Nonasymptotic results for finite-memory WLS filters

A nonasymptotic analysis of properties of weighted least squares (WLS) adaptive filters used for identification of time-varying systems is presented. It is shown that the problem of mean-square boundedness of WLS estimates is closely related to the problem of invertibility-in the mean sense-of the corresponding regression matrix. Necessary and sufficient conditions are discussed for such invertibility to hold. Based on that, a number of results are derived paralleling those already obtained for least mean-square (LMS) filters, and the problem of statistical robustness of the WLS estimator is briefly discussed.