Imaging a moving point source in R^3 from the time of arrival at sparse observation points

Fuente: arXiv
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Main Authors: Ma, Guanqiu, Zhang, Haonan, Guo, Hongxia
Format: Preprint
Published: 2025
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author Ma, Guanqiu
Zhang, Haonan
Guo, Hongxia
author_facet Ma, Guanqiu
Zhang, Haonan
Guo, Hongxia
contents In this paper, we introduce a novel numerical method for reconstructing the trajectory within three-dimensional space, where both the emission moment and spatial location of the point source are unknown. Our approach relies solely on measuring the time of arrival at five or seven properly chosen observation points. By utilizing the distinctive geometric configuration of these five or seven observation points, we establish the uniqueness of the trajectory and emission moment of the point source through rigorous mathematical proofs. Moreover, we analyze the stability of our proposed method. The effectiveness of the method is also verified by numerical experiments.
format Preprint
id arxiv_https___arxiv_org_abs_2507_20204
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Imaging a moving point source in R^3 from the time of arrival at sparse observation points
Ma, Guanqiu
Zhang, Haonan
Guo, Hongxia
Numerical Analysis
In this paper, we introduce a novel numerical method for reconstructing the trajectory within three-dimensional space, where both the emission moment and spatial location of the point source are unknown. Our approach relies solely on measuring the time of arrival at five or seven properly chosen observation points. By utilizing the distinctive geometric configuration of these five or seven observation points, we establish the uniqueness of the trajectory and emission moment of the point source through rigorous mathematical proofs. Moreover, we analyze the stability of our proposed method. The effectiveness of the method is also verified by numerical experiments.
title Imaging a moving point source in R^3 from the time of arrival at sparse observation points
topic Numerical Analysis
url https://arxiv.org/abs/2507.20204