Evaluation Algorithm Based on Markov Process for GPS Per-slot and Constellation Availability

In civil aviation and other navigation application fields, the per-slot availability and constellation availability of global positioning system (GPS) is a key indicator to evaluate the performance of GPS. In this paper, the per-slot availability and constellation availability of GPS is evaluated and analyzed. Based on Markov process, the model of per-slot availability is set up. In this model, the failure rate and restoration rate of per-slot are taken into account. Moreover, combined with the backup situation of satellites, the constellation availability evaluation models of signal-in-space (SIS) and service are proposed. Based on the above evaluation models, the performance of GPS per-slot availability and constellation availability are evaluated by using the measured data. The results show that GPS per-slot availability and constellation availability have had a very high availability probability. The per-slot availability probability is larger than 0.998. And the constellation availability probability of SIS and service can respectively reach 0.999 999 963 and 0.955 3 respectively when there is no faulted satellites. Meanwhile, the results are instructive for the study of the availability performance evaluation of global BeiDou Navigation Satellite System (BDS).