Geometric Performance Analysis of Doppler-Based Positioning with a Single LEO Satellite

Low Earth Orbit (LEO) satellites have gained increasing attention as potential signal sources for Positioning, Navigation and Timing (PNT) applications. However, while most existing studies focus on multi-satellite LEO constellations, the fundamental positioning performance achievable with a single LEO satellite remains less extensively explored. This paper analyzes the geometric characteristics and positioning performance of single-satellite Doppler positioning through a theoretical analysis of the Dilution of Precision (DOP) and extensive numerical simulations. The results reveal a strong directional error behavior, with severe error in the cross-track direction but a significantly less error along the satellite track, reflecting an intrinsic geometric limitation of single-satellite LEO positioning. While these features were already identified at the early stages of satellite PNT missions, the present work provides an in-depth analysis and unveils the fundamental limitations and characteristics that could make LEO-based Doppler positioning feasible nowadays, using one single satellite only. In this way, the results of this work not only provide valuable insights into the role of observational geometry in Doppler navigation, but also offer guidance for optimizing geometric configurations in future small or single-satellite LEO constellations for strategic applications.