用四元数域提升3D定位精度，抗测量误差更强
Quaternion Domain Super MDS for 3D Localization
- 将3D坐标转为四元数，融合距离与角度信息
- 构建秩1格拉姆边核矩阵，降噪效果显著提升
- 适合高噪声环境下无线传感器网络定位
我们提出一种新型低复杂度三维（3D）定位算法，称为四元数域超多维缩放（QD-SMDS）。该方法将原始在实数域构建的SMDS算法重构至四元数域。通过将3D坐标表示为四元数，该方法能够构建一个秩-1的格拉姆边核（GEK）矩阵，整合节点间的相对距离与角度（相位）信息，利用奇异值分解（SVD）进行低秩截断时最大化降噪效果。仿真结果表明，与传统SMDS算法相比，该方法在存在较大测量误差的场景下显著提升了定位精度。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。