A Novel Mixture Distributions-Based Robust Kalman Filter for Cooperative Localization

In cooperative localization for autonomous underwater vehicles (AUVs), the practical state and measurement noises may be non-stationary non-Gaussian distributed because of sensor outliers, multi-path effect of acoustic channel, and changeable underwater environment. In this paper, a couple of novel mixture distributions, i.e., the Gaussian-Slash mixture distribution and the Gaussian-generalized hyperbolic skew Student's t mixture distribution, are proposed to model such state and measurement noises, respectively. By introducing two Bernoulli distributed random variables, both the proposed mixture distributions can be expressed as hierarchically Gaussian forms. Based on this, a novel mixture distributions based robust Kalman filter (MDRKF) is derived by exploiting the variational Bayesian inference. A lake experiment about the cooperative localization for AUVs demonstrated that the proposed MDRKF has better localization accuracy but higher computational complexity than the existing state-of-the-art filtering algorithms.