Joint parameter and time-delay estimation for a class of Wiener models based on a new orthogonal least squares algorithm

Abstract

This paper focuses on the identification of multiple inputs Wiener systems with piecewise-linear nonlinearity. The main objective is to jointly estimate the parameters and time-delays by using limited samples when the system orders are unknown. In order to identify the over-parameterized sparse system under the framework of greedy method, a Householder transformation-based greedy orthogonal least squares algorithm is proposed. In this scheme, the active columns of the information matrix are selected one by one according to a new greedy strategy, then the Householder transformation is employed to maintain an upper-triangular structure for the sub-information matrix, the back-substitution method is adopted to avoid the matrix inversion. Thus the problem of ill-conditioning frequently appears in nonlinear models can be eliminated. The Bayesian information criterion is used to choose the optimal sparsity level. Numerical experiments show that this new scheme can achieve almost optimal generalization performance while requiring less observations than the traditional schemes.