Adaptive Square-root Extended cubature Kalman filter based on Huber M−estimation for Multi-AUV cooperative navigation

In the complex ocean environment, the cooperative navigation of multiple Autonomous Underwater Vehicles (AUVs) encounters numerous challenges, including ocean current dynamics, multipath propagation, and time delays. These issues often result in abrupt state changes, non-Gaussian noise distributions, and loss of measurement information. To address these problems, this paper proposes an adaptive square-root extended cubature Kalman filter based on Huber M−estimation (SRAECKF-H). Initially, QR decomposition replaces Cholesky decomposition in the traditional adaptive extended cubature Kalman filter (AECKF) framework. This adjustment allows the matrix's square root to be directly propagated during the filtering process, thereby reducing errors associated with matrix operations. Subsequently, Huber M−estimation is employed to transform the measurement update process into a linear regression problem, enhancing the suppression of outliers and improving the robustness of the algorithm. We conduct a comprehensive performance evaluation of the SRAECKF-H under state mutations, non-Gaussian noise distributions, and measurement information loss. The experimental results reveal that the developed algorithm significantly improves positioning precision and robustness. The RMSE of positioning error is reduced by more than 20%. The positioning accuracy is improved by at least 40%, while the positioning precision shows an improvement of over 10%.