A Novel Heavy-Tailed Mixture Distribution Based Robust Kalman Filter for Cooperative Localization

Abstract

In cooperative localization for autonomous underwater vehicles (AUVs), the practical stochastic noise may be heavy-tailed, and nonstationary distributed because of acoustic speed variation, multipath effect of acoustic channel, and changeable underwater environment. To address such noise, a novel heavy-tailed mixture (HTM) distribution is first proposed in this article, and then expressed as a hierarchical Gaussian form by employing a categorical distributed auxiliary vector. Based on that, a novel HTM distribution based robust Kalman filter is proposed, where the one-step prediction, and measurement likelihood probability density functions are, respectively, modeled as an HTM distribution, and a Normal-Gamma-inverse Wishart distribution. The proposed filter is verified by a lake experiment about cooperative localization for AUVs. Compared with the cutting-edge filter, the proposed filter has been improved by 50.27% in localization error but no more than twice computational time is required.