Fast Multiple Fault Exclusion with a Large Number of Measurements

Juan Blanch, Todd Walter, Per Enge

Abstract: In this paper we describe two methods to exclude faulty radio navigation measurements in a situation where there is a large number of measurements (>20) and the probability that any measurement might be faulty is very high (50% and more). This situation can arise in many applications, as in the case of multiple GNSS measurements in an urban environment, when using terrestrial range measurements (and therefore very prone to be affected by multipath), or when using signals of opportunity (which might have faulty or not calibrated clocks). Previous work in fault detection for radio navigation has focused in the ability of fault detection methods to detect the outlier measurements [1]. In this work we will first argue that finding the outliers is actually not an issue in the sense that there is a known algorithm that provides an optimal exclusion option (under some assumptions) [3]. This algorithm consists in evaluating all the subsets of measurements for consistency and in choosing the best consistent subset (under some sense). However, this algorithm relies on a combinatorial search which can become intractable as the number of measurements increases. It is therefore useful to develop methods that can achieve the performance of the combinatorial search at a lower computational cost. In this work, we study two simple and fast exclusion algorithms. The first one is based on a greedy search. In this algorithm the measurements are removed sequentially based on the size of the least squares residual. The second one is based on L1 norm minimization. For this purpose, we analyze the link between outlier exclusion and sparse signal recovery, for which there is a large body of work (compressed sensing) [5]. In particular, there are rigorous results on the sparsity promoting nature of L1 norm minimization [6]. Then, we test an implementation of fault detection using both algorithms. We will investigate examples based on two and four core GNSS constellations and attempt to answer the following two questions: how well does each of these algorithms approach the exhaustive algorithm.
Published in: Proceedings of the 2015 International Technical Meeting of The Institute of Navigation
January 26 - 28, 2015
Laguna Cliffs Marriott
Dana Point, California
Pages: 696 - 701
Cite this article: Blanch, Juan, Walter, Todd, Enge, Per, "Fast Multiple Fault Exclusion with a Large Number of Measurements," Proceedings of the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, California, January 2015, pp. 696-701.
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