ROBUSTNESS OF GAUSS-NEWTON RECURSIVE METHODS - A DETERMINISTIC FEEDBACK ANALYSIS

This paper provides a time-domain feedback analysis of the robustness performance of Gauss-Newton recursive methods that are often used in i dentification and control. These are recursive estimators that also in volve updates of sample covariance matrices. Several free parameters a re included in the filter descriptions while combining the covariance updates with the weight-vector updates. One of the contributions of th is work is to show that by properly selecting the free parameters, the resulting filters can be made to impose certain bounds on the error q uantities, thus resulting in desirable robustness properties (along th e lines of H-infinity filter designs). It is also shown that an intrin sic feedback structure, mapping the noise sequence and the initial wei ght error to the a priori estimation errors and the final weight error , can be associated with such schemes. The feedback configuration is m otivated via energy arguments and is shown to consist of two major blo cks: a time-variant lossless (i.e., energy preserving) feedforward pat h and a time-variant feedback path, Emphasis is further given to filte red-error variants that give rise to dynamic time-variant feedback loo ps rather than memoryless loops. Such variants arise in IIR modeling.