Least-square approximation of second-order nonlinear systems using quasi-perfect periodic sequences

We consider the identification of nonlinear filters using periodic sequences. Perfect periodic sequences have already been proposed for this purpose. A periodic sequence is called perfect for a nonlinear filter if it causes the basis functions to be orthogonal and the autocorrelation matrix to be diagonal. In this paper, we introduce for the same purpose the quasi-perfect periodic sequences. We define a periodic sequence as quasi-perfect for a nonlinear filter if the resulting auto-correlation matrix is highly sparse. The sequence is obtained by means of a simple combinatorial rule and is formed by samples having few discrete levels. These characteristics allow an efficient implementation of the least-squares method for the approximation of certain linear-in-the-parameters nonlinear filters. A real-world experiment shows the good performance obtained.