Low-order discrete linear filters: Their optimal structure

The right side of the difference equation describing a nonlinear filter of order equal to the number of estimated components of the Markov vector of the state of the observed object is determined. Relations for exactly determining the mean-square optimal structure of the vector function of the filter, the joint probability distributions of the states of the object and filter, and the measurer output an derived. They are used in developing approximate methods of synthesizing suboptimal, low-order, nonlinear filters. An example is given.