This paper proposes a new class of local polynomial modeling (LPM)-based variable forgetting factor (VFF) recursive least squares (RLS) algorithms called the LPM-based VFF RLS (LVFF-RLS) algorithms. It models the time-varying channel coefficients as local polynomials so as to obtain the expressions of the bias and variance terms in the mean square error (MSE) of the RLS algorithm. A new locally optimal VFF (LOVFF) is then derived by minimizing the resulting MSE and the theoretical analysis is found to be in good agreement with experimental results. Methods for estimating the parameters involved in this LOVFF are also developed, resulting in an improved RLS algorithm with VFF.
The algorithm is further extended to include variable regularization and a QR decomposition (QRD) version which is numerically more stable and amenable to multiplier-less implementation using coordinate rotation digital computer (CORDIC) algorithm. Applications of these algorithms to frequency estimation and adaptive beamforming in time-varying speech and audio signals are also presented to illustrate the effectiveness of the proposed algorithms. Simulations show that the convergence and tracking performance of the proposed algorithms compare favorably with conventional algorithms.