FIR system identification for correlated noise using the convolution matrix, an investigation

Abstract

A novel approach to finite-impulse response system identification is given. The method is formulated differently from ordinary least mean squares (LMS) or block LMS, which are traditional approaches and has a significant advantage of speed improvement when the correlation matrix has a large condition number. Unlike other approaches which are numerically complex, this method has a similar computational burden as LMS and gives the same optimal solution after convergence. It avoids transformation matrices by writing the system description in terms of a convolution matrix which has a special lower-triangular format. In this way the correlation matrix is different from conventional least-squares approaches and maintains a modest condition number as the correlation matrix in ordinary least-squares climbs high. The method has as wide a range of applications as ordinary LMS-based solutions but can also work on deterministic inputs.