Clock Synchronization & Navigation in the Vicinity of the Earth

Clock synchronisation is the backbone of applications such as high-accuracy satellite navigation, geolocation, space-based interferometry, and cryptographic communication systems. The high accuracy of synchronisation needed over satellite-to-ground and satellite-to-satellite distances requires the use of general relativistic concepts. The role of geometrical optics and antenna phase centre approximations are discussed in high accuracy work. The clock synchronisation problem is explored from a general relativistic point of view, with emphasis on the local measurement process and the use of the tetrad formalism as the correct model of relativistic measurements. The treatment makes use of J. L. Synge''s world function of space-time as a basic co-ordinate independent geometric concept. A metric is used for space-time in the vicinity of the Earth, where co-ordinate time is proper time on the geoid. The problem of satellite clock syntonisation is analysed by numerically integrating the geodesic equations of motion for low-Earth orbit (LEO), geosynchronous orbit (GEO), and highly elliptical orbit (HEO) satellites. Proper time minus co-ordinate time is computed for satellites in these orbital regimes. The frequency shift as a function of time is computed for a signal observed on the Earth''s geoid from a LEO, GEO, and HEO satellite. Finally, the problem of geolocation in curved space-time is briefly explored using the world function formalism.