Bayesian Inference of GNSS Failures

The probability of failure (failure rate) is a key input parameter to integrity monitoring systems used for safety, liability or mission critical applications. A standard approach in the design of Global Positioning System (GPS) integrity monitoring is to utilize the service commitment on the probability of major service failure, often by applying a conservative factor. This paper addresses the question of what factor is appropriate by applying Bayesian inference to real and hypothetical fault histories. Global Navigation Satellite System (GNSS) anomalies include clock or signal transmission type faults which are punctual (may occur at any time) and incorrect ephemeris data which are broadcast for a nominal two hours. These two types of anomaly, classified as continuous and discrete respectively are addressed. Bounds on the total probability of failure are obtained with given confidence levels subject to well defined hypotheses relating past to future performance. Factors for the GPS service commitment of 10-5 per hour per satellite are obtained within the range two to five with high confidence (up to 1-10-9).

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