Measuring Unit Ultratight Coupling Method, U. S. Patent 6,516,021, 4 Feb. 2003.

[193] Kushner, H. J., Budhiraja, A. S., "A Nonlinear Filtering Algorithm Based on an Approximation of the Conditional Distribution," IEEE Trans. on Automatic Control, Vol. 45, No. 3, pp. 580-585, Mar. 2000.

[194] Landis, D., Thorvaldsen, T., Fink, B., Sherman, P., and Holmes, S., "A Deep Integration Estimator for Urban Ground Navigation," Proc. of IEEE PLANS Conference, San Diego, 25-27 Apr. 2006.

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[196] Nunes, F., Sousa, F., and Leitao, J., "Innovations-Based Code Discriminator for GPS/Galileo BOC Signals," IEEE Vehicular Technology Conference, pp. 4127-4131, Sept. 2004.

[197] Li, Y., Rizos, C., Wang, J., Mumford, P., and Ding, "Sigma-Point Kalman Filtering for Tightly Coupled GPS/INS Integration," Navigation, Journal of ION, Vol. 55, No. 3, Fall 2008.

[198] Yannis A. Phillis and Vassilis S. Kouikoglou, "Algorithms for System Minimax Estimation and Control with Multiplicative Noise of Multiplicative System," Control and Dynamic Systems, Vol. 31: Advances in Aerospace Systems, Part 1, edited by C.T. Leonides, pp. 93-124, 2012.

[199] Weiwei Li, Emanuel Todorov, and Robert E. Skelton, "Estimation and Control of Systems with Multiplicative Noise via Linear Matrix Inequalities," Proceedings of the American Control Conference, Portland, OR, pp. 1811-1816, 8-10 June, 2005.
Abstract: This paper provides estimation and control design methods for linear discrete-time systems with multiplicative noise. First, we present the design of the state feedback controller, such that the closed loop system is mean square stable. Second, we provide sufficient conditions for the existence of the state estimator; these conditions are expressed in terms of linear matrix inequalities (LMIs), and the parametrization of all admissible solutions is addressed. Finally, an estimator design approach is formulated using LMS, and the performance of the estimator is examined by means of numerical examples.

[200] Owen, A.B., Empirical Likelihood, CRC Press, 2001. (QA 276.8.094, Hayden, MIT).

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[202] Tam, P. K. S., and Moore, J. B., "A Gaussian Sum Approach to Phase and Frequency Estimation,"
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Abstract: In this paper, a theory of optimal nonlinear estimation from sampled data signals where the a posteriori probability densities are approximated by Gaussian sums is adapted for application to phase and frequency estimation in high noise. The nonlinear estimators (demodulators) require parallel processing of the received signal. In the limit as the number of parallel processors becomes infinite the FM demodulators become optimum in a minimum mean square error sense and the PM demodulators become optimum in some well defined sense. For the clearly sub-optimal case of one processor, the demodulators can be readily simplified to the familiar phase-locked loop. On the other hand, for the intermediate case, significant extension of the phase-locked loop threshold is achieved where (say) six parallel processors are involved. 

[203] Raytheon-UTC merger wins approval, pending divestitures:
The Biggest Defense Merger Ever Gets Key Antitrust Approval — With These Conditions:
US Coast Guard protests GPS disruption to UN body: ‘urgent issue’ - GPS World | RNTF:

[204] GPS/JTIDS/INS Integration Study-Final Report, Vol. II of IV, Details, Technical Report Report R-1151, The Charles Stark Draper Laboratory, Inc., Cambridge, MA, Oct. 1977 to June 1978.

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[219] Hurras, K., Winter, H., "Gyro Accuracy Requirements in a Strap-Down INS with GPS Aiding for RPV Missions,"

[220] R. Baldassini Fontana, "Strapped Down Inertial Guidance System Study," AGARD-CP-116, Proceedings of Guidance and Control Panel of AGARD, held in Florence, Italy, 2-5 Oct. 1972.

