An unbiased and cost-effective leaky-LMS filter

We propose a modified leaky-LMS filter that ensures stability of the estimates w(k) in the presence of bounded noise, without introducing any bias term and with the added cost of only a comparison and a multiplication per iteration when compared to the classical LMS algorithm. The new algorithm is further shown to converge for l(p) noise and persistently exciting regressors. Ir also provides bounded estimates even infinite precision arithmetic. The stability and convergence properties of the new algorithm are established through a deterministic analysis that is based on the Lyapunov theory for the stability of nonlinear difference equations.