Efficient Fault Detection and Exclusion for GNSS Receivers Using Greedy Euclidean Distance Matrix Algorithms
Core Concepts
This paper presents a greedy fault detection and exclusion algorithm using Euclidean distance matrices that outperforms greedy residualbased methods in computation time while maintaining high fault exclusion accuracy.
Abstract
The paper outlines a novel greedy approach that uses an improved Euclidean distance matrixbased fault detection and exclusion (FDE) algorithm for GNSS receivers. The key highlights are:

The paper introduces a new fault detection test statistic that uses the n+1 and n+2 eigenvalues of the Gram matrix, which provides a clearer indication of measurement faults despite noise.

The fault exclusion strategy identifies the satellite measurements most influencing the increasing n+1 and n+2 eigenvalues and greedily removes the measurement with the largest effect.

Experimental results on both a simulated dataset and a realworld dataset show that the greedy EDM FDE algorithm runs an order of magnitude faster than a comparable greedy residual FDE method while achieving similar fault exclusion accuracy.

The paper provides a detailed theoretical runtime complexity analysis, showing that greedy EDM FDE scales better than greedy residual FDE and solution separation FDE as the number of measurements and faults increase.

Several potential modifications to the greedy EDM FDE algorithm are discussed, such as removing multiple faults at once or automatically setting the detection threshold based on the noise characteristics of the measurements.
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Greedy Detection and Exclusion of Multiple Faults using Euclidean Distance Matrices
Stats
The number of satellite measurements available can exceed 48 in opensky conditions.
The simulated dataset includes 2,601 different satellite geometries across 9 global locations.
The realworld dataset includes 68 urban traces from 7 different Android phones.
Quotes
"The advent of LEO constellations will only increase the number of available PNT satellites."
"Solution separation is an excellent algorithm choice with some optimality guarantees for cases similar to aviation where the opensky condition of the receiver affords few faults and pseudorange measurements closely follow a known error distribution."
"Greedy EDM FDE outperforms greedy residual FDE in terms of computation time by an order of magnitude when averaged across all 68 realworld data traces."
Deeper Inquiries
How could the greedy EDM FDE algorithm be further optimized to reduce computation time, such as by parallelizing the eigenvalue decomposition or using a more efficient matrix decomposition method
To further optimize the greedy EDM FDE algorithm for reduced computation time, several strategies can be implemented. One approach is to parallelize the eigenvalue decomposition process, which can significantly speed up the computation by distributing the workload across multiple cores or processors. By leveraging parallel computing techniques, the algorithm can exploit the capabilities of modern multicore systems to perform the eigenvalue decomposition step more efficiently.
Another optimization strategy is to utilize more efficient matrix decomposition methods that can reduce the computational complexity of the algorithm. For example, using specialized algorithms or libraries optimized for eigenvalue decomposition, such as the divide and conquer strategy implemented in LAPACK, can improve the speed of the computation. By selecting the most suitable matrix decomposition method and optimizing the implementation for performance, the greedy EDM FDE algorithm can achieve faster fault detection and exclusion while maintaining accuracy.
What are the potential drawbacks or limitations of the greedy approach compared to other FDE methods, and how could these be addressed
The greedy approach in the EDM FDE algorithm, while efficient in quickly identifying and excluding faulty measurements, may have limitations compared to other FDE methods. One potential drawback is the lack of optimality guarantees, as the greedy strategy aims to find a locally optimal solution in each iteration without considering the global optimum. This can lead to suboptimal fault exclusion decisions, especially in complex scenarios with multiple faults and noisy measurements.
To address this limitation, one possible solution is to incorporate a backtracking mechanism in the greedy algorithm to backtrack and reconsider previous decisions if a better solution is found later in the process. By introducing backtracking, the algorithm can explore alternative paths and potentially reach a more optimal fault exclusion outcome.
Additionally, the greedy approach may struggle with scalability when dealing with a large number of measurements and faults, as the iterative nature of the algorithm can become computationally intensive. One way to mitigate this limitation is to implement heuristics or adaptive strategies that dynamically adjust the threshold values or the number of faults removed in each iteration based on the complexity of the dataset. By incorporating adaptive mechanisms, the greedy EDM FDE algorithm can adapt to different scenarios and improve its performance in challenging environments.
How could the greedy EDM FDE algorithm be integrated with a temporal localization filter to leverage both the fast fault exclusion and the probabilistic guarantees of the filter
Integrating the greedy EDM FDE algorithm with a temporal localization filter can offer a comprehensive solution that combines fast fault exclusion with probabilistic guarantees. By leveraging the strengths of both approaches, the integrated system can provide efficient fault detection and exclusion while ensuring robust localization performance over time.
One way to integrate the algorithm with a temporal localization filter is to use the output of the EDM FDE as an input to the filter for refining the receiver's position estimate. The filter can incorporate the faultexcluded measurements from the EDM FDE to improve the accuracy and reliability of the localization solution. This integration can enhance the overall system's resilience to measurement faults and environmental disturbances.
Furthermore, the temporal localization filter can provide additional context and historical information to the greedy EDM FDE algorithm, enabling it to make more informed decisions about fault exclusion. By combining the realtime fault detection capabilities of the greedy approach with the longterm consistency checks of the filter, the integrated system can achieve a balance between speed and accuracy in fault mitigation.
Overall, integrating the greedy EDM FDE algorithm with a temporal localization filter can create a synergistic solution that capitalizes on the strengths of both methods, leading to enhanced performance and reliability in GNSS fault detection and exclusion.