A novel switching Gaussian-heavy-tailed distribution based robust fixed-interval smoother

In nonlinear systems, the stochastic process and measurement noises may be non-stationary heavy-tailed distribution due to the dynamic outliers induced by unreliable sensors and complicated environments. The main purpose of this paper is to address the problem by establishing a new switching Gaussian-heavy-tailed (SGHT) distribution. We model the noise with the help of switching between the Gaussian and the newly designed heavy-tailed distribution. Then, utilizing two auxiliary parameters satisfying categorical and Bernoulli distributions respectively, we construct the SGHT distribution as a hierarchical Gaussian presentation. Furthermore, applying variational Bayesian inference, a novel SGHT distribution based robust fixed-interval smoother is derived. The experiment results of the synthetic data and real vehicle localization dataset demonstrate the superior performance of the proposed smoother as compared with cutting-edge smoother.