Abstract: Using the Global Positioning System (GPS) and the mobility of marine surface vehicles, this paper addresses the navigation problem between unmanned surface vehicles (USVs) and autonomous underwater vehicles (AUVs). We propose a moving AUV state estimation method based on the trajectory optimization of the USV. In particular, by exploring the Doppler effect on the frequency of arrival (FOA) of the acoustic signals received by a single-surface USV, the position and velocity of the AUV can be estimated simultaneously, offering a robust solution that eliminates the need for time synchronization. Moreover, the USV trajectory is dynamically adjusted to achieve optimal USV–AUV measurement geometry, thereby improving the AUV's observability and enhancing state estimation performance. The innovation lies in a tailored cost function grounded in observability analysis via the Cramér–Rao lower bound (CRLB) and geometric constraints. It integrates (1) the CRLB to optimize system observability, thereby enhancing estimation accuracy, (2) a distance term to ensure that the USV maintains appropriate proximity to the AUV, and (3) a turning rate term that adjusts the USV's orientation to improve following capability. The cost function is then minimized using a particle swarm optimization algorithm, balancing these components to achieve a robust AUV tracking framework. We conduct comprehensive simulations to examine the potential influences of different factors, including the complexity of the USV trajectory, AUV depth, measurement frequency, packet loss rate, and noise levels, on navigation performance. Simulation results demonstrate the effectiveness of the proposed method in estimating and tracking the AUV.

Key words: Frequency of arrival; Rolling horizon estimation; Trajectory optimization; Unmanned surface vehicles; Autonomous underwater vehicles; Navigation

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