Local Identification of Hammerstein Parameter Varying Systems with Asymmetric Noise Characteristics

The paper studies the multi-model structure parameter identification of the Hammerstein parameter varying system with asymmetric noise characteristics. And the multimodel structure is composed of weighted combinations of several local models, with the local model being the Hammerstein output-error model. We propose a variational Bayes robust identification algorithm based on a shifted asymmetric Laplace distribution (VBRIA_SAL). Firstly, the SAL distribution is used to describe the asymmetric noise. Then in variational Bayes (VB) framework, all unknown variables are seen as hidden variables and their prior information is introduced to iteratively update the estimates. In addition, to overcome the difficulty of directly obtaining the intermediate unmeasurable output, an auxiliary model is established using the measurement information of the system, including the calculated information. Its output replaces the intermediate output, enabling the algorithm procedure to execute smoothly. A numerical simulation has verified that the proposed algorithm is robust to the asymmetric noise compared to studies based on symmetric distributions.