Next Article in Journal
The Reliability of Offshore Jacket Platforms Based on Bayesian Calibration
Previous Article in Journal
Assessing the Environmental Impact of Deep-Sea Mining Plumes: A Study on the Influence of Particle Size on Dispersion and Settlement Using CFD and Experiments
Previous Article in Special Issue
Quasi-Infinite Horizon Nonlinear Model Predictive Control for Cooperative Formation Tracking of Underactuated USVs with Four Degrees of Freedom
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A Novel Cooperative Navigation Algorithm Based on Factor Graph and Lie Group for AUVs

1
National Key Laboratory of Science and Technology on Underwater Acoustic Antagonizing, Shanghai 201108, China
2
Shanghai Marine Electronic Equipment Research Institute, Shanghai 201108, China
3
School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
*
Author to whom correspondence should be addressed.
J. Mar. Sci. Eng. 2025, 13(10), 1988; https://doi.org/10.3390/jmse13101988
Submission received: 8 September 2025 / Revised: 13 October 2025 / Accepted: 14 October 2025 / Published: 16 October 2025
(This article belongs to the Special Issue Autonomous Marine Vehicle Operations—3rd Edition)

Abstract

Traditional cooperative navigation algorithms for multiple AUVs are typically designed for a single specific configuration, such as parallel or leader-slave. This paper proposes a novel cooperative navigation algorithm based on factor graph and Lie group to address the multi-AUV localization problem, which is applicable to various multi-AUV configurations. First, the motion state of an AUV is represented within the two-dimensional special Euclidean group (SE(2)) space from Lie theory. Second, the motion of the AUV and acoustic-based range and bearing measurements are modeled to derive the motion error function and the range and bearing error function, respectively. Depending on the formulation of the motion error function, the proposed approach comprises two methods: Method 1 and Method 2. Third, the Gauss-Newton method is employed for nonlinear optimization to obtain the optimal estimates of the motion states for all AUVs. Finally, a parameter-level simulation system for AUV cooperative navigation is established to evaluate the algorithm’s performance under two different multi-AUV configurations. Method 1 is designed for parallel configurations, reducing the average RMSE of position and orientation errors by 29% compared to the EKF. Method 2 is tailored for leader-slave configurations, reducing the average RMSE of position and orientation errors by 38% compared to the EKF. Simulation results demonstrate that the proposed algorithm achieves superior performance across different AUV configurations compared to conventional EKF-based approaches.
Keywords: factor graph; Lie group; cooperative navigation factor graph; Lie group; cooperative navigation

Share and Cite

MDPI and ACS Style

Liu, J.; Bu, X.; Wu, C. A Novel Cooperative Navigation Algorithm Based on Factor Graph and Lie Group for AUVs. J. Mar. Sci. Eng. 2025, 13, 1988. https://doi.org/10.3390/jmse13101988

AMA Style

Liu J, Bu X, Wu C. A Novel Cooperative Navigation Algorithm Based on Factor Graph and Lie Group for AUVs. Journal of Marine Science and Engineering. 2025; 13(10):1988. https://doi.org/10.3390/jmse13101988

Chicago/Turabian Style

Liu, Jiapeng, Xiaodong Bu, and Chao Wu. 2025. "A Novel Cooperative Navigation Algorithm Based on Factor Graph and Lie Group for AUVs" Journal of Marine Science and Engineering 13, no. 10: 1988. https://doi.org/10.3390/jmse13101988

APA Style

Liu, J., Bu, X., & Wu, C. (2025). A Novel Cooperative Navigation Algorithm Based on Factor Graph and Lie Group for AUVs. Journal of Marine Science and Engineering, 13(10), 1988. https://doi.org/10.3390/jmse13101988

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop