Global Navigation Satellite Systems Fault Detection and Exclusion: A Parameterized Quadratic Programming Approach

Abstract

In this article, the problem of detecting and excluding faulty global navigation satellite systems (GNSSs) measurements at the receiver end is formulated as a parameterized quadratic programming (PQP) problem. Compared to the existing fault detection and exclusion (FDE) methods, which mostly rely on exhaustive search, the PQP method is computationally efficient for finding the outliers even when the number of outliers is moderate or large. In the context of multiconstellation GNSS where the probability of multiple simultaneous faults is increased, the PQP method is ideal for the task of fault exclusion since the computation time does not increase with the number of fault hypotheses. It is noted that this article addresses the computational load due to the exclusion function only. The integrity risk bound and continuity risk bound are of fundamental importance to assess the performance of FDE algorithms for safety-critical applications. With the aim to benefit safety-critical applications, the PQP method is integrated with the integrity risk bound and the continuity risk bound derived for FDE using Chi-squared receiver autonomous integrity monitoring (RAIM). It is emphasized that the integration of the PQP method and the integrity and continuity risk bounds do not make the PQP method a practical integrity monitoring method. This is because the computation of the integrity risk bound is still combinatorial and the resulting integrity risk bound is rather conversative. Instead, the integration allows for the opportunity to refine the PQP method so that it can be considered a practical integrity monitoring method. In particular, improvements to reduce the computational load for the Chi-squared RAIM FDE integrity risk bound calculation can readily be applied to the integrity risk bound calculation for the PQP method. Also, further research on PQP parameter tuning can be pursued to tighten the integrity risk bound.