Synchronization independent three-dimensional localization of LEO satellites using passive distributed ground antennas and staged dimensionality reduction

This paper presents a novel synchronization-free method for three-dimensional (3D) positioning of Low Earth Orbit (LEO) satellites using a network of distributed passive ground antennas. By combining improved relative Received Signal Strength (RSS) measurements with Apollonius circle geometry, the proposed method leverages a multi-stage dimensionality reduction technique to enhance the precision of target estimation in multi-receiver systems. The initial stage estimates the projection of the satellite’s position onto the two-dimensional (2D) XY plane through an improved relative RSS algorithm. In the second stage, the satellite altitude is estimated by minimizing a cost function formulated from the Rician channel amplitude model. A multi-snapshot averaging strategy is utilized to mitigate Rician fading and additive noise, reducing the amplitude estimation variance by a factor of N through the coherent averaging of N independent snapshots. Theoretical results demonstrate that the proposed method achieves a 3D positioning median accuracy of approximately 31.41 km and a 3D angular error of 6.55 degree over 200 Monte Carlo trials with randomly distributed satellite positions spanning altitudes from 100 to 500 km. The robustness and sensitivity of the proposed algorithm are further evaluated under variations in receiver height, SNR, receiver antenna gain, shadowing and Rician channel parameters. Notably, these performance levels are attained without the need for inter-receiver synchronization, complex hardware, complex computational burden or prior knowledge of satellite ephemeris.