Hierarchical Variational Bayesian Cooperative Positioning with Position Protection Level-Based Equivalent Ranging Noise

Inspired by collective navigation and information-sharing behaviors in animal groups, the leader–follower architecture provides a promising framework for cooperative navigation among multiple unmanned underwater vehicles (UUVs). In this architecture, follower UUVs utilize navigation information provided by leader UUVs, whose positioning uncertainty may degrade cooperative positioning performance. To address the positioning uncertainty of leader UUVs and the non-stationary heavy-tailed acoustic ranging noise, a hierarchical variational Bayesian cooperative positioning algorithm with leader-UUV position protection level (PPL)-based equivalent ranging noise is proposed. First, a PPL computation method under the multiple-fault assumption is developed to construct the equivalent ranging noise. Then, the acoustic ranging noise is modeled using Student’s t and inverse Wishart (STIW) mixture distribution. Finally, the acoustic ranging noise is retained as an auxiliary latent variable in the variational inference to avoid the covariance coupling caused by marginalization of the equivalent and acoustic ranging noise components. This preserves the conditional conjugacy of the hierarchical probabilistic model and enables joint posterior estimation of the navigation state and distribution parameters. Multiple sets of simulations and outdoor near-surface underwater experiments have validated the effectiveness of the proposed algorithm. In the outdoor near-surface underwater experiments, the root mean square error calculated from the positioning error of the proposed algorithm was 6.56 m, representing reductions of 17.4% and 16.4% compared with the variational Bayesian adaptive Kalman filter and the STIW-based variational Bayesian filter, respectively.