A Novel Moving Horizon Estimation-Based Robust Kalman Filter with Heavy-Tailed Noises

Abstract

The degree of freedom (DOF) parameter plays a crucial role in the Student’s t distribution as it affects the thickness of the distribution tails. Therefore, choosing an appropriate DOF parameter is essential for accurately modeling heavy-tailed noise. To improve estimation accuracy, this paper introduces a new robust Kalman filter based on moving window estimation to handle heavy-tailed noise. First, a sliding window based on Moving Horizon Estimation (MHE) is designed. By continuously utilizing the latest measurement information through the silding window, outliers that cause heavy-tailed noise can be better identified. Second, the noise is modeled as a Student’s t distribution, and an appropriate conjugate prior distribution is selected for the unknown noise covariance matrix. The Variational Bayesian (VB) method is combined with the proposed MHE framework to jointly infer the unknown parameters, updating the DOF parameter to a Gamma distribution. Finally, through simulation experiments, the optimal number of iterations and MHE window length are determined to ensure estimation accuracy while reducing computational complexity. The simulation results show that the proposed filtering algorithm exhibits better robustness in handling heavy-tailed noise compared to traditional filters.