A Novel Cooperative Positioning Algorithm Based on Variational Bayesian Filter via Student's t and Inverse Wishart Mixture Distribution

The cooperative positioning technology based on hydroacoustic ranging sensors and inertial navigation sensors has become a critical development priority for multiple unmanned underwater vehicles (UUVs) system. However, due to the multipath effect of acoustic signals and dynamic variations of the marine environment, time-varying noise and outliers are prone to occur in hydroacoustic ranging measurements. This results in non-stationary and heavy-tailed characteristics in hydroacoustic ranging noise, rendering traditional Gaussian-assumption-based algorithms ineffective. Consequently, we propose a cooperative positioning algorithm based on variational Bayesian filter via Student's t and inverse Wishart (IW) mixture distribution. Firstly, a cooperative positioning model considering spatial offsets between hydroacoustic sensors and inertial navigation sensors is established. Secondly, to address the heavy-tailed nature of ranging noise, it is modeled using a Student's t distribution, while the IW distribution is employed to model the scale matrix, characterizing the non-stationarity of channel. Finally, probabilistic estimation of both system states and distribution parameters is jointly performed using the variational Bayesian approach. Simulations and unmanned vehicles cooperative experiments demonstrate the effectiveness of the proposed algorithm, showing 51.0% and 20.7% reductions in positioning error compared with variational Bayesian adaptive Kalman filter respectively.