Identification of Time-Varying System Based on Fourier Series

The identification problem of time-varying systems is considered in this paper. It is demonstrated that the parameters of the time-varying model can be approximated by Fourier series in the continuous range, but the Gibbs phenomenon occurs at discontinuous points. The identification algorithms with compensation of the estimation error caused by Gibbs phenomenon are investigated and the method is proposed to reduce computational complexity. Furthermore, the recursive identification algorithms are developed for on-line estimation. In contrast to RLS or LMS, the proposed approaches converge quickly to the varying parameters and show good tracking performance.