Distribution of Test Statistic for Euclidean Distance Matrices

TL;DR

This paper derives the distribution of a test statistic used in satellite fault detection with Euclidean Distance Matrices, enabling practical application by matching theoretical and empirical distributions.

Contribution

It provides the first derivation of the test statistic's distribution, facilitating its use in fault detection methods.

Findings

Theoretical distribution closely matches simulated data.

Derivation enables practical fault detection in satellite navigation.

Supports improved reliability of Euclidean Distance Matrix methods.

Abstract

Methods for global navigation satellite system fault detection using Euclidean Distance Matrices have been presented recently in the literature. Published methods define a test statistic in terms of eigenvalues of a certain matrix, but the distribution of the test statistic was not known, which presented a barrier to practical implementation. This document was a personal correspondence from Beatty to Derek Knowles. It includes a brief derivation of the distribution of the test statistic and a representative case showing that the theoretical distribution closely matches a simulated empirical distribution.