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.
摘要
本文利用全球定位系统 (GPS) 与海洋水面载具的机动性, 研究了无人水面航行器 (USV) 与自主水下航行器 (AUV) 间的导航问题, 提出一种基于USV轨迹优化的移动AUV状态估计方法。 通过分析多普勒效应对单一水面USV接收的声学信号到达频率 (FOA) 的影响, 可同步估计AUV的位置与速度, 提供了一种不需要时间同步的鲁棒解决方案。 此外, 通过动态调整USV轨迹来构建最优的USV–AUV测量几何构型, 从而提高AUV的可观测性并提升状态估计性能。 该方法的创新点是一个基于Cramér–Rao下界 (CRLB) 进行可观测性分析与几何约束的定制化成本函数。 该函数整合了: (1) CRLB——用于优化系统可观测性, 从而提高估计精度; (2) 距离项——确保USV与AUV保持适当距离; (3) 转向率项——用于调整USV航向以增强跟踪能力。 采用粒子群优化算法对该成本函数进行最小化求解, 通过多组件平衡实现稳健的AUV跟踪框架。 我们通过全面仿真验证了USV轨迹复杂度、AUV下潜深度、测量频率、数据丢包率及噪声水平等不同因素对导航性能的潜在影响。 仿真结果表明, 所提方法在AUV状态估计与跟踪方面具有显著有效性。
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The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Authors and Affiliations
Contributions
Wen XU conceptualized the study, acquired the funding, and administered the project. Huarong ZHENG and Wen XU supervised the research. Sitian WANG proposed the methodology, developed the software, performed the visualization, and drafted the paper. Huarong ZHENG and Jianlong LI validated the results. Huarong ZHENG and Wen XU reviewed and finalized the paper.
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All the authors declare that they have no conflict of interest.
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Project supported by the National Natural Science Foundation of China (Nos. 42227901 and 62473332)
List of supplementary materials
1 Sequential EKF process
2 Fisher information matrix for AUV state estimation
3 Optimal USV trajectory planning for AUV state estimation
4 Parameter selection and sensitivity analysis for the cost function
5 Simulation parameters and experimental setup
6 Comparative analysis of USV trajectory performance
Table S1 Parameter sensitivity analysis in Case 1
Table S2 Default parameters for the USV–AUV navigation
Table S3 Default noise standard deviations
Table S4 Initial USV state settings for the simulation
Figs. S1–S4 Relationship between the USV’s velocity direction (relative to the x-axis) and the sum of the FIM diagonal elements under varying relative positions
Fig. S5 AUV trajectories in Cases 1–5
Fig. S6 Four USV specific trajectories labeled for the true AUV trajectory in Case 3
Figs. S7–S9 USV moves along the optimized trajectory and the four specific trajectories in Cases 1, 3, and 5
Fig. S10 USV speed control inputs
Fig. S11 USV turning rate control inputs
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Frequency of arrival-based state estimation and trajectory optimization for the navigation of autonomous marine vehicles
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Wang, S., Zheng, H., Li, J. et al. Frequency of arrival-based state estimation and trajectory optimization for the navigation of autonomous marine vehicles. Front Inform Technol Electron Eng 26, 2000–2015 (2025). https://doi.org/10.1631/FITEE.2500235
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DOI: https://doi.org/10.1631/FITEE.2500235
Key words
- Frequency of arrival
- Rolling horizon estimation
- Trajectory optimization
- Unmanned surface vehicles
- Autonomous underwater vehicles
- Navigation