Fast, fixed-order, least-squares algorithms for adaptive filtering

Fast, fixed-order, exact-least-squares algorithms for tapped-delay-line adaptive-filtering applications are presented in this paper. These new recursive algorithms require fewer operations per iteration and exhibit better numerical properties than the so-called Fast-Kalman algorithm of Ljung and Falconer [1978] and the unnormalized, least-squares, joint-process-lattice algorithms of Morf and Lee [1978]. In comparison with the currently used stochastic-gradient or LMS adaptive algorithm of Widrow and Hoff, the new, fixed-order, least-squares algorithms yield substantial improvements in transient behavior at a modest increase in computational complexity. Additionally, over a wide range of practical applications, the new algorithms demonstrate numerical properties comparable to those of the normalized lattice introduced by Lee, Morf, and Friedlander [1981], but at a considerable reduction in complexity.