Sagnac and orbital eccentricity-based pseudo-range modeling for GPS navigation

Abstract

GPS involves the one-way transmission of RF signal from a satellite in space to the receiver on the earth. Since the satellites and the receivers are at different gravitation potentials and are relatively in motion, the GPS measurements are biased by the relativistic effects. The Special Theory of Relativity (STR) and General Theory of Relativity (GTR) need to be considered in order to obtain the precise navigation solution. The relativistic effects on Signal Emission Time (SET) are significant and will affect range measurements and satellite position estimates. Ignoring these effects will make the GPS ineffective for precise navigation applications. Among the relativistic effects, the Sagnac effect and the orbital eccentricity have a major impact on GPS performance. In this paper, a pseudo-range modeling and the satellite position correction algorithm are presented which takes Sagnac effect and orbital eccentricity into consideration. The algorithm given in this paper can be implemented to achieve higher accuracy for navigation applications like civil aviation and category I/II Precision Approach (PA) aircraft’s landing.