Defining Model(s)


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.

Entries of the requisite matrices, depicted below, can be explicitly numerical (shown here below as constants) or be in symbolic form consisting of functions of the independent variable time (or of its obvious alias) and possible algebraic operations or combinations of such functions. Sufficient space is availed within each tabular representation of each entry field. TK-MIP performs the necessary conversions automatically, exactly where they need to occur internal to the software, without the USER needing to explicitly intervene to invoke such conversions themselves. We do the right thing, as can be confirmed with copious test problems, using either ours, as suggested, or the USER'S own personal favorites.

Statisticians (and others working with financial data) appear to be more comfortable with entering system models in this equivalent alternative AR, ARMA, or ARMAX time-series 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): 

Bayesian Information Criterion (BIC): 

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, which can all be accomplished much faster by using TK-MIP!

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