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[272] Bell, C. M., and Babitch, D., "A Systems Analysis of the Cesium Beam Atomic Clock," IEEE Trans. on Instrumentationand Measurement, Vol. 17, No. 2, pp. 155-166, June 1968.

[273] Wrigley, W., Woodbury, R. B., Hovorka, J., Inertial Guidance, Institute of Aeronautical Science, N. Y. Jan. 1957.

[274] Naval Workshop in Differential Games, Office of Naval Research, 31 July - 3 Aug. 1973. 

[275] Gelb, A., and Palosky, P., "Generating Discrete Colored Noise from Discrete White Noise," IEEE Trans. on Automatic Control, Vol. 11, No. 1, pp. 148-149, Jan. 1966.

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[277] Cruz, Jr., J. B., "Stackelberg Strategies for Multilevel Systems," 

[278] Shapiro, J. F., A Survey of Lagrangian Techniques for Discrete Optimization, Technical Report No. 133, Operations Research Center, MIT, May 1977.

[279] Ho, Y. C., The First International Conference on the Theory and Applications of Differential Games, Division of Engineering and Applied Physics, Harvard University, Cambridge, MA, Final Report to Air Force Office of Scientific Research, Jan. 1970.

[280] Chu, K.-C., Team Decision Theory and Information Structures in Optimal Control Problems, Technical Report No. 622, Division of Engineering and Applied Physics, Harvard University, Cambridge, MA, Aug. 1971.

[281] Goshen-Meskin, D., Bar-Itzhack, I. Y., "On the connection between Estimability and Observability," IEEE Trans. on Automatic Control, Vol. 37, No. 8, pp. 1225ff, August 1992.

[282] Bar-Itzhack, I. Y., Harman, R. R., "The MAP Spacecraft Angular State Estimation After Sensor Failure," https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20030020821.pdf

[283] Bar-Itzhack, I. Y., “New Method for Extracting the Quaternion from a Rotation Matrix”, AIAA Jour. of Guidance, Control, and Dynamics, Vol. 23, No. 6, pp. 1085-1087, Nov.-Dec. 2000.

[284] Azor, A., I. Y. Bar-Itzhack, J. Deutschmann and R. R. Harman, “Angular-Rate Estimation Using Delayed Quaternion Measurements”, AIAA J. of Guidance, Control, and Dynamics, AIAA J. of Guidance, Control, and Dynamics, Vol. 24, No. 3, pp. 436-443, May-Jun. 2001.

[285] Bar-Itzhack, I. Y., “Classification of Algorithms for Angular Velocity Estimation”, AIAA J. of Guidance, Control, and Dynamics, Vol. 24, No. 2, pp. 214-218, Mar.-Apr. 2001.

[286] Harman, R. R. and Bar-Itzhack, I. Y., “Pseudolinear and State-Dependent Riccati Equation Filters for Angular Rate Estimation”, AIAA J. of Guidance, Control, and Dynamics, Vol. 22, No. 5, pp. 723-725, Sept.-Oct. 1999.

[287] Olson, D. K., "Converting Earth-Centered, Earth-Fixed Coordinates to Geodetic Coordinates," IEEE Trans. on Aerospace and Electronic Systems, Vol. 32, No. 1, pp. 473-476, Jan. 1996.

[288] Chung, D, Lee, J. G., Park, C. G., Park, H. W., "Strapdown INS Error Model for Multiposition Alignment," IEEE Trans. on Aerospace and Electronic Systems, Vol. 32, No. 4, pp. 1362-1366, Oct. 1996. 

[289] James L. Melsa, Computational Programs for Computational Assistance in the Study of Linear Control Theory, McGraw-Hill, NY, 1970.

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[291] How to Combine Oversampling and Undersampling for Imbalanced Classification:

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[293] Marvin May, "MK 2 MOD 6 SINS History," The Quarterly Newsletter of The Institute of Navigation, Vol. 14, No. 3, p. 8, Fall 2004.

