Optimal Nonlinear Recurrent Finite Memory Filter

A problem of best estimation of the current values of part of the state variables of a discrete stochastic Markovian plant using measurement results is considered. To ensure that these measurements are sufficiently simply processed, it is proposed to synthesize a finite-dimensional filter that stores only the last few measurements in its state vector. The filter's memory size is arbitrary and can be chosen as a compromise between the attained estimation accuracy and complexity of the hardware implementation of the filter. The root-mean-squarely optimal structure of the filter is represented via the respective probability distribution, a recurrent way to find this distribution is found, and the algorithm for the numerical construction of the filter by the Monte Carlo method is given. Since it is cumbersome, analytical Gaussian and linearized approximations to the proposed filter are considered. A comprehensive example to compare the accuracies of these approximations with their known analogues is shown.