Improved Effectiveness of GPS RAIM Through Ridge Regression Signal Processing

Robert J. Kelly, Frank van Graas, Mark R. Kuhl

Abstract:	A new measurement processing technique is presented which significantly improves the effectiveness of GPS Receiver Autonomous Integrity Monitoring (RAIM). RAIM is a software-based algorithm implemented in a GPS receiver to detect satellite signal failures. The detection of a satellite failure is based on the consistency of a redundant set of pseudorange measurements. GPS positioning requires four satellites to solve for three-dimensional position and clock offset from GPS time. When five satellites are in view, five different sub-solutions can be calculated, each omitting one of the five satellites. If no satellite failures are present, the five sub-­solutions will be close to one another. However, if one of the satellites has failed, the sub-solutions will be scattered. The integrity alarm is triggered based on comparisons of the sub-solutions. Unfortunately, a poor distribution of the satellites also causes the sub-solutions to be scattered. Poor geometry, usually expressed in terms of the horizontal dilution of precision (HDOP), frequently exists for some sub-solutions, thus limiting the availability of RAIM. As the HDOP increases, position errors are correspondingly inflated. In 197 0, Hoerl and Kennard developed Ridge Regression to combat near collinearity when it arises in the predictor matrix of a linear regression model. Since a nearly collinear predictor matrix is directly related to a large HDOP, Ridge Regression processing can be applied to reduce the effect of the HDOP, thus permitting GPS to work. It is also shown that the effects of near collinearity cannot be reduced by choosing the estimator error covariance matrix Q0 such that the innovations of the Kalman filter are minimized. However, a methodology for selecting Q0 is presented which incorporates Ridge Regression into the Kalman filter. Finally, a computer simulation is implemented to illustrate the improved availability of GPS RAIM by using Ridge Regression processing to reduce those sub-solution errors due to a high HDOP.
Published in:	Proceedings of the 2nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1989) September 27 - 29, 1989 The Broadmoor Hotel Colorado Spring, CO
Pages:	363 - 371
Cite this article:	Kelly, Robert J., van Graas, Frank, Kuhl, Mark R., "Improved Effectiveness of GPS RAIM Through Ridge Regression Signal Processing," Proceedings of the 2nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1989), Colorado Spring, CO, September 1989, pp. 363-371.
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