A second order recursive algorithm for adaptive signal processing

Abstract

A second order recursive algorithm is proposed for adaptive signal processing. The algorithm is derived and analyzed for the autoregressive exogenous (ARX) case and it encompasses both the recursive least squares (RLS) and least mean squares (LMS) algorithms as special cases. The algorithm can be extended to instrumental variables (IV) and prediction error (PE) like algorithms. Furthermore, a similar algorithm is derived for signal subspace tracking. The computational complexity is the same as for the RLS algorithm but some extra memory storage is required. Furthermore, it is demonstrated that the proposed algorithm has a higher ability to track time varying signals than has the RLS algorithm. The proposed algorithm especially handles those situations well where there is a simultaneous system change and decrease of signal power.