Estimating Relativistic Errors in Satellite-Based Geolocation Algorithms with Passive Sensors

This study focuses on improving geolocation accuracy in satellite systems using passive sensors through relativistic error estimation. Geolocation, the determination of a target's position using signals from electromagnetic emitters, becomes increasingly challenging when relativistic effects are considered, especially in space-based systems. The system under study involves a passive receiver mounted on a satellite and an emitter located on Earth's surface. The primary goal is to integrate relativistic corrections—such as time dilation, changes in potential energy, and satellite orbit eccentricity—into traditional geolocation algorithms, which primarily rely on signal time delay.

To achieve this, a theoretical model is developed, which examines the relativistic contributions to position errors arising from the finite speed of light and the effects of the satellite relative motion. Using an analytical approach, the study evaluates how these relativistic factors influence geolocation accuracy. A comparison between a Newtonian model for time delay and a modified algorithm incorporating relativistic corrections is presented. The relativistic correction algorithm, implemented through adjustments in the software layer, does not require system-level changes, making it feasible for current satellite operations.

Simulation in worst case scenarios results demonstrate that while relativistic effects are often considered negligible in many applications, they can introduce significant errors, particularly in high-precision tracking scenarios or in systems with highly eccentric orbits. In conclusion, incorporating relativistic corrections in satellite-based geolocation algorithms can enhance the precision of passive sensors, offering valuable improvements in both Earth and deep-space missions.