Robust Kalman filtering with Moving Horizon Estimation and multivariate Laplace modeling

This study introduces a novel approach for state estimation in linear systems impacted by measurement outliers. By analyzing measurement information within a time window, the method enhances measurement utilization efficiency, leading to more accurate identification and mitigation of outliers. Noise is modeled as a Multivariate Laplace (ML) distribution, which effectively avoids the complexity of estimating the degrees of freedom (DOF) parameter. Moreover, the integration of the Variational Bayesian (VB) method with Moving Horizon Estimation (MHE) enables joint inference of unknown parameters, increasing the flexibility and accuracy of the noise model while improving the system's robustness against outliers. Simulation results show that the proposed algorithm outperforms existing methods in both effectiveness and robustness when handling outliers.