A Novel Robust Kalman Filter Based on Normal-Bernoulli Distribution for Non-Stationary Heavy-Tailed Measurement Noise

In this paper, the state estimation problem with non-stationary heavy-tailed measurement noise (NHMN) is considered. The mixture of two Gaussian distributions, with a Bernoulli random variable, is expressed as an exponential multiplication form, which we refer to as the Normal-Bernoulli (NB) distribution. We utilize the marginalization of the NB (MNB) distribution to model NHMN, leading to the derivation of a robust NB-based Kalman filter that does not require any iterative process. In contrast to conventional algorithms, the analytical closed-form solutions for the states and modeling distribution parameters are derived by using Bayes’ rule and minimizing the Kullback-Leibler divergence. The first two order moments of MNB-distributed state posterior are then calculated as filtering outputs. Simulation results demonstrate the superiority of the proposed filter in terms of estimation accuracy, consistency, and computational complexity under NHMN.