Laplace Distribution Based Robust Identification of Errors-in-Variables Systems With Outliers

This article considers a robust identification problem of errors-in-variables (EIVs) system with nonlinear input generation process. In addition, we consider that the output data has both measurement noise and disturbance with outliers. The disturbance is described by a Laplace distribution to account for the outliers. Simultaneously, the input data is also contaminated by measurement noise. The parameters and posterior distributions of the proposed model are estimated by utilizing the expectation maximization algorithm as well as particle filter. Since the integrals of posterior state estimation cannot be derived analytically due to nonlinearity, a bank of weighted particles is utilized to approximate the states. The efficacy of the proposed model is demonstrated by simulation and experimental studies. Finally, the proposed robust modeling method is compared with three other robust modeling methods through comparison of mean absolute error (MAE) and mean relative error (MRE) values. The results demonstrate that the proposed method achieves smaller MAE and MRE, indicating its superior robustness in handling both noisy input–output data and outlier-corrupted outputs.