Bayes criterion conditionally optimal filtering methods for observable implicit stochastic systems

I. N. Sinitsyn

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

Abstract: The paper is devoted to methods of conditionally optimal filter (COF) synthesis by Bayes criterion (BC) in continuous and discrete implicit non-Gaussian stochastic systems (StS) reducible to explicit. A short COF survey by mean square, energetic, and complex statistical criteria for explicit and implicit continuous and discrete StS is given. Reduction methods for smooth and nonsmooth implicit functions are developed. Exact and approximate (based on normal approximation and statistical linearization) methods for BC COF in reducible implicit continuous and discrete StS are considered. Special attention is paid to normal BC COF. The problem of equivalence of non-Gaussian noises in BC COF is discussed. Future directions of research and applications are presented.

Keywords: Bayes criterion (BC), conditionally optimal filter (COF), implicit StS, normal COF, stochastic system (StS).

Received: 23.12.2024
Accepted: 15.08.2025

DOI: 10.14357/19922264250301