A novel robust Kalman filter with unknown non-stationary heavy-tailed noise

Abstract

In this article, the state estimation with unknown non-stationary heavy-tailed process and measurement noises (HPMN) is considered. The measurement likelihood and the one-step state prediction are modelled as the mixture of two Gaussian (M2G) distributions, respectively. In the proposed M2G, one is a high probability Gaussian distribution with a nominal covariance and the other is a low probability Gaussian distribution with an adaptive large covariance. The adaptive large covariance is formulated as the nominal covariance multiplied by a time varying scale parameter. An indicator is introduced to identify whether it is generated by the nominal covariance or the larger covariance. The unknown nominal covariance is modelled as an inverse Wishart distribution. Using hierarchical priors on the indicator and scale parameter, a robust model is formulated and a variational Bayesian algorithm is developed. Experiments with synthetic data and real intelligent vehicle data show the effectiveness of the proposed filter under unknown non-stationary HPMN.