A Sequential Probability Test for RAIM

Steven Chan and Jason L. Speyer

Abstract:	The multiple hypotheses Shiryayev sequential probability test (MHSSPT) processes a sequence of conditionally independent and identically distributed (iid) random variables, and announces a change in the probability of that sequence in minimum time with a given probabilities of false and miss alarms. It is shown that the residual formed from the linearized GPS code measurements, such as the difference between the code measurement and the estimated code measurement, is approximately in the class of conditionally iid random variables for which the MHSSPT applies. Given the time sensitivity of detecting GPS faults, it is desirable to apply such a test to process GPS measurement residuals to enhance receiver autonomous integrity monitoring (RAIM). This paper presents first results obtained with the incorporation of the MHSSPT into pseudorange fault isolation in RAIM. So far the algorithm used only redundant satellite measurements for fault isolation; no external measurements like an IMU were used, although a GPS/IMU fused system will be considered in the future. Our simulations had shown that, when 8 satellites are in view, the algorithm can isolate faults very well. For 20 meters step fault, the algorithm can isolate the fault in about 5 seconds. For ramp faults, the algorithm can isolate the fault when the fault magnitude is about 20 to 30 meters. works in the past associated with Receiver Autonomous Integrity Monitoring (RAIM) are fault detection of GPS satellites. For example, in range comparison method, the user receiver makes an estimation of its current position and calculates its range to each satellite. The user will calculate the residual, the difference between the calculated range and the measured range. The residual will be analyzed in a statistical test and a fault is announced if the probability of a fault is high enough [1]. When navigation systems are increasingly depending upon GPS measurements, fault detection alone is not enough. The faulted satellites are to be isolated, so that the measurements of the unfaulted satellites can still be used. Numerous efficient fault isolation methods from different approaches have been developed in the past. In [2] and [3] some fault isolation algorithms have been shown to isolate faults efficiently. One of the most crucial performance criteria in fault isolation is the time required for isolating the fault. For a certain criterion of optimality, it could be shown that the multiple hypotheses Shiryayev sequential probability test (MHSSPT) [4] detects and isolates the occurrence of a change in the conditionally independent measurement sequence in minimum time. It is thus interesting to apply such a test in RAIM.
Published in:	Proceedings of the 17th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2004) September 21 - 24, 2004 Long Beach Convention Center Long Beach, CA
Pages:	1798 - 1802
Cite this article:	Chan, Steven, Speyer, Jason L., "A Sequential Probability Test for RAIM," Proceedings of the 17th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2004), Long Beach, CA, September 2004, pp. 1798-1802.
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