REGULARIZED FAST RECURSIVE LEAST-SQUARES ALGORITHMS FOR FINITE MEMORY FILTERING

New fast recursive least squares algorithms are developed here, for finite memory filtering, by using a sliding data window. These algorithms allow the use of statistical priors about the solution, and they allow maintaining a balance between the a priori and the data informations. They are then well suited to compute a regularized solution, which has better numerical stability properties than the conventional least squares solution. An important advantage of the algorithms presented in this paper lies in the fact that they have a general matrix formulation, such that the same equations are suitable for the prewindowed as well as the covariance case, independently of the used a priori information. Only the initialization step and the numerical complexity change through the dimensions of the intervening matrix variables. The lower bound of O(16m) is achieved in the prewindowed case when the estimated coefficients are assumed to be uncorrelated, m being the order of the estimated model. It is shown that a saving of 2m multiplications per recursion can always be obtained. The lower bound of the resulting numerical complexity becomes O(14m), but then the general matrix formulation is lost. Simulation results are given to illustrate the interest of incorporating priors in the estimation problem.