Emitter Tracking by Passive Sensors Onboard Satellites: Relativistic Error Estimation in Geolocation Algorithm

The framework of the article is the simulation of space sensors and the aim of this study is the proposal of an algorithm for the relativistic correction on time delay used in position error estimation for geolocation applications. The reference scenario considers an electromagnetic field emitter placed on the surface of the Earth and a passive receiver embarked on a satellite. The focus is on the implementation of the relativistic correction on time clock due to the elliptic shape of the orbit of the satellite, time dilation and changes in potential energy. The adopted methodology is theoretical and involves the analytical description of the position error through the study of the relative geometry between the satellite and the emitter and the relativistic correction on times is derived. Input-output analysis of the model for simulation software development, useful for sensor performance prediction, shows that a relativistic correction can be implemented without changes at system level, but it only requires an update at algorithm level and the information on time clock synchronization. Starting from a Newtonian version of the algorithm, a more general relativistic algorithm is then presented and discussed. The paper concludes with an order of magnitude analysis of the relativistic contributions in worst cases scenario.