Quaternion Domain Super MDS for 3D Localization
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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_ | 1866912348964388864 |
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| author | Masuoka, Keigo Takahashi, Takumi de Abreu, Giuseppe Thadeu Freitas Ochiai, Hideki |
| author_facet | Masuoka, Keigo Takahashi, Takumi de Abreu, Giuseppe Thadeu Freitas Ochiai, Hideki |
| contents | We propose a novel low-complexity three-dimensional (3D) localization algorithm for wireless sensor networks, termed quaternion-domain super multidimensional scaling (QD-SMDS). This algorithm reformulates the conventional SMDS, which was originally developed in the real domain, into the quaternion domain. By representing 3D coordinates as quaternions, the method enables the construction of a rank-1 Gram edge kernel (GEK) matrix that integrates both relative distance and angular (phase) information between nodes, maximizing the noise reduction effect achieved through low-rank truncation via singular value decomposition (SVD). The simulation results indicate that the proposed method demonstrates a notable enhancement in localization accuracy relative to the conventional SMDS algorithm, particularly in scenarios characterized by substantial measurement errors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quaternion Domain Super MDS for 3D Localization Masuoka, Keigo Takahashi, Takumi de Abreu, Giuseppe Thadeu Freitas Ochiai, Hideki Signal Processing Robotics Metric Geometry We propose a novel low-complexity three-dimensional (3D) localization algorithm for wireless sensor networks, termed quaternion-domain super multidimensional scaling (QD-SMDS). This algorithm reformulates the conventional SMDS, which was originally developed in the real domain, into the quaternion domain. By representing 3D coordinates as quaternions, the method enables the construction of a rank-1 Gram edge kernel (GEK) matrix that integrates both relative distance and angular (phase) information between nodes, maximizing the noise reduction effect achieved through low-rank truncation via singular value decomposition (SVD). The simulation results indicate that the proposed method demonstrates a notable enhancement in localization accuracy relative to the conventional SMDS algorithm, particularly in scenarios characterized by substantial measurement errors. |
| title | Quaternion Domain Super MDS for 3D Localization |
| topic | Signal Processing Robotics Metric Geometry |
| url | https://arxiv.org/abs/2504.17890 |