Regularization based reweighted estimation algorithms for nonlinear systems in presence of outliers

Outliers usually occur during industrial data collection process and can lead to poor system identification performance. This paper considers the parameter estimation probelm for Hammerstein nonlinear systems whose output measurements are contaminated with additive outliers. By incorporating a lasso-type penalty on the outlier vector, a regularization based least squares identification algorithm that can interactively estimate the system parameters and outliers is proposed based on the auxiliary model identification idea. To further reduce the impact of outliers on the identification effect, each observation is assigned an individual weight, which decreases as the number of iterations increases once the corresponding data is determined to be an outlier. Finally, the outliers can be excluded from the contaminated data without any prior knowledge and the estimation bias is reduced. A numerical example and a benchmark system are given to confirm the effectiveness of the proposed algorithm.