Limitations and Pitfalls in the Application of Test Statistics to Integrity Monitoring.

Lee Etnyre

Abstract:	Three statistics that have been proposed for integrity monitoring of GPS precision approach systems are ana-lyzed to identify any limitations and pitfalls in their appli-cation. Examples illustrate how small changes in assumed error distributions can significantly increase the probabil-ity 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). A test statistic computed as the difference between the differential corrections broadcast by two stations is de-scribed 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 integ-rity monitoring is described in the literature as a test for a specified upper limit on pseudorange correction bias plus noise errors. However, it can be shown to be a test for zero bias error. The analysis demonstrates that an event where a test sta-tistic 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 integ-rity vary with the relative fraction of integrity apportioned between the missed detection probability and the assumed failure probability. Two 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 sta-tions’ corrections, and the same average without the dif-ferential correction for the station under test. Because the sample average is influenced more by the fault-free sta-tions, the use of these statistics in the manner described needs to be reevaluated. The deviations from sample averages are not independent. If fault isolation is not implemented appropriately with these statistics, there is a significant probability of elimi-nating an error-free station. If a station exhibiting a suffi-ciently large bias error is retained in the process of fault isolation using these statistics, there may be a possibility of HMI. Analysis of variance (ANOVA) and the multivariate nor-mal distribution are alternatives that may offer more accu-rate 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 pres-ent application.
Published in:	Proceedings of the 54th Annual Meeting of The Institute of Navigation (1998) June 1 - 3, 1998 The Adams Mark Hotel Denver, CO
Pages:	199 - 209
Cite this article:	Etnyre, Lee, "Limitations and Pitfalls in the Application of Test Statistics to Integrity Monitoring.," Proceedings of the 54th Annual Meeting of The Institute of Navigation (1998), Denver, CO, June 1998, pp. 199-209.
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