A Greedy Orthogonal Least Squares Algorithm for Nonlinear Systems with Time-Delays

This paper focuses on the identification of multiple variables Wiener systems with unknown time-delays and system orders. In order to jointly estimate the time-delays and parameters using small amounts of sampling data, an over-parameterized identification model with a sparse parameter vector is established by introducing a redundant rule, and a novel greedy orthogonal least squares identification method based on the Householder transformation is proposed. The active columns of the information matrix are selected one by one with the help of the Householder transformation-based greedy strategy, maintaining an upper-triangular structure for the sub-information matrix. The back-substitution method is adopted to solve the linear equation set instead of a matrix inversion, so that ill-conditioned solutions can be avoided. Finally, the Bayesian information criterion is used to choose the optimal sparse level. Numerical experiments show that this new scheme can achieve almost optimal generalization performance while requiring less computation than the traditional schemes.