Complex statistical 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: Paper is devoted to exact and approximate based on complex statistical criterion (CSC) conditionally-optimal filtering (COF) methods for continuous and discrete observable implicit non-Gaussian stochastic systems (StS) reducible to explicit. Survey of COF based on mean square criterion for explicit and implicit StS and CSC COF for explicit StS is given. Reduction methods for smooth and discontinuous implicit functions are presented. The CSC COF exact synthesis methods for reducible differential, regression, and autoregression StS are developed. For reduced StS with additive Gaussian noises and statistically linearized implicit functions generalization of Kalman and Kalman–Bucy filters is considered. Some future generalizations of exact and approximate CSC COF are mentioned.

Keywords: conditionally-optimal (in Pugachev sense) filter, normal approximation method (NAM), normal suboptimal filter (NSOF), stochastic process (StP), stochastic system (StS).

Received: 09.12.2024
Accepted: 15.05.2025

DOI: 10.14357/19922264250204