Student's t-Based Robust Kalman Filter for a SINS/USBL Integration Navigation Strategy

In order to satisfy the requirements of the placement, the operation, and the high-precision navigation and positioning for the underwater vehicles and the underwater operational platform, a SINS/USBL integration navigation strategy is proposed. This paper presents a robust Student's t-based Kalman filter for strap-down inertial navigation system and ultra-short base line (SINS/USBL) integration system, which is proposed to suppress the measurement uncertainty induced by the acoustic outliers. Firstly, a SINS/USBL integration prototype system is designed and presented, which is constructed by an inertial measurement unit (IMU) and an USBL acoustic array in an inverted configuration, and they can be entirely designed and developed in-house. Furthermore, an improved robust Student's t-based Kalman filter with the degree of freedom (dof) parameter is proposed to better address the acoustic outliers in the measured range and directions information, the heavy-tailed measurement noise induced by the acoustic outliers can be modelled as a Student's t distribution, the posterior probability density functions (PDFs) of the state variable, the auxiliary random variable and the dof parameter are updated as Gaussian, Gamma, and Gamma prior PDF, respectively, and the corresponding statistics and the state vector are jointly inferred using the variational Bayesian (VB) approach. Finally, based on the state error equations and the derived measurement equation of SINS/USBL integration navigation system, the mathematical simulation test and the field trial are performed to demonstrate the feasibility and the superiority of the proposed SINS/USBL integration approach.