Generic weighted filtering of stochastic signals

Abstract

In this paper, a new theory of optimal weighted nonlinear filtering is presented. Two filter models are considered. The first model is based on a representation of the filter in the polynomial-like form with q terms where each term consists of weighted matrices and the matrix determined from the error minimization problem. The second model extends the first one to the case of the filter concatenation. The filter models are given in terms of pseudo-inverse matrices, i.e., the requirement of invertibility for covariance matrices is omitted. Thus, our filters always exist. We develop methods which allow us to exploit advantages associated with the proposed nonlinear filter models. The methods c..