[294] Mahmood R. Azimi-Sadjadi, Tongxin Lu, Eduardo M. Nebot, "Parallel and Sequential Block Kalman Filtering and Their Implementations Using Systolic Arrays." IEEE Trans.
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[299] Gustaf Hendeby, Performance and Implementation Aspects of Nonlinear Filtering, Linköping studies in science and technology. Dissertation. No. 1161, Department of Electrical Engineering Linköping University, SE–581 83 Linköping, Sweden Linköping 2008.

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[301] William S. Widnall, Stability of Alternate Designs for Rate-Aiding of Non-Coherent Mode of a GPS Receiver, Intermetrics Report No. IR-302, 25 Sept. 1978.

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USS Cobra Judy Radar Ship is the sister ship of the U.S.S. Compass Island. The Compass Island had been used in the early and mid 1970s as a test suite for demonstration and shake down of SSBN Navigation changes and upgrades before deploying within the submarine fleet. Both sister ships had little lateral fins on the bottom of the hull below the water line that could be extended out horizontally from the hull to stabilize the platform in rough seas (of a high sea state). A complete SSBN Navigation Room was present on the Compass Island, but intentionally installed backwards from its orientation aboard SSBNs. A prior NASA observation ship, the U.S.S. Vangard, replaced the Compass Island in this role in the late 1970s.

Pre- (and post-)GPS Relative Navigation (RelNav) enabled networks of different platforms to reference both friendlies and enemy targets with respect to a single common (virtual) grid using the L-band JTIDS (time-slotted and frequency hopped from 960 MHz to 1215 MHz, with gaps imposed for TACAN and IFFN). This capability was especially useful when all participants were at sea and far from any geographic landmarks of absolute location. The grid tended to move and rotate slightly. Its location was dictated by the Navigation Controller (NC), the platform having the best navigation accuracy (as a self-assessment), but in lieu of the demise of the original NC, the NC was replaced by the next best platform in this role to avoid possessing a single point vulnerability. JTRS (pronounced Jitters) is slated to replace JTIDS as an entirely software radio system (with its own unique set of problems yet to be solved). JTIDS included NTDS/ATDS. Air Force JTIDS used DTDMA protocol without RelNav. Navy version was TDMA with RelNav. Marine version of JTIDS was PLRS. Reed Solomon Code throughout. GPS uses Gold Code in two flavors or cycle lengths (to be upgraded).

Hybrid High-Rate Output Candidate Design for JTIDS/GPS/INS Integration and INS Navaid Selection.

Sam Blackman (Raytheon/Hughes), the (late) Oliver Drummond, Yaakov Bar-Shalom (UCONN), and Rabinder Madan.


Blazers of the exciting area of multi-sensor\multi-target tracking (sometimes pursued even in clutter) [related to optimal resource allocation and solved by invoking Munkres or the Hungarian or Jonker- Volgenent- Castanons (J-V-C) or Murtys (1968) or Sam Blackman's Multi- Hypothesis Testing (MHT) algorithms. The first 3 techniques are all from the Operations Research area; the last is based on Bayesian Statistical analysis.

Not shown here: Prof. David Castanon (Boston University) and Charles Morefield (originally of Aerospace Corporation in the 1970s when he posed multi-target tracking as a 0-1 Integer Programming Problem, more recently Chairman of the Board at Alphatech (after Michael Athans stepped down and went to Portugal) before Alphatech became part of BAE in Burlington, MA), and Thomas Kurien (Raytheon). Also see Particle Filter variations in: Vermaak, J., Godsill, S. J., Perez, P., Monte-Carlo Filtering for Multi-Target Tracking and Data Association, IEEE Trans. on Aerospace and Electronic Systems, Vol. 41, No. 1, pp. 309-331, Jan. 2005. Also see Miller, M. L., Stone, H, S., Cox, I. J., Optimizing Murtys Ranked Assignment Method, IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 7, pp. 851-862, July 1997. Another: Frankel, L., and Feder, M., Recursive Expectation-Maximizing (EM) Algorithms for Time-Varying Parameters with Applications to Multi-target Tracking, IEEE Trans. on Signal Processing, Vol. 47, No. 2, pp. 306-320, February 1999. Yet another: Buzzi, S., Lops, M., Venturino, L., Ferri, M., Track-before-Detect Procedures in a Multi-Target Environment, IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 1135-1150, July 2008.

