Normal Pugachev filters for state linear stochastic systems

The applied theory of analytical synthesis of normal conditionally optimal (Pugachev) filters (NPF) in state linear non-Gaussian stochastic systems (StS) is presented. Special attention is paid to NPF for differential StS satisfying Liptzer–Shiraev conditions based on the normal approximation of a posteriori density and quasi-linear NPF based on statistical linearization of nonlinear functions depending on observations. For StS of high dimension and real-time problems, NPF are more effective than the suboptimal filters. The NPF algorithms are the basis of the “StS-Filters” software tool. Test examples are given.