Despite its low computational cost, and steady state behavior, some well known drawbacks of the least means squares (LMS) algorithm are: slow rate of convergence and unstable behaviour for ill conditioned autocorrelation matrices of input signals. Several modified algorithms have been presented with better convergence speed, however most of these algorithms are expensive in terms of computational cost and time, and sometimes deviate from optimal Wiener solution that results in a biased solution of online estimation problem. In this paper, the inverse Cholesky factor of the input autocorrelation matrix is optimized to pre-whiten input signals and improve the robustness of the LMS algorithm. Furthermore, in order to have an unbiased solution, mean squares deviation (MSD) is minimized by improving convergence in misalignment. This is done by regularizing step-size adaptively in each iteration that helps in developing a highly efficient optimal preconditioned regularized LMS (OPRLMS) algorithm with adaptive step-size. Comparison of OPRLMS algorithm with other LMS based algorithms is given for unknown system identification and noise cancelation from ECG signal, that results in preference of the proposed algorithm over the other variants of LMS algorithm.
Statistical-Mechanical Analysis of LMS Algorithm for Time-Varying Unknown System