Fourth ONR/GTRI Workshop on Target Tracking and Sensor Fusion, Naval Postgraduate School, Monterey, CA, 17 May 2001.Notice the guy (i.e., THK III) apparently in sun glasses (actually transitions) in the back row there (left of center, as always).

Lockheed Martins Paveway II Dual Mode Laser-Guided Bomb (DMLGB), which uses both laser-guided and inertial/GPS guidance, has achieved the U.S. Navy's initial operational capability and is now preparing for operational employment.


The DMLGB is designed to execute precision strike missions against stationary and mobile targets in all stationary and mobile targets in all weather conditions, according to Lockheed. The kits can operate in laser only, inertial/GPS, or dual-mode to provide pilots with flexibility to engage various types of targets in a single mission, says Lockheed Martin.

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Extra! Extra! Read all about it!

JAVAD GNSS has announced that its customers with JAVAD GNSS triple-frequency type OEM boards (TR-G2T, TR-G3T, TRE-G2T, TRE-G3T, TRE-G3TAJ) and receivers (TRIUMPH-1, Alpha TR-G2T/TR-G3T, DeltaS TRE-G2T/TRE-G3T/TRE-G3TAJ, SigmaS TRE-G2T/TRE-G3T/TRE-G3TAJ) can now track the L5 demonstration signal.

The first GPS satellite with the L5 signal [Block IIR-20(M)] was successfully launched on 24 March 2009 and its L5 = 1176.45 MHz payload activated on 10 April 2009.

The signal characteristics clearly indicate that JAVAD GNSS receivers allow high-quality code and carrier-phase measurements of the L5 signal. The signal-to-noise ratio typically varies from about 30 dB*Hz at low elevations up to 57 dB*Hz at zenith (see figures below: top is SNR for L5; bottom is SNR for GPS PRN 1).

The white-noise and multipath tracking errors are comparable to what is normally seen for the L1 and L2 signals.

Those interested in sample raw data with the triple-frequency(L1-L2-L5) code and carrier phase measurements from IIR-20(M), can download sample data from GNSS Almanac Archive (see the ADVANCED section on www.javad.com). Note that these sample raw data are available in the JAVAD GNSS proprietary binary format as well as Rinex 3.0. http://sc.gpsworld.com/gpssc/data/articlestandard/gpssc/182009/595183/javad-1.jpg


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Air Force Successfully Transmits an L5 Signal From GPS IIR-20(M) Satellite

4/13/2009 - LOS ANGELES AIR FORCE BASE, Calif. -- The U.S. Air Force GPS IIR-20(M) satellite successfully transmitted for the first time a GPS signal in the L5 frequency band today. L5, the third civil GPS signal, will eventually support safety-of-life applications for aviation and provide improved availability and accuracy.

This broadcast brings into use the GPS International Telecommunication Union filing at 1176.45 MHz in the highly protected and co-allocated Radio Navigation Satellite Service and Aeronautical Radio Navigation Service band. A joint team consisting of the GPS Wing, Lockheed Martin, ITT and The Aerospace Corporation developed the L5 Demonstration signal payload and integrated it onto the GPS IIR-20(M) spacecraft, which launched March 24, 2009.

The initial broadcast of the L5 Demonstration signal was monitored and validated by SRI International in Menlo Park, Calif, in cooperation with the GPS Wing, 2nd Space Operations Squadron, Lockheed Martin, Draper Laboratory and The MITRE Corporation.

