Decrease in Computational Load and Increase in Accuracy for Filtering of Random Signals

This paper describes methods for optimal filtering of random signals that involve large matrices. We develop a procedure that allows us to significantly decrease the computational load needed to numerically realize the associated filter and increase the associated accuracy. The procedure is based on the reduction of a large covariance matrix to a collection of smaller matrices. It is done in such a way that the filter equation with large matrices is equivalently represented by a set of equations with smaller matrices. The filter Fp we develop is represented by Fp(v1,…vp)=∑j=1pMjvj and minimizes the associated error over all matrices M1,…,Mp. As a result, the proposed optimal filter has two degrees of freedom to increase the associated accuracy. They are associated, first, with the optimal determination of matrices M1,…,Mp and second, with the increase in the number p of components in the filter Fp. The error analysis and results of numerical simulations are provided.