Parametric Filtering: Optimal Synthesis on a Nonlinear Dynamic Variety

We analyze the optimal parametric filtering problem for a wide class of nonlinear stochastic systems. Much attention is paid to validation of formed models of observation and estimation since derivation of equations that determine the mean-square optimal filter directly depends on a rational choice of the models. We find conditions under which the original optimal filtering problem is equivalent to the dual optimal control problem. Synthesis of the optimal filter is accompanied by the analysis of properties of solutions of filtering equations obtained.