Three statistics that have been proposed for integrity monitoring of GPS precision approach systems are analyzed to identify any limitations and pitfalls in their application. Examples illustrate how small changes in assumed error distributions can significantly increase the probability of undetected hazardously misleading information (HMI). Results apply to the detection method for integrity monitoring in Special Category I (SCAT I) applications, Local Area Augmentation Systems (LAAS), and Receiver Autonomous Integrity Monitoring (RAIM).rnA test statistic computed as the difference between the differential corrections broadcast by two stations is described in the Special Category I (SCAT-I) Minimum Aviation Performance Standards (MASPS), RTCA/DO-217. This study demonstrates that the MASPS procedures do not account for all components of the maximum bias and noise errors. The MASPS detection method for integrity monitoring is described in the literature as a test for a specified upper limit on pseudorange correction biasrnplus noise errors. However, it can be shown to be a test for zero bias error.rnThe analysis demonstrates that an event where a test statistic value exceeds a critical limit does not necessarily occur concurrently with an actual pseudorange correction error exceeding a corresponding limit. The analysis also demonstrates that critical values for a given level of integrity vary with the relative fraction of integrity apportioned between the missed detection probability and the assumed failure probability.rnTwo other proposed test statistics for integrity monitoring using three or more stations are equivalent. The first is the deviation of a station's correction from the average. The second is the difference between an average of all stations' corrections, and the same average without the differential correction for the station under test. Because the sample average is influenced more by the fault-free stations, the use of these statistics in the manner described needs to be reevaluated.rnThe deviations from sample averages are not independent. If fault isolation is not implemented appropriately with these statistics, there is a significant probability of eliminating an error-free station. If a station exhibiting a sufficiently large bias error is retained in the process of fault isolation using these statistics, there may be a possibility of HMI.rnAnalysis of variance (ANOVA) and the multivariate normal distribution are alternatives that may offer more accurate characterization of the distribution of the deviations from the sample mean, and a more reliable method for fault isolation. The chi-square distribution also offers advantages over use of the normal distribution in the present application.
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