Robust Adaptive Hammerstein Filtering for Censored Regression under Contaminated Gaussian Noise

This paper extends the traditional Hammerstein system to a censored regression (CR) model, studying the issue of robust adaptive filtering for censored data in contaminated Gaussian (CG) noise environment. Outliers and data truncation are critical challenges in engineering environments, where the CG distribution is usually employed to model system noise with outliers. To tackle the issue of data truncation, a cost function is constructed to recover censored data and solve the parameter estimation problem, by utilizing the maximum likelihood (ML) method. This approach enables the implementation of a robust adaptive filtering algorithm for the censored Hammerstein system, effectively compensating for computational biases caused by censored data. The robust method integrates issues of CG noise and censored data, and the theoretical analysis of the proposed algorithm is performed focusing on the convergence and mean-square performance. Finally, the correctness of the theoretical analysis is validated and the effectiveness of this method is verified through CR in system identification, nonlinear acoustic echo cancellation (NAEC) and aerospace electrohydraulic servovalves (AES) applications under CG noises.