Numerous methods have been proposed for global navigation satellite system (GNSS) receivers to detect faulty GNSS signals. One such fault detection and exclusion (FDE) method is based on the mathematical concept of Euclidean distance matrices (EDMs). This paper outlines a greedy approach that uses an improved Euclidean distance matrix-based fault detection and exclusion algorithm. The novel greedy EDM FDE method implements a new fault detection test statistic and fault exclusion strategy that drastically simplifies the complexity of the algorithm over previous work. To validate the novel greedy EDM FDE algorithm, we created a simulated dataset using receiver locations from around the globe. The simulated dataset allows us to verify our results on 2,601 different satellite geometries. Additionally, we tested the greedy EDM FDE algorithm using a real-world dataset from seven different android phones. Across both the simulated and real-world datasets, the Python implementation of the greedy EDM FDE algorithm is shown to be computed an order of magnitude more rapidly than a comparable greedy residual FDE method while obtaining similar fault exclusion accuracy. We provide discussion on the comparative time complexities of greedy EDM FDE, greedy residual FDE, and solution separation. We also explain potential modifications to greedy residual FDE that can be added to alter performance characteristics.

翻译：针对全球导航卫星系统（GNSS）接收机检测故障信号的问题，已有多种方法被提出。其中一种基于欧氏距离矩阵（EDM）数学概念的故障检测与排除（FDE）方法备受关注。本文提出一种利用改进的欧氏距离矩阵故障检测与排除算法的贪婪方法。新型贪婪EDM FDE算法采用新的故障检测检验统计量和故障排除策略，相较于先前工作大幅简化了算法复杂度。为验证该算法，我们利用全球接收机位置构建仿真数据集，在2601种不同卫星几何构型下验证结果。此外，使用七款不同安卓手机采集的真实数据集对贪婪EDM FDE算法进行测试。在仿真和真实数据集上的实验表明，贪婪EDM FDE算法的Python实现版本在保持相近故障排除精度的同时，计算速度比同类型的贪婪残差FDE算法快一个数量级。本文还对比分析了贪婪EDM FDE、贪婪残差FDE和分离解法的计算时间复杂度，并探讨了可通过修改贪婪残差FDE算法来改变其性能特征的潜在方案。