Optimal structure of continuous nonlinear reduced-order Pugachev filter

A non-parametric synthesis problem is considered for a fast nonlinear low-memory filter consisting of the same number of equations as the number of only information components of the diffusion Markovian state vector of the observation plant. The algorithm for finding mean-square locally optimal structural functions of the filter and the reduced Fokker-Planck-Kolmogorov equation to be used to find the respective instantaneously conditional probability distribution are obtained. The proposed filter in its full order is proved to coincide with the linear Kalman-Bucy filter in various linear Gaussian cases. Ways to construct Gaussian and linearized suboptimal filters are proposed. The example is given where the latter are compared with their analogues.