A Robust Two-step Iterative Approach for the Identification of Hammerstein Box-Jenkins Systems

Impulse interference widely exists in engineering practices, and makes the noise disturbance of the system present a heavy-tailed distribution. Therefore, the performance of traditional parameter estimation methods based on Gaussian noise assumption will be seriously degraded when used in the system affected by heavy tail noise. Since industrial objects usually have nonlinear characteristics, this paper takes Hammerstein Box-Jenkins model as the object under the background of heavy tail noise, and proposes a novel two-step iterative robust identification method based on the least absolute criteria. Firstly, the Gaussian mixture model is used to generate the input signal to distinguish the influence of nonlinear characteristic and heavy-tailed noise. Secondly, a two-step iterative identification method based on least absolute criteria is proposed. The two-step iterative method not only guarantees a global optimal parameter estimation of the model, but also avoids the non-convergence of noise model estimation. Finally, the identification experiments on nonlinear model affected by heavy-tailed noise with Student’ s t distribution proved the effectiveness of the proposed method. Compared with other identification algorithms, the proposed algorithm has better robustness to heavy -tailed noise.