Outlier robust identification of dual-rate Hammerstein models in the presence of unmodeled dynamics

Abstract

The article considers the outlier-robust recursive least squares algorithm for identification of SISO (single-input single-output) dual-rate Hammerstein model. The output sampling period is an integer multiple of the input sampling period. By using polynomial transformation technique we get a model which is suitable for parameter estimation for dual-rate measurement data. After that deterministic dual-rate Hammerstein model is extended with stochastic disturbance (which includes outliers) and unmodeled dynamics. Synthesis of identification algorithm is based on Newton–Raphson method which requires that loss function should be twice differentiable. Huber loss function, relevant for outliers treatment, has just first derivative. In order to overcome problem pseudo-Huber loss function is introduced. This function behaves similarly to Huber loss function and has derivatives of arbitrary orders. Given recursive algorithm is based on synergy of Huber and pseudo-Huber loss functions. Then we consider the robustness of algorithm. The main contributions of the article are: (i) determination of dual-rate Hammerstein model which includes stochastic disturbance with outliers and unmodeled dynamics; (ii) derivation of robust recursive algorithm; (iii) determination of robustness for parameter estimate.