Time-Dependency and Coordinate System Issues in GPS Measurement Models

Raymond DiEsposti

Abstract:	Recent changes (Interface Revision Notice, IRN-200C- 003) to the Navstar GPS Space Segment/Navigation User Interface Control Document (ICD-GPS-200C) emphasize a more precise definition for the Geometric Range and an introduction of an Earth-Centered, Inertial (ECI) coordi- nate system and transformation to an Earth-Centered, Earth-Fixed (ECEF) coordinate system. The new defini- tions provide more clarity on how a user set should model the pseudorange measurement. Although the orbit determination of GPS satellites is per- formed in ECI coordinates, the ephemeris coefficients that are broadcast to the user are for a model that computes the satellite position in ECEF coordinates. When the user processes a pseudorange measurement, the satellite posi- tion at the time of transmission must be used. During the time it takes the signal to propagate to the user’s antenna, the ECEF coordinate frame rotates slightly by an amount that is determined by the earth’s rotation rate and the sig- nal propagation time. In order to obtain the full accuracy in the GPS position fix, this small amount of rotation must be computed and compensated. If this compensation is not performed properly, the result- ing position fix will be in error. If this compensation is completely ignored, the error is a function of the cosine of the latitude and can be as large as 41 meters at the equator and zero at the poles of the earth. This paper discusses the equations for the proper compensation of this effect and relates the discussion to the latest revision of ICD-GPS-200C. The paragraph that described the earth rotation compensation in the prior version of ICD-GPS-200C caused some confusion in the past. In addition, equations are provided for the pseudorange model, which explicitly shows the time dependency of dynamic variables and the coordinate system used for the position variables. Since Selective Availability (SA) has been recently set to zero, errors that can arise due to miss-modeling and the neglect of small terms now become more relevant. Re- ceivers that operate in the differential fashion must model processes the same way to avoid introducing additional errors. A precise measurement model and notation for time dependency, as provided in this paper, can help to reduce any ambiguity that can lead to such errors.
Published in:	Proceedings of the 13th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2000) September 19 - 22, 2000 Salt Palace Convention Center Salt Lake City, UT
Pages:	1925 - 1929
Cite this article:	DiEsposti, Raymond, "Time-Dependency and Coordinate System Issues in GPS Measurement Models," Proceedings of the 13th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2000), Salt Lake City, UT, September 2000, pp. 1925-1929.
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