A MATHEMATICAL MODEL OF GPS SATELLITE TIME AND FREQUENCY BASED ON THE SPECIAL THEORY OF RELATIVITY

Abstract

The Global Positioning System (GPS) relies on highly precise atomic clocks in satellites and ground stations to determine global time and position accurately. Relativistic effects, including gravitational fields and satellite orbital motion, induce frequency shifts in these clocks, necessitating corrections for accurate navigation. This study developed a novel approach to integrate general coordinates into GPS, emphasizing implementation simplicity. We investigated the application of special relativity to calculate time and frequency shifts in GPS satellites. Our analysis estimated a daily relativistic correction of approximately 21.6 microseconds, with a positional imprecision of 6.48 km per day if uncorrected. By employing a general time-space coordinate system, we calculated position-4 and velocity-4 vectors, accounting for special relativistic effects on GPS time and frequency. The proposed method simplifies relativistic corrections while enhancing their conceptual clarity. Results demonstrate improved precision and efficiency in GPS positioning through the integration of general coordinates with a streamlined approach. This research offers valuable insights for international engineering communities, scholars, and practitioners, advancing the understanding of relativity’s impact on GPS satellite operations.