Normal suboptimal filtering methods in implicit observable Gaussian stochastic systems

I. N. Sinitsyn<sup>ab

a</sup> Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
^b Moscow State Aviation Institute (National Research University), 4 Volokolamskoe Shosse, Moscow 125933, Russian Federation

Abstract: The article is dedicated to the theory of normal suboptimal filters (NSOF) and modified NSOF (MNSOF) for Gaussian continuous and discrete implicit stochastic systems (StS) reducible to explicit. It is supposed that observations do not influence the observable object and are described by explicit stochastic differential and difference equations. A short survey in the field of suboptimal NSOF (MNSOF) synthesis is given. Basic algorithms of NSOF (MNSOF) for the first type synthesis for nonlinear and quasi-linear reducible StS with smooth and nonsmooth implicit nonlinearities are described. The theory of NSOF of the second type for reducible implicit StS is developed on the basis of generalized Kalman–Bucy and Kalman filters. Such NSOF unlike NSOF (MNSOF) of the first type do not permit to estimate accuracy of filtering beforehand applications: quick (or real-time) information processing in technical or organization-technical-economical systems is described by small dimension equations when it is possible to neglect time constants at high derivatives (differences). The results are also applicable to implicit hereditary StS reducible to explicit differential (discrete) StS. Directions for future research are formulated.

Keywords: Gaussian stochastic system (StS), implicit StS, modificated NSOF (MNSOF), normal suboptimal filter (NSOF) of the first and second types.

Received: 24.09.2024
Accepted: 15.02.2025

DOI: 10.14357/08696527250102