Adaptive Kalman Filters Based on Elliptically Contoured Distributions for Heavy-Tailed and Nonstationary Measurement Noises

Traditional Kalman filters (KF) struggle with heavy-tailed (HTMN) and non-stationary (NSMN) measurement noise. To address these issues, we propose two adaptive Kalman filters based on elliptically contoured (EC) distributions, enhancing the accuracy of state estimation. First, we develop a numerical fitting method to obtain the parameterized expression of the weighting function for the exponential elliptically contoured (EEC) distribution. Building on this method, we introduce a variational Bayesian adaptive Kalman filter based on EC distributions (VBAKF-EC) to effectively handle HTMN. By integrating VBAKF-EC into the interacting multiple model (IMM) framework, we propose another adaptive filter (IMM-VBEC) capable of autonomously selecting EC distributions for NSMN. The proposed VBAKF-EC under HTMN and IMM-VBEC under NSMN were evaluated in two independent target tracking scenarios. Relative to the top-performing comparison method in each scenario: VBAKF-EC (with EEC distribution) achieved a 2.1% reduction in average position error compared to the robust Student’s t-based KF (RSTKF), despite a 0.15% increase in average velocity error; IMM-VBEC reduced the average position error by 0.21% and average velocity error by 4.2% compared to the IMM filter with Pearson Type VII (IMM-PTVII). The proposed algorithms exhibit significant scalability for extension to heavy-tailed and non-stationary process noise.