Imaging a moving point source in R^3 from the time of arrival at sparse observation points
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866916866932342784 |
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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 |