Test Statistic and Position Error Correlation in (Advanced) RAIM

Previous investigation on the measurement temporal correlation effect on Probability of Hazardously Misleading Information (PHMI) [1] has proposed how to map the operational integrity risk to that for a single sample. However, a well-known assumption that the stochastic components of position error and the test statistic are independent was taken to evaluate the actual risk over a given time interval. This paper examines the level of cross-correlation present between the estimated states and the fault detection statistics for (Advanced) Receiver Autonomous Integrity Monitoring (RAIM) and determines its impact on the PHMI to generalize the proposed approach. In this study, we take several experimental and simulation methods. Dual-frequency GPS and Galileo measurements were collected and processed to measure the correlation between the position error and monitor test statistic. We also evaluate actual integrity risk when they are correlated through using simple satellite geometries and error models as well as those for H-ARAIM applications. It was found that the cross-correlation between the position and test domains is present when the measurement error inflation model, e.g., commonly used Gaussian overbounding method, is applied to the weighted least-squares estimation Also, the numerical results of the integrity risk evaluation showed that the assumption taken in the previous assessment is valid with respect to correlation resulting from sigma inflation even though the additional risk of up to 60% is observed due to the correlation effect.