Correlation-weighted least squares residual algorithm for RAIM

The Least Squares Residual (LSR) algorithm, one of the classical Receiver Autonomous Integrity Monitoring (RAIM) algorithms for Global Navigation Satellite System (GNSS), presents a high Missed Detection Risk (MDR) for a large-slope faulty satellite and a high False Alarm Risk (FAR) for a small-slope faulty satellite. From the theoretical analysis of the high MDR and FAR cause, the optimal slope is determined, and thereby the optimal test statistic for fault detection is conceived, which can minimize the FAR with the MDR not exceeding its allowable value. To construct a test statistic approximate to the optimal one, the Correlation-Weighted LSR (CW-LSR) algorithm is proposed. The CW-LSR test statistic remains the sum of pseudorange residual squares, but the square for the most potentially faulty satellite, judged by correlation analysis between the pseudorange residual and observation error, is weighted with an optimal-slope-based factor. It does not obey the same distribution but has the same non-central parameter with the optimal test statistic. The superior performance of the CW-LSR algorithm is verified via simulation, both reducing the FAR for a small-slope faulty satellite with the MDR not exceeding its allowable value and reducing the MDR for a large-slope faulty satellite at the expense of FAR addition.