Two Receiver Autonomous Integrity Monitoring (RAIM) architectures, Advanced RAIM (A-RAIM) and Relative RAIM (R-RAIM), are compared with two different RAIM algorithms, the Classic method and the Multiple Hypothesis Solution Separation (MHSS) method. The difference between A-RAIM and R-RAIM is in the positioning methods that produce different error models and projection matrices for integrity monitoring. The difference between RAIM algorithms lies in the methods of risk distribution. The influences of different positioning methods on integrity results are analysed in this paper via a generalized RAIM framework. Simulation results for the LPV-200 service with worldwide coverage show that the R-RAIM position domain method has the best results, while the differences between these methods decrease with application of the optimization method.