Thanks to the men and women of the Air Force, our industry partners and national research institute, this mornings successful L5 transmission marks an important milestone in GPS civilian applications. This new third civil signal will make possible the research and development of safety-of-life applications for the commercial transportation sector, and in the future, will play a vital role in improving safety, fuel efficiency, and capacity in our airspace, waterways, highways, and railroads. Todays event marks another important step in the ongoing effort to maintain and modernize GPS as the global standard for space-based positioning, navigation, and timing, said Joel Szabat, Deputy Assistant Secretary for Transportation Policy, U.S. Department of Transportation.

The L5 demonstration payload effort shows the can-do spirit and dedication of all who work in this industry and is an example of a government/industry team working together to meet a significant challenge in a very short time. Development of a solid plan and schedule, adherence to that plan, and consistently looking ahead allowed for a timely and successful completion of the L5 effort, said Col. Dave Madden, Commander, and Global Positioning Systems Wing.

Air Force Space Command
s Space and Missile Systems Center, located at Los Angeles Air Force Base, Calif., is the U.S. Air Forces center of acquisition excellence for developing, acquiring, fielding and sustaining the worlds best space and missile systems for the joint warfighter and the nation.

L5 Signal

Time series and power spectrum of the L5 demonstration signal

New GPS Satellite’s Problems Indicated on 4 May 2009

Lt Col David Goldstein, chief engineer for the GPS Wing, told the plenary session at the European Navigation Conference in Naples, Italy, that the Wing is experiencing some out of family measurements from the recently launched IIRM (20) satellite. This appears to corroborate some unofficial rumors that have circulated recently about problems with legacy signals from the satellite, that is, L1 and L2. The April 10 broadcast of the first L5 signal secured that frequency for the U.S. GPS program; since that signal contains no navigation message at present, it is presumably not affected by these problems.

Goldstein told the ENC opening session, Monday 4 May 2009, that the Air Force will not launch any further satellites until this issue is resolved. IIR(M) 21, the last of the IIR(M) series, is currently scheduled to rise sometime in August, with the first of the IIF generation to follow in late 2009 or early 2010.

Normally, a satellite is set healthy within 28 days of launch, after extensive testing, but this has not occurred with the satellite launched on 24 March 2009. The U.S. Air Force has formed a response team and is working nearly round the clock to resolve the problem, but according to Goldstein is not rushing the issue, seeking a thorough solution since the overall constellation is robust at 30 satellites.

We are currently examining data from the satellite that is not consistent with data from the other IIR(M)s, he stated, characterizing the variances as measurements with larger than expected pseudorange errors that are elevation-dependent, and that we have not seen before. We have experimented with a few fixes and it looks very promising.

He described the response team’s approach as making a fishbone diagram of all potential failure mechanisms, and working through them methodically. We think we have identified the failure but it may be several more months before the analysis is complete, and the situation is fully resolved.

The big delay in preventing GPS from being completed by the planned date of 1984 was the Space Shuttle Challenger disaster. Most GPS satellites were planned to be inserted from a Space Shuttle but instead had to be inserted from Delta rockets as a fall back that delayed a full GPS satellite constellation from existing until 1994.

The open literature discussion of L3 in the early 1980s for GPS was that like L2 (=1227.5 MegaHertz) and L1 (=1575.42 MegaHertz), it was also an integer multiple of a single onboard clock frequency being L3 (= 1381 MegaHertz). It was speculated that L3 was used to cross-communicate between GPS satellites like a JTIDS RelNav network in the sky. Some have speculated that it had related to autonomously maintaining proper satellite ephemeris of the network since in the bad old days of Mutually Assured Destruction (MAD) as a policy strategy, he who had the last accurate weapon fired won. Land-based Minuteman ICBMs (with AIRS navigation systems) utilized GPS for a midcourse nav fix. Ship launched SLBMs did not (at least not in the 1970s). GPS supposedly had sufficient untended (by human intervention) ephemeris to last for 6 months unaided, according to NADC in the early 1980s. 

