Hammerstein System Identification with Skewed and Asymmetric Noise

To eliminate the negative effect brought by the skewed and asymmetric measurement noise, this paper proposes a robust identification algorithm for the Hammerstein output error (OE) system based on the shifted asymmetric Laplace (SAL) distribution, where the skewness and scale parameters are used as the hyper-parameters to adjust the statistical properties of the SAL distribution to obtain robustness in handling the skewed and asymmetric noise problem. In Hammerstein system identification, to handle the problem of over-parameterization, the key-term separation principle is applied to simplify the identification model and at the same time, the auxiliary model is also used to estimate the unmeasurable process variables. The complete identification problem is formulated in the framework of the generalized expectation maximization (GEM) algorithm, and estimation formulas of the model and noise parameters are derived simultaneously. Finally, the effectiveness of the proposed algorithm is verified by the simulation experiments.