Multivariance Nonlinear System Identification Using Wiener Basis Functions and Perfect Sequences

Multivariance identification methods exploit input signals with multiple variances for estimating the Volterra kernels of nonlinear systems. They overcome the problem of the locality of the solution, i.e., the fact that the estimated model well approximates the system only at the same input signal variance of the measurement. The estimation of a kernel for a certain input signal variance requires recomputing all lower order kernels. In this paper, a novel multivariance identification method based on Wiener basis functions is proposed to avoid recomputing the lower order kernels with computational saving. Formulas are provided for evaluating the Volterra kernels from the Wiener multivariance kernels. In order to further improve the nonlinear filter estimation, perfect periodic sequences that guarantee the orthogonality of the Wiener basis functions are used for Wiener kernel identification. Simulations and real measurements show that the proposed approach can accurately model nonlinear devices on a wide range of input signal variances.