Sufficiency, Data Reduction, and Sensor Fusion for GPS

James W. Chaffee, Jonathon S. Abel

Abstract:	The notion of sufficiency in statistics is an old one, of fundamental importance, but it does not seem to have caught the attention of the GPS community. According to the theorem of Rae-Blackwell a sufficient statistic of the data is as good as the original data for computing fur- ther estimates. In fact, any estimator can be improved by conditioning on a sufficient statistic. This has significant implications for the design of GPS navigation processors. A GPS receiver outputting a time independent sequence of sufficient point estimates for user position and bias would retain all the information in the original pseudo ranges relevant to these parameters while lending itself to extremely simple sensor fusion. The advantages for GPS/INS integration are particularly striking, since the use of position obviates the need for linearization. Though the raw data are always sufficient, the search for a sufficient statistic of fixed finite dimension inde- pendent of the number of data points is difficult. The existence of finite dimensional sufficient statistics is only guaranteed in restrictive cases. In this paper, we examine the notion of sufficiency as applied to GPS position esti- mation. In particular, we introduce the statistical view- point, which seems to have been overlooked by the GPS community in their reliance on cookbook methods such as linearized least squares and the extended Kalman fil- ter. Our approach is to consider point estimators based on algorithms which reduce to exact solutions in the case of four pseudoranges, assuming no prior information.
Published in:	Proceedings of the 1992 National Technical Meeting of The Institute of Navigation January 27 - 29, 1992 Catamaran Resort Hotel San Diego, CA
Pages:	407 - 413
Cite this article:	Chaffee, James W., Abel, Jonathon S., "Sufficiency, Data Reduction, and Sensor Fusion for GPS," Proceedings of the 1992 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 1992, pp. 407-413.
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