A novel variational robust filter with Gaussian mixture model for unknown non-Gaussian noises

In numerous practical applications, the presence of unpredictable abnormal behaviors often leads to random measurement outliers, causing the random measurement noises are no longer Gaussian but unknown non-Gaussian distributions, and it is intractable to obtain accurate a priori information about the noises. To address this challenge and enable nonlinear state estimation under such measurement noises, we propose a novel robust filter based on Gaussian mixture model (GMM). Firstly, a GMM is introduced to model the unknown non-Gaussian measurement likelihood probability density function (ML-PDF). Without relying on any prior noise statistics, the GMM can accurately model the ML-PDF utilizing a set of model parameters adaptively learned by the variational Bayesian (VB) method. Then, considering the high computational burden associated with the existing variational iterative process, we develop an improved VB method, which independently calculates the posterior distributions of state and unknown model parameters, thereby improving the computational efficiency. Finally, a new robust filter is derived by integrating the GMM with the improved VB approach, The effectiveness and superiority of the filter are demonstrated through both numerical simulations and real-world data analysis.