Theoretical Error Analysis of GEO Orbit Determination by TDOA of Multiple Ground Stations and its Applications to Geolocation

Geolocation of interference sources using Time Difference Of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) observed via two geostationary satellites requires precise orbit information of the satellites, as the geolocation accuracy depends on the precision of orbit determination. This paper proposes a method for estimating satellite orbits using TDOA data among multiple known ground stations and derives theoretical error equations for both orbit determination and geolocation of interference source. Detailed accuracy analyses reveal that, with three ground stations and 24 hours of TDOA measurements, satellite position and velocity accuracies are approximately 0.4 km and 0.03 m/s, respectively. Furthermore, the geolocation of interference source accuracy using the determined orbit achieves approximately 8.0 km. The results also demonstrate that orbit determination accuracy heavily depends on the spatial distribution of ground stations. Notably, the northeast-southwest elongated geography of Japan necessitates careful selection of station locations to ensure high orbit determination accuracy. The theoretical formulas derived in this paper for orbit determination and subsequent geolocation accuracy enable comprehensive accuracy evaluations under various conditions without relying on Monte Carlo simulations.