L3  is now both known by the private sector and is controversial in the civilian Radio Astronomy community, as seen below.

The Global Positioning Satellite system has a mode, L3 at 1381 MHz, which is used for global alarm. If it is within your observing band, then all astronomical signal gets swamped. With advanced notice, the observatory is in a position to alert the responsible authorities and request rescheduling GPS L3 transmission. 

As circulated in unclassified literature in the 1980s, L3 is a part of NUGET, GPS satellites monitor and report on whether they have detected a nuclear blast anywhere in the world.

GPS L3 Interference and Radio Astronomy

European radio astronomy stations operating in the frequency band 1330 - 1400 MHz are experiencing harmful interference at a frequency of about 1381 MHz, which is so strong that it ruins the observations in this frequency range when it occurs. This interference is generated by transmissions from the GPS L3 channel.

An example of this type of interference observed with the Westerbork Synthesis Radio Telescope, WSRT, in the Netherlands is shown in Figure 1 for the amplitude and Figure 2 for the phase of the observed signal. The radio astronomical observation concerns a radio source at 23h36m35.20s right ascension and 26o40’36.00” declination (epoch J2000). The absolute scale for the amplitude of the interference signal is not calibrated since the antenna gain into the direction of the satellite, which was emitting in the far sidelobes of the antennas, is not known.

The indicated level of detrimental interference for the observations presented in the figures below is -239 dB(W/m2/Hz), which was determined using the methodology of Recommendation ITU-R RA.769. This methodology includes the assumption that the interference is received through the far antenna sidelobes, where an antenna gain of 0 dBi applies.

Fig.1: Intensity of the interference signal from GPS L3 observed through the far sidelobes at the WSRT on August 25/26, 2002. The figure shows a detailed spectrum in two linear polarization channels (noted as XX and YY) for an integration time of 0.8 minutes. The amplitude scale is in arbitrary units (see text); the astronomical signal of interest occurs at a level of 0.005 (!) only on this scale. Note that the signal rings throughout the entire 20 MHz band that is displayed.

Fig.2: Signal phase corrupted by GPS L3 interference at the WSRT during the same observation as for Figure 1. The spiky comb in the phase is due to the interfering signal, again in two polarizations.

The L3 spread spectrum transmissions centered at 1381 MHz also transgresses into the frequency range 1400 - 1427 MHz, a spectral band where the radio astronomy has a primary allocation to which RR footnote 5.340 applies, which states that all emissions are prohibited. Using a band-stop filter the signal could be suppressed to a level of -252 dB(W/m2/Hz), i.e. still 3 dB above the level of interference detrimental to radio astronomy continuum observations as given in Recommendation ITU-R RA.769.

The fundamental problem remains that the GPS L3 emission is intentionally produced in the band 1400 - 1427 MHz and is therefore in conflict with footnote 5.340 of the ITU-R Radio Regulations.

It should be noted that in the ITU Radio Regulations for Region 1 the band 1300 - 1350 MHz includes a primary allocation to RADIONAVIGATION-SATELLITE (Earth-to-space) and no allocation to a space service in the band 1350-1400 MHz. Thus no space-to-Earth transmissions are allowed according to these Regulations. For the frequency band 1330-1400 MHz footnote 5.149 applies, which states that administrations are urged to take all practicable steps to protect the radio astronomy service from harmful interference. Emissions from spaceborne or airborne stations can be particularly serious sources of interference to the radio astronomy service (...).

CRAF considers that a regulatory solution for this issue is required, in order to avoid the creation of an undesirable regulatory precedent, where the operation of an application is allowed in conflict with the ITU Radio Regulations.

On this matter CRAF is currently in the process of negotiation with concerned Administrations and expects that it can be solved in due course.

