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