Fuzzy adaptive bounded fraction non-Gaussian filter

In this paper, a novel non-Gaussian filter named the fuzzy adaptive bounded fraction non-Gaussian filter (FABFF) is proposed for addressing the filtering problem of linear non-Gaussian systems. The proposed filter integrates a robust loss function with a fuzzy membership function. First, a bounded fraction loss function is designed, which exhibits high robustness and numerical stability, effectively mitigating the impact of outliers. In addition, an adaptive parameterization scheme is developed based on the sample error for the bounded fraction loss function, which achieves a balance between the filtering accuracy and real-time performance compared to approaches using fixed parameters. Second, a novel weighted cost function is designed by incorporating sample weights, thereby improving the filtering accuracy compared to the cost function using average weights. The sample weights are determined based on the degrees of abnormality of each sample, which is quantified through a fuzzy membership function. By applying the fixed-point iterative method, the new cost function is solved, and FABFF is obtained. Subsequently, the performance of the bounded fraction loss function, the computational complexity, and the convergence of the proposed algorithm are analyzed. Finally, simulation results are presented to validate the effectiveness of the proposed algorithm.