Optimization of LEO Doppler-Smoothed Code Positioning and Velocity Estimation

Low Earth Orbit Navigation Augmentation (LEO-NA) has emerged as a promising next-generation satellite navigation solution. Although the processing of pseudorange and carrier-phase data for positioning is similar in GNSS and LEO-NA, the applicability of existing Doppler-processing strategies to LEO-NA remains uncertain. The high velocities of LEO satellites introduce unique challenges in Doppler-based measurement processing that are absent in traditional GNSS. This study revisits GNSS-based Doppler-processing techniques for LEO-NA and identifies the key challenges posed by the much larger Doppler shifts. While conventional GNSS Doppler methods have proven effective in standard applications, this study reveals that their direct application to LEO-NA is inadequate. Therefore, adapting these strategies—particularly Doppler-smoothed code and carrier-phase-derived Doppler—is essential. The Trapezoidal integration method, commonly used for Doppler smoothing, introduces significant range biases—up to 5 m at 700 km altitude—far exceeding typical GNSS noise levels and degrading Single-Point Positioning (SPP) accuracy, especially in the Up component. In contrast, Simpson’s 1/3 integration reduces these biases to near zero, yielding a clear performance improvement. Similarly, for velocity determination, the widely used 3-point central difference method, though reliable in GNSS, introduces biases exceeding 0.5 Hz at 700 km altitude in LEO-NA. Switching to a 5-point central difference method nearly eliminates these biases, improving the velocity estimation RMS by approximately 19—31. These findings demonstrate that GNSS Doppler-processing strategies cannot be applied directly to LEO-NA. Therefore, we recommend using Simpson’s 1/3 integration for Doppler-smoothed code and the 5-point central difference method for carrier-phase-derived Doppler to optimize performance in LEO-NA systems.