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 developed a procedure that allows us to significantly decrease the computational load associated with numerically implementing the associated filter and increase its accuracy. The procedure is based on the reduction of a large covariance matrix to a collection of smaller matrices. This 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 we developed is represented by (Formula presented.) and minimizes the associated error over all matrices (Formula presented.). As a result, the proposed optimal filter has two degrees of freedom that increase its accuracy. They are associated, first, with the optimal determination of matrices (Formula presented.) and second, with an increase in the number p of components in the filter. The error analysis and results of numerical simulations are provided.