A Novel Heavy-Tailed Kalman Filter Based on Normal-Exponential-Gamma Distribution

We focus on state estimation in linear systems characterized by Gaussian process noise and heavy-tailed measurement noise. In the state space model, we assume that process noise obeys a Gaussian distribution with known covariance, while measurement noise obeys a Normal-Exponential-Gamma (NEG) distribution with unknown parameters. Therefore, Gaussian and NEG distributions are used to model predicted and likelihood probability density functions, respectively. We then employ joint posterior density and variational Bayesian methods to approximately obtain the state and parameters estimated results. The results of the target tracking simulation and loosely coupled inertial measurement unit (IMU)/Ultra-Wideband (UWB) positioning experiment verify the superiority of the proposed algorithm.