Nonlinear system identification using quasi-perfect periodic sequences

摘要

Perfect periodic sequences are currently used for modeling linear and nonlinear systems. A periodic sequence, applied as input to a linear or nonlinear system, is called perfect if the basis functions of the modeling filter are orthogonal to each other, and thus the autocorrelation matrix is diagonal. In this paper, we introduce quasi-perfect periodic sequences for a sub-class of linear-in-the-parameters nonlinear filters, called functional link polynomial filters, which is derived by using the constructive rule of Volterra filters. A periodic sequence is defined as quasi-perfect for a nonlinear filter if the resulting autocorrelation matrix is block-diagonal and highly sparse. Moreover, the samples of the sequence are represented by only a few discrete levels. It is shown in the paper that quasi-perfect periodic sequences for third-order systems can be obtained by means of a simple combinatorial rule. The derived sequences, which are the same for all functional link polynomial filters, allow an efficient implementation of the least-squares approximation method. Simulation results and a real-world experiment show good performance of the proposed identification method.