Iterative identification for multiple-input systems with time-delays based on greedy pursuit and auxiliary model

Abstract

This paper focuses on the identification of multiple-input single-output output-error systems with unknown time-delays. Since the time-delays are unknown, an identification model with a high dimensional and sparse parameter vector is derived based on overparameterization. Traditional identification methods cannot get sparse solutions and require a large number of observations unless the time-delays are predetermined. Inspired by the sparse optimization and the greedy algorithms, an auxiliary model based orthogonal matching pursuit iterative (AM-OMPI) algorithm is proposed by using the orthogonal matching pursuit, and then based on the gradient search, an auxiliary model based gradient pursuit iterative algorithm is proposed, which is computationally more efficient than the AM-OMPI algorithm. The proposed methods can simultaneously estimate the parameters and time-delays from a small number of sampled data. A simulation example is used to illustrate the effectiveness of the proposed algorithms.