This article is cited in 2 papers

Conditionally optimal filtering and extrapolation for differential Gaussian implicit stochastic systems at autocorrelated noise in observations

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 theory of Pugachev conditionally-optimal filtering and extrapolation of stochastic processes described by explicit stochastic differential equations at autocorrelated noise in observations is widely used in modern real-time information processing. The paper is devoted to implicit Gaussian stochastic systems (StS) reducible to explicit StS at observational autocorrelated noises. The main results are: ($i$) typical mathematical models of observable implicit StS reducible to differential explicit StS; ($ii$) basic equations for nonlinear conditionally-optimal filters (COF) and conditionally-optimal extrapolators (COE) at noncorrelated and autocorrelated noises; and ($iii$) illustrative examples for reducible StS. Main conclusions and perspective directions for COF and COE design in the case of implicit differential and functional differential StS are given.

Keywords: autocorrelated observation noise, conditionally-optimal extrapolation, conditionally-optimal filtering, explicit stochastic system, implicit stochastic system.

Received: 13.05.2024

DOI: 10.14357/19922264240403