Solution separation versus residual-based RAIM

Future multi-constellation Global Navigation Satellite Systems (GNSS) will offer the possibility to fulfill stringent navigation integrity requirements using Receiver Autonomous Integrity Monitoring (RAIM). This paper presents a detailed comparison of residual-based (RB) and solution separation (SS) RAIM. A complete step-by-step derivation of the two methods, which is currently missing in the literature, is given for the detection of single and multi-measurement faults, starting from common definitions of the integrity and continuity risks. In addition, a parity-space representation of SS RAIM is developed. It is shown that the integrity monitoring performance of SS RAIM can be superior to RB RAIM because SS test statistics are tailored to the fault hypotheses, and to the state of interest. However, for practical reasons of computational efficiency in conventional SS implementations, which are fully detailed in the paper, RB RAIM ultimately provides tighter bounds on integrity risk.