RAIM Fault Detection and Exclusion with Spatial Correlation for Integrity Monitoring

For safety-of-life applications used together with global navigation satellite systems, such as in civil aviation and autonomous driving, integrity is of paramount importance. Integrity monitoring protects the user safety based on two general approaches: mitigating large signal failures and bounding the residual errors. The fault detection and exclusion (FDE) of faulty satellites is part of the former approach. In the classical integrity monitoring algorithms in civil aviation, the use of test statistics based on least squares residuals relies on the assumption that the observations from different satellites are independent. When applied to urban environments with spatial correlation introduced by large multipath errors, a review of the FDE method is needed. With the optimal FDE method defined as the one with minimized integrity risk, we propose two optimization criteria for use in fault detection and fault exclusion. The optimal test statistics were obtained by analytical derivation for cases with and without correlations among different satellites. This method was theoretically compared with another commonly used test statistic using the minimum detectable bias, and it was numerically compared using the horizontal protection level under the scenario of advanced receiver autonomous integrity monitoring. The optimal test produces less conservative protection level results, and its advantage is especially obvious when the geometries are weak, or when the correlation coefficients among the satellites are high.