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Using TeK Associates’ TK-MIP^TM commercial PC software for Kalman Filtering, for Extended Kalman Filtering (EKF), and for other linear and nonlinear estimation applications and associated design and evaluation projects keeps you out of the “red” and well into the “black” or “blue” in terms of being on-time and under budget. Then, as a consequence of using TK-MIP, you really will be “in the pink”!

As in the cute example above (that flexibly moves to wherever USER clicks his mouse pointer and then quickly recovers perfectly to “save the day”), “time will dilate” to satisfy your constraints and needs for getting projects done on time. Since time is “relative”, we jokingly claim to conform to the “twin paradox” of Einstein's special relativity theory by allowing you to 1) get more done 2) in less time than with other conventional programming tools. You will progress so quickly that time will appear to dilate because TK-MIP doesn't require that you do any real programming per se. You can do further programming if you really want to tailor our extensible TK-MIP software to unusual non-standard situations (since we grant you this option within the existing TK-MIP framework) but we have already utilized our 30+ years experience of working in this technology area to anticipate a variety of standard user needs (that we have experienced ourselves first hand in our own navigation and target tracking applications for the U.S. Department of Defense) to provide you with flexible software modules already tested and certified to be bug-free. For further testing after your own controlled modifications (to certain aspects that we make accessible to you for modification) and to bolster your confidence in the correctness of the TK-MIP software that we offer, we encourage you to use our innovative collection of analytic test problems of known closed-form solution:

1. Kerr, T. H., “Multichannel Shaping Filter Formulations for Vector Random Process Modeling Using Matrix Spectral Factorization,” MIT Lincoln Laboratory Report No. PA-500, Lexington, MA, 27 March 1989 (BSD limited distribution).

2. Kerr, T. H., “An Analytic Example of a Schweppe Likelihood Ratio Detector,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-25, No. 4, pp. 545-558, July 1989.

3. Kerr, T. H., “Rationale for Monte-Carlo Simulator Design to Support Multi-channel Spectral Estimation and/or Kalman Filter Performance Testing and Software Validation/Verification Using Closed-Form Test Cases,” MIT Lincoln Laboratory Report No. PA-512, Lexington, MA, 22 December 1989 (BSD limited distribution).

4. Kerr, T. H., “A Constructive Use of Idempotent Matrices to Validate Linear Systems Analysis Software,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-26, No. 6, pp. 935-952, November 1990 (minor correction appears in Nov. 1991 issue).

5. Kerr, T. H., “Numerical Approximations and Other Structural Issues in Practical Implementations of Kalman Filtering,” a chapter in Approximate Kalman Filtering, edited by Guanrong Chen, 1993.

6. Kerr, T. H., “Emulating Random Process Target Statistics (using MSF),” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-30, No. 2, pp. 556-577, April 1994.

7. Kerr, T. H., and Satz, H., S., “Applications of Some Explicit Formulas for the Matrix Exponential in Linear Systems Software Validation,” Proceedings of 16th Digital Avionics System Conference, Vol. I, pp. 1.4-9 to 1.4-20, Irvine, CA, 26-30 Oct. 1997.

8. Kerr, T. H., “Verification of Linear System Software Sub-Modules using Analytic Closed-Form Results,” 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, 17 May 2001.

9. Kerr, T. H., “Exact Methodology for Testing Linear System Software Using Idempotent Matrices and Other Closed-Form Analytic Results,” Proceedings of SPIE, Session 4473: Tracking Small Targets, pp. 142-168, San Diego, CA, 29 July-3 Aug. 2001.

to confirm for yourself the quality of our TK-MIP product and the veracity of our claims of providing only accurate results. These same test problems may be similarly used to verify or crosscheck any other software that claims to solve comparable problems that typically arise in estimation and control applications.

When you are ready to test TK-MIP for yourself or to buy this PC product, please contact us, care of Dr. Thomas H. Kerr III, at TeK Associates, TK-MIP R&D Software Development Department, 9 Meriam Street, Suite 7-R, Lexington, Massachusetts 02420-5336. An alternative is to telephone or fax us at (781) 862-5870 for more information.

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