Screen shot #3 (Merely a picture to illustrate that our
GUI is totally self-explanatory)
Select the data source from the indicated menu appearing within
the screen below that also allows the user to appropriately enter the system and
measurement model and its additive plant (or system) and measurement noise structure (which can be Pure independent Gaussian White Noises [GWN] or
cross-correlated or serially correlated in time of known correlation structure
expressed either in the time-domain or in the frequency domain as a power
spectrum matrix). Can also accommodate mixtures of Gaussian and Poison White
Noises to test robustness in the accuracy performance of the estimator when
required assumptions of the noises being purely Gaussian are not strictly met.
The availability of
****10
Megabyte Ethernet****
is a relatively new option for an Input/Output protocol. Since **The MathWorks**
claims that **VME** is an older protocol that **The MathWorks** currently
(in 2010) doesn****t
bother to support, we at **TeK Associates** are in possession of an Annual
Buyer****s
guide entitled *VME and Critical Systems*, Vol. 27, No. 3, December 2009
and we feel obligated to distinguish our **TK-MIP** software product from
that of **The MathWorks** by **TeK Associates** eventually offering **VME**
compatibility within **TK-MIP** in its later versions beyond the current
Version 2.
Click here to get the (draft
copy) of AIAA Standards for Atmospheric Modeling, as specified by the various U.S.
and other International agencies.
Click here to get the (draft
copy) of AIAA Standards for Flight Mechanics Modeling, as specified by the
pertinent responsible U.S. and other International agencies.
Statisticians appear to be more comfortable with entering
system models in this equivalent alternative AR, ARMA, or ARMAX formulation (to
start with):
The close (equivalent) model relationship between a
Box-Jenkins time-series representation and a state variable representation has
been known for at least 4 or 5 decades, as spelled out in: A. Gelb
(Ed.), *Applied
Optimal Estimation*,
MIT Press, Cambridge, MA, 1974. This book also shows how to routinely convert
from a discrete-time representation (i.e., a difference equation) to a
continuous-time representation (i.e., differential equation) representation and
vice versa. It is the **state variable model** that is usually used in
scientific and engineering applications, where detailed models are available **from
physical laws** that are part of the prerequisite curriculum. From what I have
seen in a *Data Analytics* *Conference* at Boston University in
September 2018, they are searching in the dark for an appropriate black box
model in the financial applications areas to use as reasonable models (in
conjunction with using parameter estimation and AIC and BIC in order to know
when they have a model that captures the essence of the application yet stops
with a reasonable size ****n**,
**as appears in the model equations below. In the preceding
discussion, the 2 undefined acronyms are: Akaike Information Criterion (AIC):
https://en.wikipedia.org/wiki/Akaike_information_criterion
Bayesian Information Criterion (BIC): https://en.wikipedia.org/wiki/Bayesian_information_criterion Pertaining
to the above discussion:
| Kerr, T. H., ****Applying Stochastic Integral Equations to Solve a Particular Stochastic Modeling
Problem,**** Ph.D. Thesis in the Department of Electrical Engineering, University of Iowa, Iowa City, Iowa, January 1971.
**(This offers a simple algorithm for easily
converting an ARMA time-series into a more tractable AR one of higher
dimension.)** |
| 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. **(This offers a simple algorithm for easily
converting an ARMA time-series into a more tractable AR one of higher
dimension.)** |
| Kerr, T. H., ****Emulating
Random Process Target Statistics (Using MSF),**** *IEEE
Trans. on Aerospace and Electronic Systems*, Vol. 30, No. 2, pp. 556-577,
Apr. 1994. **(This offers a simple algorithm
for easily converting an ARMA time-series into a more tractable AR one of
higher dimension.)** |
| What follows below is a discrete-time (i.e., difference equation based)
ARMA model put into standard discrete-time state variable form: |
****Gearing up****
to complete the modeling, simulation, and
implementation tasks can be accomplished much faster by using **TK-MIP**!
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