Theoretical Limits of Differential Doppler Positioning Using LEO Satellite Signals

Paper in proceeding, 2025

As the need for more accurate and reliable positioning systems grows, satellite-based navigation techniques are gaining significant attention, particularly those utilizing Doppler shifts from Low Earth Orbit (LEO) satellites. Traditional Doppler positioning systems often suffer from errors induced by atmospheric disturbances, satellite clock biases, and other signal impairments, especially in dynamic environments. This has motivated the exploration of differential Doppler positioning as a promising solution to mitigate these common-mode errors. This paper explores the theoretical limits of differential Doppler positioning, focusing on Doppler-only methods where position and velocity estimates are derived from Doppler measurements without relying on time-of-arrival (TOA) measurements. By leveraging the Cramér-Rao lower bound (CRLB), we provide a theoretical performance benchmark for the accuracy of position, velocity, and frequency bias estimation. Furthermore, we present a correlation model for atmospheric effects to demonstrate the impact of baseline distance on the estimation performance of differential Doppler positioning. The results show that differential Doppler positioning notably outperforms traditional non-differential Doppler positioning, particularly in low-SNR environments, with substantial gains in frequency bias, 3D velocity, and 3D position estimation accuracy.