– This paper aims to develop and analyse a new multiple-hypothesis receiver autonomous integrity monitoring (RAIM) algorithm. The proposed algorithm can handle simultaneous multiple failures as well as a single failure.

– The proposed algorithm uses measurement residuals and satellite observation matrices of several consecutive epochs for failure detection and exclusion. It detects failures by monitoring the error vector itself instead of monitoring the projection of the error vector. The algorithm reduces the minimum detectable bias via the relative receiver autonomous integrity monitoring (RRAIM) scheme.

– The algorithm is able to detect any instance of multiple failures, including failures that are not detected by the conventional RAIM algorithm. It is able to detect multiple failures with magnitudes of several tens of meters, although the algorithm has to solve an ill-conditioning problem. The detection capability of the proposed algorithm is not dependent on satellite geometry.

– The algorithm assumes that the error vectors in three consecutive epochs have biases of similar magnitude. As a result, although the algorithm detects occurrences of drifting error, it cannot identify which measurement(s) has the critical error.

– The paper includes implications for the development of the RAIM algorithm for aviation users. Especially, it can be a candidate for future standard architecture in multiple constellations, multiple frequency satellite-based augmentation system (SBAS) users.

– The paper proposes a new multiple-hypothesis RAIM algorithm with an RRAIM concept. A detailed explanation of the algorithms, including rigorous mathematical expressions, is presented. The paper also includes an analysis of differences in detection capability between conventional algorithm and the proposed algorithm depending on satellite geometry.