Detecting Multi-Dimensional Threats: a Comparison of Solution Separation Test and Uniformly Most Powerful Invariant Test

Integrity for GNSS (Global Navigation Satellite Systems) at user level is monitored by means of RAIM (Receiver Autonomous Integrity Monitoring) algorithms. Most RAIM algorithms are based on detection tests, which are able to detect and identify possible anomalies in the measurements and eventually exclude suspected measurements from the position solution or forward a warning to the pilot. In this paper the two most commonly used tests, the standard Uniformly Most Powerful Invariant (UMPI) test and the Solution Separation (SS) test, are compared and differences are pointed out, both from a general statistical point of view and a more specifically integrity point of view. The detection regions of the two methods are compared and a numerical example is provided. The results show that the two methods are equivalent in case the anomaly or threat model has only one dimension, whereas differences arise in case of multi-dimensional threats.