REGULARIZED FAST RECURSIVE LEAST-SQUARES ALGORITHMS FOR ADAPTIVE FILTERING

We develop here new fast recursive least squares (FRLS) algorithms by using factorization techniques which represent an alternative way to the geometrical projections approach or the matrix partitioning based derivations. The estimation problem is formulated within a regularization approach, and priors are used to get a regularized solution which presents better numerical stability properties than the conventional least squares one. The numerical complexity of the algorithms we present here is explicity related to the displacement rank of the priori covariance matrix of the solution. It then varies between 0(5m) and that of the slow RLS algorithms to update the Kalman gain vector, m being the order of the solution. An important advantage of our algorithms is that they admit a unified formulation such that the same equations may treat equally the prewindowed and the covariance cases independently from the used priors. The difference lies only in the involved numerical complexity, which modifies through a change of the dimensions of the intervening variables. Simulation results are given to illustrate the the performances of these algorithms.