Doppler Dilution of Precision Analysis for GNSS and Starlink LEO Satellite Positioning

In global navigation satellite system (GNSS) positioning, Doppler shift-based methods suffer from low accuracy due to the low dynamics and high altitude of medium Earth orbit (MEO) satellites. In contrast, low Earth orbit (LEO) satellites, such as Starlink, exhibit high dynamics and low altitude, leading to a significant Doppler shift effect that can enhance user terminal (UT) positioning accuracy. However, the accuracy of Doppler-based positioning is influenced mainly by the Doppler dilution of precision (DDOP) of the satellites, which quantifies the influence of satellite velocity direction and geometric diversity. Unlike conventional geometric dilution of precision (GDOP), which only quantifies the satellite's geometric diversity, DDOP accounts for velocity vectors, making it a critical factor in Doppler-based positioning. This paper presents an intuitive analysis of DDOP and drives the Doppler geometry matrix. To evaluate the DDOP performance of Starlink satellites and GNSS, we calculate the DDOP values for evenly-spaced random places on Earth. A simulator GUI is designed to calculate the DDOP value on any place on Earth. Moreover, we establish the correlation between DDOP and Doppler-based positioning accuracy, demonstrating that lower DDOP values yield higher positioning accuracy. Our numerical analysis also confirms that Starlink LEO satellites offer significantly better DDOP than GNSS, underscoring its potential as an alternative positioning solution, particularly in the GNSS-denied environment.