Recent solutions to GNSS incursions into frequencies reserved for Radio Astronomy have been advertised (but the band of concern apparently differs from what is complained about above): Julien, O., Issler, J.-L., "Mitigating the Impact of GNSS Signals in the Radio Astronomy Band 1610.6-1613.8 MHz,"  Navigation: Journal of the Institute of Navigation, pp. 229-240, Vol. 56, No. 4, Winter 2009.

In 1957, Walter Marrow (Lincoln Laboratory of MIT), who later became its head but retired from that position early in the new millennium, launched a missile full of thousands of small metal space needles into LEO, which took about six months to decay out of orbit and burn up in the atmosphere. The entire event was viewed by Lincolns Haystack radar. Radio Astronomers were livid since reception was impossible during that time period. 

The activation of the L2C signal in January 2006 will be of great benefit to the civil community, said Colonel Jester, Chief, Space Operations Branch, Air Force Space Command. But they will be using this signal at their own risk until the command and control of L2C is realized in the Fiscal Year 2013 timeframe. Receivers able to fully utilize the L2C signal will be the responsibility of the civil community. The military will build receivers focused on the new M-code signal.

L2C is stronger than L1.

The premiere civilian GPS manufacturer (TomTom GPS internationally headquartered in the Netherlands, US headquarters in Concord, MA) had been stiffed by ~ $8 million when Circuit City went out of business. Negotiations between Microsoft and TomTom GPS about licensing Microsoft patents broke off around March  2009 and Microsoft was starting to sue TomTom GPS. TomTom GPS subsequently formed a collective with other European companies that held a number of patents similar to Microsofts in order to counter-sue Microsoft over the same issue. It will be interesting to see how this one plays out....

GPS at Risk: Doomsday 2010

The United States Government Accountability Office (GAO) issued on 7 May 2009 an alarming report on the future of GPS, characterizing ongoing modernization efforts as shaky. The agency appears to single out the IIF program as the weak link between current stability and ensured future capability, calling into doubt whether the Air Force will be able to acquire new satellites in time to maintain current GPS service without interruption. It asserts the very real possibility that in 2010, as old satellites begin to fail, the overall GPS constellation will fall below the number of satellites required to provide the level of GPS service that the U.S. government commits to. read more»

L5 and Rorschach Shock

“There is a very minor problem with the L1, L2, and M-code navigation signals. Any causes would be pure speculation at this point, but the issue is the satellite will not be set healthy until these problems are fixed…. The ITT, LMCO and GPS Wing teams are working the problem hard. It may be a few weeks before the satellite is set healthy, but when that time comes I am sanguine that all the signal issues will be mitigated and the navigation message will be on par with the other IIR(M) payloads.” — Colonel Mark Crews

BY DON JEWELL | djewell@questex.com

I am sure that many of you remember Colonel Mark Crews when he served with distinction as the chief engineer for the GPS Wing at SMC. Mark made some legendary and landmark contributions to the future of the GPS constellation as we know it, nationally and internationally. After you read what Dr. Crews has to say about the L5 payload, I will launch into an issue concerning user equipment that has been on mind for sometime — with a trip to the shrink’s couch. read more»



Parkinson Prescribes Remedy for GAO Report Alarm

Brad Parkinson, the first GPS Program Office director, chief architect and advocate for GPS, submitted written testimony to Congress on mitigation options for possible GPS brownouts. His presentation comes in reference to the recent GAO report highlighting the risk that the GPS constellation may fall below the minimum level of 24 satellites required for full operational capability. In his opening, Parkinson states that ”GAO correctly points out the possibility that the GPS constellation will be reduced to less than the current number of 30 to 32 satellites. In fact, it is possible that the constellation will be at a level of less than 24 satellites. I would like to focus on the options that would help reduce this risk." read more»  Click here to download a 91KByte pdf file conveying Sir Brad Parkinsons excellent 10 side PowerPoint presentation to Congress.                    Prof. Parkingsons original 228KByte PowerPoint is here, including his speaker's notes as prompters.

