Robust Student’s <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math> </inline-formula>-Based Cooperative Navigation for Autonomous Underwater Vehicles

Abstract

A robust leader–slave cooperative navigation (CN) algorithm for autonomous underwater vehicles (AUVs) based on the Student’s $t$ extended Kalman filter (SEKF) is proposed. Compared with the conventional EKF based on a Gaussian distributed noise assumption, which has been widely used in the field of CN, the Student’s $t$ -based filtering algorithms show an improved robustness against outliers existing in the process and measurement noises. The utilization of the Student’s $t$ distribution can minimize the negative effect induced by the outliers existing in the underwater acoustic communication system and the cheap but unreliable dead reckoning sensors equipped on the slave AUVs. After a detailed derivation of the robust CN algorithm based on the SEKF, two approximation methods that are required in the Student’s $t$ -based filter are discussed and compared. Simulation results show the efficiency and superiority of the robust SEKF-based leader–slave CN algorithm as compared with the conventional EKF-based CN algorithm. The validity of the proposed CN algorithm is also evaluated on field trial data, and the performance of different degrees of freedom (DOF) values, which determine the tail behavior of the Student’s $t$ distribution is compared and analyzed, and then the link between the DOF value and the robust effect of the Student’s $t$ distribution is revealed, which will act as a guide when applying the Student’s $t$ -based filter in the field of CN.