A note on Global Positioning System (GPS) and Euclidean distance matrices

2025/07/06 by Alfakih, A. Y.
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2507.04358

Abstract

Let D be an n × n Euclidean distance matrix (EDM) with embedding dimension r; and let d ∈ Rⁿ be a given vector. In this note, we consider the problem of finding a vector y ∈ Rⁿ, that is closest to d in Euclidean norm, such that the augmented matrix [ 0 · amp; y^T
y · amp; D] is itself an EDM of embedding dimension r. This problem is motivated by applications in Global Positioning System (GPS). We present a fault detection criterion and three algorithms: one for the case n=4, and two for the case n ≥ 5.

Citations

• Satellite Autonomous Clock Fault Monitoring with Inter-Satellite Ranges Using Euclidean Distance Matrices
• Distribution of Test Statistic for Euclidean Distance Matrices
• Julia: A Fresh Approach to Numerical Computing
• Julia: A Fresh Approach to Numerical Computing
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• Explicit Sensor Network Localization using Semidefinite Representations and Facial Reductions

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