Statistical Validation for GPS Integrity Test

Abstract

Having studied extensively the issues of alarm rates and detection probabilities, the GPS integrity community appears poised on the verge of a higher level of sophistication. Immediately upon recognizing that detection thresholds are set on the basis of perceived error parameters (e.g., sample variance), it becomes clear that those thresholds are random variables themselves. Thus even alarm and detection probabilities would be random. Upon initial reflection, characterization of probabilities themselves as random variables might seem an unnecessary escalation in level of abstraction—until one realizes that related issues have been faced countless times before. Indeed, the whole science of statistics is concerned with imperfect probabilistic representations, giving rise to concepts such as sample means and sample variances. As applied to receiver test, these concepts lead to confidence coefficients enabling integrity algorithm performance to be quantified with rigorous justification. Specific examples are investigated herein, and results are given for illustrative cases.