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Abstract

The effect of changing satellite geometry on the achievable accuracy of GPS relative positioning under the full GPS constellation has been researched. A mathematical model has been developed for the quantitative analysis of the accuracy of GPS relative positioning with respect to the changing satellite/station configuration, observation starting time and session length. A method based on modeling the relative dilution of precision (RDOP) has been developed for the optimum design of GPS relative positioning with carrier phase observable. The RDOP surface, a mathematical surface, has been generated based on the broadcast almanac file. The optimum observation windows, optimum session starting time and optimum observation session length have been derived from the study of the RDOP surface. The method and mathematical model based on the RDOP are compared with those based on the PDOP (position dilution of precision) for application purposes. An important phenomenon, the shift of the RDOP curve as a function of observing session length, has been discovered. The relation between PDOP and RDOP is explained based on this finding. The results and analyses are given with practical examples. Array algebra filtering, a generalized sequential estimation technique, has been investigated and further developed for the fast generation of the RDOP surface. The mathematical principle and statistical properties of array algebra filtering have been researched and the characteristics of this filtering technique are analyzed. The algorithmic development, processing run streams, data and results are included. The potentials of this technique for use in fast real-time GPS data processing and real-time accuracy prediction are outlined.

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