A recursive least-squares algorithm with data-adaptive step size

A recursive least-squares (RLS) algorithm for adaptive filtering that requires no exponential weighting or finite memory for filtering nonstationary data is proposed. The algorithm is a generalization of the normalized least-mean-square (NLMS) algorithm. For noiseless observations, the algorithm is analyzed from a deterministic viewpoint and is shown to converge after exactly M iterations, where M is the filter length. The convergence properties of this algorithm also lend some insight into the convergence of the conventional RLS algorithm. Experimental results that demonstrate the improved convergence of this algorithm over the standard RLS algorithm in a time-varying system identification application are reported. These algorithms also easily lend themselves to fast implementations