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. Conditions under which such invertibility is guaranteed are discussed. A number of results are derived paralleling those already obtained for least-mean-square filters, and the problem of statistical robustness of the WLS estimator is discussed.