Neural networks bayes synthesis of multidimensional linear stochastic system

I. N. Sinitsyn, V. I. Sinitsyn, E. R. Korepanov, T. D. Konashenkova

Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: New method of optimal synthesis of multidimensional linear stochastic system on Bayes criterion (BC) based on quantitative estimate of output stochastic process (StP). Stochastic system is described by Pugachev equation for input and output StP. Input StP contains useful signal and random additive multidimensional normal noise with zero mathematical expectation and known matrix of covariance functions. Random noise does not depend upon vector of random parameters of useful signal. Distribution of random vector parameters is known. Model of BC optimal estimate of output StP is constructed on the basis of wavelet canonical expansion (CE) of random noise and wavelet CE of input StP. For finding unknown parameters in optimal output StP estimate, the architecture of multilayer wavelet neural networks (WNN) is developed. The WNN training algorithm for inverse error prevalence by method steepest descent is used. Formulae for mathematical expectation, second initial probabilistic moment, and error covariance matrix of BC optimal estimate of output StP is obtained. Numerical example illustrates CE WNN preference with wavelet CE.

Keywords: Bayes criterion, canonical expansion, covariance function, covariance matrix, modeling, loss function, optimal estimate, stochastic process, stochastic system, wavelet, wavelet-neural network.

Received: 26.04.2025
Accepted: 15.09.2025

DOI: 10.14357/08696527250303