Extreme value theory-based integrity monitoring of global navigation satellite systems

Abstract

Measurements consistency based Receiver Autonomous Integrity Monitoring (RAIM) is the main technique for monitoring the integrity of Global Satellite Navigation Systems (GNSS) at the user level. Existing RAIM algorithms utilize two tests, in the position domain a test for RAIM availability and in the measurement domain a test for failure detection. These tests involve the computation of three parameters: test statistic, decision threshold and protection level. The test statistic is based on the actual measurements in the form of the Sum of the Squared Errors (SSE). The decision threshold is chosen on the basis of the statistical characteristics of the SSE including the assumption that the errors are normally distributed. However, in practice residual error distributions exhibit heavier tails than predicted by the Gaussian model. Therefore, this paper challenges the normality assumption of the residual navigation errors in three ways. First, real data are used to assess its impact on the traditional RAIM algorithm. Second, Extreme Value Theory (EVT) is applied to the tails and the Generalized Extreme Value (GEV) distribution is derived to capture residual navigation errors. Third, the performance of the traditional RAIM approach is compared with that employing the GEV distribution. The results demonstrate that the GEV model is a more accurate representation of the distribution of residual navigation errors than the conventional Gaussian model and should be used in the development of integrity monitoring algorithms.

Vision-Aided RAIM: A New Method for GPS Integrity Monitoring in Approach and Landing Phase

“…The former is generally evaluated with the current observations only, while the latter uses both the current and historical measurements. Compared with the filtering method, the snapshot scheme is more widely used due to its faster response to sudden failures [ 25 , 26 ]. Given the measurement Equation (19), the weighted least-squares solution for the estimation of x ( k ) is given by: …”

GNSS/INS Integration with Integrity Monitoring for UAV No-fly Zone Management

“…Results show that the computed vertical protection levels are reduced by 50% without degrading integrity. Panagiotakopoulos et al [23] applied extreme value theory to the tails of position errors, and the generalized extreme value (GEV) distribution is derived to capture residual navigation errors. The results indicated that GEV is more powerful in characterizing the tails than Gaussian models when "blunder" errors are present.…”

Fault exclusion method for ARAIM based on tight GNSS/INS integration to achieve CAT‐I approach

“…The wrong exclusion means the excluded satellite is normal but it cannot pass the FD test (false alarm) and subset‐identifying test, it also means the failing satellite is not detected (miss detection) and excluded. The miss detection probability is set to 0.001 in [32, 33]. The wrong exclusion probability is set to 0.001 in [34].…”