On Bias Compensated Recursive Least-Squares Algorithm for FIR Adaptive Filtering

Abstract It is known that recursive least squares (RLS) algorithm or least mean square (LMS) algorithm leads to biased FIR filter coefficients in the presence of input and output noise. In this paper, a new type of bias compensated recursive least squares (BCRLS) algorithm is proposed to produce consistent results for adaptive FIR filtering in the input and output noise case. The proposed algorithm introduces an auxiliary estimator to estimate unknown input noise variance. Owing to this, the bias of the RLS solution due to the input noise can be compensated to yield the consistent filter coefficients. Computational simulations indicate that the proposed algorithm is very efficient