A novel weight function-based robust iterative learning identification method for discrete Box–Jenkins models with Student's t-distribution noises

Abstract

In the engineering areas, the impulsive disturbances widely exist due to the presence of outliers. The current identification theories based on Gaussian assumptions cannot meet the needs. In the view of above situations, a weight function-based iterative learning identification method is firstly proposed for discrete Box–Jenkins models, and the robust parameter estimation is achieved under Student's t noises. Firstly, according to robust estimation theories, the characteristic weight function is designed for residuals and measurement outputs. This results in the reduced impacts of outliers. Secondly, the effective weights, derived from the robust M-estimator, are applied into the iterative least squares procedure. Thus, the each iteration process is similar to the weighted least squares algorithm. From continuous learning of the estimated residuals, the proposed method realizes an effective fusion of robust estimation and optimization techniques. Finally, the simulation examples verify the theoretical findings.