A novel dynamic outlier-robust Kalman filter with Moving Horizon Estimation

The existence of dynamic outliers poses a significant challenge to the Kalman filter (KF). In addressing this challenge, this paper presents an innovative solution: Firstly, by analyzing a period of measurement information to more accurately identify state and measurement dynamic outliers, the system's capacity to adapt to dynamic changes is significantly improved. Next, noise is modeled as a Gaussian-Student's t mixture distribution (GSTM), with mixed model parameters inferred using the variational Bayesian (VB) method based on measurement information, cleverly integrated into the Moving Horizon Estimation (MHE) framework, thus enhancing the flexibility and accuracy of the noise model. Lastly, the optimal window size was identified through simulation experiment analysis to further increase the estimation accuracy. Simulation results demonstrate that the proposed filter exhibits stronger robustness in resisting dynamic outliers compared to existing filters.