Advanced Receiver Autonomous Integrity Monitoring (ARAIM) based on multi-constellation of the Global
Navigation Satellite System (GNSS) has attracted more and more attention. The baseline ARAIM algorithm is based
on the Multiple Hypothesis Solution Separation (MHSS) method. With the development and perfection of GNSS,
the increased number of satellites leads to more fault hypothesis situations and subset solutions need to be evaluated.
This situation represents a severe challenge for receivers in terms of the computational load. Therefore, it is necessary to reduce the computational burden by reducing the number of monitoring subsets. In this paper, we propose a fast satellite selection algorithm based on the characteristic slope and optimize the number of subsets of MHSS based on this method. The proposed fast satellite selection algorithm does not require the sophisticated selection of baseline four-satellites subset but also avoids most of the matrix operations. It can get closer to the optimal geometry with a small amount of computation. This approach calculates and compares the characteristic slope of each satellite, then eliminates the satellite with the minor characteristic slope in each iteration. Instead of a given number of satellites to be selected, this method sets the rate of change of the geometric dilution of precision (GDOP) as the termination condition of the iteration. The MHSS multi-fault detection is performed on the selected satellites to obtain a faultfree subset, and the number of subsets is reduced as the number of satellites decreases. Then the Range Consensus (RANCO) algorithm is used to detect faults of the unselected satellites. The experimental results based on BDS/GPS multi-constellation illustrate that the GDOP of the proposed method is reduced by 17.34% and more than 99.99% computational complexity is saved compared with the traditional optimal satellite selection algorithm. The number of subsets is reduced by 67.51% and the computational time is decreased by 31.76%. This study verifies that the monitoring subsets and the calculation time are dramatically reduced by the proposed method.

Keywords: GNSS, satellite selection, characteristic slope, MHSS, RANCO