Theoretical analysis of RAIM in the occurrence of simultaneous two-satellite faults

Most algorithms on receiver autonomous integrity monitoring (RAIM) are under the assumption of a single-satellite fault, because there is an extremely small probability that significant simultaneous multiple-satellite faults may occur. However, after the implementation of the Galileo system in a few years, there will be more satellites in view for the user to utilise together with GPS satellites, and a combination of them will bring better performance for RAIM. On the other hand, with the help of wide area augmentation system and the use of dual-frequency operation, pseudo-range errors will be reduced greatly. Thus, tighter alert limits are required for RAIM, and formerly ‘small’ errors should not be neglected. All of those factors make it necessary to consider simultaneous multiple-satellite faults. A detailed theoretical analysis of RAIM under the condition of two-satellite faults for both vertical and horizontal directions is presented. The characteristic/max slopes for every pair of satellites are then deduced in order to calculate the tighter vertical/horizontal protection level for RAIM.