Trigonometric Basis Functions Based Time-Varying Identification Algorithm with Output Weight Factor

A new recursive identification algorithm with output weighted cosine basis functions (WCS) is investigated for the time-varying systems. After introducing a weight factor to the output of a time-varying process within the current time window, the weighted time-varying parameters, which are expanded into the virtual even periodic functions, are explicitly approximated by the cosine series. Following the orthogonality of the trigonometric functions, the parameter estimation problem becomes to the estimation problem of the series coefficients with respect to each degree of the cosine harmonic term in recursive manner. It is demonstrated that weight factor decreases the degree of cosine series and suppress the series approximation error so that the proposed algorithm has better tracking performance for rapid-variation than the conventional basis functions based identification algorithms and the existing standard methods such as RLS, LMS/NLMS, AP/BOP.