A localized particle filter data assimilation method coupled with a Huber loss function
摘要
Traditional particle filters suffer from reduced computational efficiency and severe weight degeneracy in high-dimensional systems, leading to a decrease in particle diversity and affecting the accuracy of the posterior distribution. However, in data assimilation, the localized particle filter (LPF) is designed to address the curse of dimensionality in high-dimensional systems, thereby improving the computational efficiency and accuracy of the particle filter (PF), particularly when dealing with nonlinear and non-Gaussian systems. To address the limitations of conventional particle filters in high-dimensional, nonlinear, and non-Gaussian systems, this study proposes an adaptive optimization strategy for the LPF based on the Huber loss function. This method introduces a Huber loss function to enhance the robustness of the PF against outliers and optimize the weight update process to alleviate weight degeneracy. Additionally, the impact of the nonnegative parameter (threshold) of the Huber loss function on the algorithm’s performance is explored. Through observing system simulation experiments (OSSEs) conducted on the parameterized forced Lorenz-96 system, the effectiveness of the proposed algorithm is validated. The experimental results demonstrate that, compared to the standard LPF, the improved LPF algorithm achieves significant improvements in reducing the root mean square error (RMSE) and increasing the effective sample size, thereby enhancing the stability and accuracy of the data assimilation process. Particularly, when dealing with outliers and noisy data, the improved LPF exhibits stronger robustness and higher estimation accuracy.