Quaternion Domain Super MDS for 3D Localization

Fuente: arXiv
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Main Authors: Masuoka, Keigo, Takahashi, Takumi, de Abreu, Giuseppe Thadeu Freitas, Ochiai, Hideki
Format: Preprint
Published: 2025
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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