Improved Chi-Square Fault Detection for GPS Navigation

Keith Brodie

Abstract:	A well-known extension to the basic Kalman filter (KF) for use in GPS navigation is the use of chi-square measurement fault detection to eliminate measurements with large errors, such as multipath. Chi-square fault detection, or innovations variance testing, is a test of the statistical hypothesis that the measurement residual being considered for processing is from the set defined by the measurement and state models. Using a measurement taken while tracking a multipath ray violates the model, and the resultant state estimate will have unmodeled errors. If these errors are large enough, complete divergence between the state estimate and its associated error covariance matrix can occur. Chi-square measurement editing is a mechanism to protect against this fault. It is common in real-time filter implementations to use sequential, scalar measurement processing for a set of uncorrelated measurements taken at a common time. There is no order dependence in the result for a KF without editing. In sequential processing, the chi-square test is typically performed in the sequence. The innovations variance is computed as part of the scalar gain calculation, so the test is performed at this step in the processing, and the measurement is edited if it fails. What has not been discussed in previous literature is that the order in which measurements are sequentially processed can have a dramatic impact on the probability of fault detection with the chi-square test. The paper introduces the concept of ordering the measurements by their increasing relative fault probability. Measurements taken at a lower elevation angle and with a lower C/N0 are more likely to have multipath faults. Processing measurements with the lowest probability of a multipath fault first increases the probability of fault detection on the later measurements, and decreases the probability of a false alarm on the measurements with a lower fault probability. A one-dimensional numerical example and some dramatic improvements in actual GPS navigation results are presented. The algorithm is now in use in the SiRFstar II chipset. The concept has also been extended for measurements taken at different times through the use of forward and backward propagation to allow for the processing of the most reliable measurements first.
Published in:	Proceedings of the 2001 National Technical Meeting of The Institute of Navigation January 22 - 24, 2001 Westin Long Beach Hotel Long Beach, CA
Pages:	438 - 441
Cite this article:	Brodie, Keith, "Improved Chi-Square Fault Detection for GPS Navigation," Proceedings of the 2001 National Technical Meeting of The Institute of Navigation, Long Beach, CA, January 2001, pp. 438-441.
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