Nonlinear system identification using quasi-perfect periodic sequences

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 auto-correlation 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 auto-correlation 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.