Heterogeneous mixed kernel correntropy-based robust iterative estimation methods and convergence analysis for the nonlinear system with outliers

In the era of big data and machine learning, system identification has become a critical area of study, particularly for nonlinear systems plagued by outliers. Traditional methods, such as least squares and gradient descent, often struggle with the presence of outliers, leading to inaccurate parameter estimations. This article addresses this challenge by introducing a heterogeneous mixed kernel correntropy-based robust iterative (HMKC-RI) algorithm. By combining the strengths of Gaussian and Cauchy kernels, the HMKC-RI algorithm adapts to data quality, reducing the influence of outliers and enhancing estimation accuracy. The article also presents a heterogeneous mixed kernel correntropy-based robust hierarchical iterative (HMKC-RHI) algorithm, which decomposes the identification model to alleviate computational burdens while maintaining robustness. Through rigorous convergence analysis and comparative simulations, the article demonstrates the superiority of the proposed algorithms over conventional methods. The simulations showcase the algorithms' ability to handle various types of outliers and complex data environments, making them a valuable tool for enhancing the adaptability and robustness of nonlinear system identification.