On hypothesis testing in RAIM algorithms: generalized likelihood ratio test, solution separation test and a possible alternative

Integrity for GNSS-based navigation can be monitored at user level by means of RAIM (receiver autonomous integrity monitoring) algorithms. Most of these algorithms are based on statistical tests that are able to detect and identify outliers or other anomalies in the measurements, and then either exclude suspected measurements from the position solution or forward a warning to the user. In this paper the two statistical tests most commonly used in RAIM algorithms, the generalized likelihood ratio (GLR) test and the solution separation (SS) test, are compared. The main differences between the two tests are pointed out, in general statistical terms and in view of their use in integrity monitoring. As both tests are found not optimal for integrity monitoring, a new test is proposed that targets only the faults that represent a threat to the integrity. Simulation results are shown to substantiate the theoretical findings, and confirm the effectiveness of the new testing procedure.