Normal Pugachev conditionally-optimal filters and extrapolators for state linear stochastic systems

The analytical synthesis theory of continuous and discrete sub- and Pugachev conditionally optimal filters and extrapolators for information processing in linear state stochastic systems (StS) is presented. For Gaussian StS, Liptzer and Shiraev performed the first works for filters and extrapolators synthesis. For non-Gaussian StS, the first works belong to Pugachev and Sinitsyn. Stochastic equatuins for state and observation of continuous and discrete StS are given. Algorithms for continuous normal sub- and conditionally optimal filters and extrapolators are presented. The corresponding algorithms for discrete StS are also given. The developed algorithms are the basis of the software tool “StS-Filter, 2016”. The results may be developed for autocorrelated noises and multiplicative noises.