An enhanced least squares residual RAIM algorithm based on optimal decentralized factor

The Least Squares Residual (LSR) algorithm is commonly used in the Receiver Autonomous Integrity Monitoring (RAIM). However, LSR algorithm presents high Missed Detection Risk (MDR) caused by a large-slope faulty satellite and high False Alert Risk (FAR) caused by a small-slope faulty satellite. In this paper, the LSR algorithm is improved to reduce the MDR for a large-slope faulty satellite and the FAR for a small-slope faulty satellite. Based on the analysis of the vertical critical slope, the optimal decentralized factor is defined and the optimal test statistic is conceived, which can minimize the FAR with the premise that the MDR does not exceed its allowable value of all three directions. To construct a new test statistic approximating to the optimal test statistic, the Optimal Decentralized Factor weighted LSR (ODF-LSR) algorithm is proposed. The new test statistic maintains the sum of pseudo-range residual squares, but the specific pseudo-range residual is weighted with a parameter related to the optimal decentralized factor. The new test statistic has the same decentralized parameter with the optimal test statistic when single faulty satellite exists, and the difference between the expectation of the new test statistic and the optimal test statistic is the minimum when no faulty satellite exists. The performance of the ODF-LSR algorithm is demonstrated by simulation experiments.