A direction set based algorithm for least squares problems in adaptive signal processing

Abstract

A fast algorithm has been developed for solving a class of least squares problems arising in adaptive signal processing. The algorithm is based on the Powell and Zangwill direction set method for unconstrained minimization problems and is designed so as to fully take advantage of the special structure of the adaptive least squares (ALS) problems. It is a fast algorithm because it requires only O( N) multiplications for each system update where N is the dimension of the problem. The algorithm has been implemented and applied to applications in signal processing. Computer simulation results have shown that the algorithm is stable and converges fast often with a rate which is comparable to that of the known CG and RLS algorithm. The convergence behavior of the algorithm is studied in detail in this paper. The algorithm is shown to converge linearly for adaptive least squares problems in general and its rate of convergence can be faster than linear for some applications. A computational procedure is also designed to generate a set of near conjugate directions as initial directions to accelerate the convergence.