New Improved Recursive Least-Squares Adaptive-Filtering Algorithms

Two new improved recursive least-squares adaptive-filtering algorithms, one with a variable forgetting factor and the other with a variable convergence factor are proposed. Optimal forgetting and convergence factors are obtained by minimizing the mean square of the noise-free a posteriori error signal. The determination of the optimal forgetting and convergence factors requires information about the noise-free a priori error which is obtained by solving a known $L_1-L_2$ minimization problem. Simulation results in system-identification and channel-equalization applications are presented which demonstrate that improved steady-state misalignment, tracking capability, and readaptation can be achieved relative to those in some state-of-the-art competing algorithms.