Discrete conditionally-optimal estimation in observable implicit stochastic systems

The paper is devoted to the approximate methods of nonlinear conditionally-optimal (by Pugachev) estimation (filtering, extrapolation, and interpolation) of stochastic processes in discrete implicit stochastic systems (StS) reducible to explicit StS. The methods are based on equivalent linearization of implicit functions. It is supposed that observations do not influence objects and are described by nonlinear equations with noncorrelated and autocorrelated noises. A survey of publications in the field of conditionally-optimal filtering and extrapolation for explicit and implicit StS is given. Two discrete mathematical models of implicit StS and equivalent linearization methods are considered. For reducible implicit StS, conditionally-optimal filtering and extrapolation basic algorithms are presented. Special attention is paid to the known types of interpolation. Implementation to reduced autoregression equations is presented. Main conclusions and directions of future investigation are discussed.