Localization Uncertainty Estimation for Autonomous Underwater Vehicle Navigation

High-precision positioning capability is a crucial technology for achieving accurate navigation in autonomous underwater vehicles (AUVs). However, due to severe electromagnetic wave attenuation underwater and the unavailability of the global positioning system (GPS), inertial-navigation-based dead reckoning is considered the primary method for underwater positioning. Unfortunately, errors accumulated during the navigation process lead to unbounded drift, and filtering-based methods have been used to mitigate the errors, but with limited success. In this paper, we propose a precise underwater dead-reckoning mathematical model that recursively calculates the ground truth and corresponding errors based on an AUV’s motion model, and we derive empirical formulas. Compared to related methods, this approach not only models the cumulative errors of relative noise measurements, but also provides recursive expressions with corresponding statistical moments. The experimental results demonstrate that this formula significantly reduces positioning errors in underwater navigation tasks.