Calling the Real Race in GNSS

Andrew Sage, a director of UK-based transport consultancy Helios, delivered a presentation at the European Navigation Conference entitled: The race to be the partner of choice for GPS. read more» 

Analyses of a Drop in GPS Satellite Numbers 

Professor Richard Langley of the University of New Brunswick (also GPS World Innovation editor) has done several analyses to see how the use of GLONASS satellites could help compensate for a potential reduction in the number of available GPS satellites. These studies came in response to a warning from the U.S. Government Accountability Office about the potential drop in the number of healthy satellites in the GPS constellation as a result of delays in both the Block IIF and Block III modernization programs. read more>>

The SVN-49 Story: What Went Wrong, How It Got Found, and Fixed 
During a very reassuring teleconference today with Colonel David Madden (GPSW/CC) and Colonel David Buckman (AFSPC - GPS Command Lead), we learned the true story of exactly what happened to SVN-49 , aka IIR-20(M), launched March 24, and why it has not been set to a healthy status. This teleconference should put an end to all the speculation concerning SVN-49 and its future status. In sum, there is nothing wrong with the L1, L2, or L5 signal transmitters, and they will not have to undergo expensive re-testing. 

read more>>

Latest GPS Satellite Early Orbit Checkout Extended 
The U.S. Air Force is investigating the cause and effects of signal distortions observed from the GPS IIR-20(M) spacecraft launched on March 24, 2009. Routine early orbit checkout procedures determined that GPS IIR-20(M) signals were inconsistent with the performance of other GPS IIR-M satellites. The signal distortion was initially observed as an elevation-dependent bias in ranging measurements from GPS monitor stations. read more>>

Coast Guard Directed to Maintain and Upgrade Loran
The U.S. Senate, in a Coast Guard Authorization Act for Fiscal Years 2010 and 2011 currently before the Committee on Commerce, Science, and Transportation, directs the Secretary of Transportation to maintain the current Loran-C navigation system and prepare for modernization to eLoran, and authorizes $37 million per year for 2010 and 2011 towards that purpose. Similar action is also currently pending in the House. 


Resource for Comparing Precise Point Positioning (PPP) Solutions
GNSS researchers at the University of New Brunswick, Canada, have created a Precise Point Positioning (PPP) Software Centre website to offer an easy means of comparing solutions from online PPP applications. Users are invited to send a RINEX observation file that will be simultaneously processed by three online PPP applications. 

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Final Modernized GPS IIR Satellite to Lift off from Cape Canaveral The last in a series of eight modernized Global Positioning System Block IIR (GPS IIR-M) satellites built by Lockheed Martin for the U.S. Air Force is set to launch aboard a Delta II rocket on Aug. 17 from Cape Canaveral Air Force Station, Florida. More....

Summary of SDI

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GPS IIR-21(M) Satellite Declared Operational

The last in the series of eight modernized Global Positioning System IIR satellites, GPS IIR-21(M), was declared operational Thursday for military and civilian users worldwide, just 10 days after launching from Cape Canaveral Air Force Station. More....

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PRN01/SVN49: Another GPS Satellite Anomaly

From monitoring at the University of New Brunswick and elsewhere around the globe, it appears that normal signals from the L1 and L2 transmitters on the GPS satellite PRN01/SVN49 were unavailable for more than two hours on the morning of September 4. More....

More problems with GPS and the end for Loran (not too wise since redundant navaids enable easy detection by comparison when GPS is being interfered with) can be found at the following link: http://www.gpsworld.com/gnss-system/out-front-rocky-road-robustness-9424 .


An INS-based Tracking device the size of a pin head:


Please click here to see the future of GNSS and the current status (as of August 2012) of the LightSquared Controversy, which had threatened GPS reception if it had been allowed to proceed.

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