Computational Aspects of Underwater and Underground Navigation Using Muons

Jaron Samson, Marnix F.L. Meersman, and Jose A. Garcia Molina

Peer Reviewed

Abstract:	Muons are charged particles which can penetrate matter such as rock and water, hereby allowing underwater and underground navigation. By time-tagging the detections of muons in a reference detector and in the user detector, the Time-of-Flight of muons can be calculated. A muon range can be computed by multiplying its Time-of-Flight with the speed of light. When having muon ranges to at least four reference detectors with known coordinates, the position and the clock error of the user can be calculated. In this paper, a laboratory tabletop set-up with three reference detectors has been used. This set-up allows a controlled assessment of muon signal processing techniques and muon positioning techniques. For muon signal processing, three methods are evaluated: the Constant Fraction Discriminator Method, the Peak Method, and a novel technique called the First Minimum Method. It is shown that the First Minimum Method is the preferred method in terms of performance. For muon positioning, the standard batch least-squares method is used. This approach led to many position outliers, which are shown to be caused by an ill-conditioned problem. These outliers are fully mitigated by applying Tikhonov regularization. In our laboratory set-up (using small detectors and a common time-frame), user position errors smaller than 30 centimeters (95% percentile) have been obtained. In a real underwater or underground campaign, the position errors are expected to be larger, especially when the user clock which is not synchronized to the clocks of the reference detectors.
Published in:	Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025) September 8 - 12, 2025 Hilton Baltimore Inner Harbor Baltimore, Maryland
Pages:	1704 - 1718
Cite this article:	Samson, Jaron, Meersman, Marnix F.L., Molina, Jose A. Garcia, "Computational Aspects of Underwater and Underground Navigation Using Muons," Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025), Baltimore, Maryland, September 2025, pp. 1704-1718. https://doi.org/10.33012/2025.20377
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In