Orbit Uncertainty Covariance Adaptation for LEO Phase and Doppler Differential Positioning

Navigating with opportunistic signals from low-Earth-orbit satellites is a promising alternative to traditional systems, yet it remains hindered by the large uncertainty of publicly accessible orbit products. Kilometer-level ephemeris errors project into the measurement domain as systematic, time-varying biases, often causing standard filters to fail because they rely too heavily on contaminated carrier-phase or Doppler observations. This paper introduces orbit uncertainty covariance adaptation (OUCA), a stochastic framework that maps orbit uncertainty directly into the observation space. By modeling satellite position and velocity uncertainty in the orbital frame and projecting it through the time-varying observation geometry, OUCA provides a physically consistent way to adapt measurement weighting in real time while preserving same-epoch coupling between phase and Doppler observations. The results show two primary findings. First, OUCA is effective for all three observation modes, namely, phase-only, Doppler-only, and phase+Doppler. A representative two-line-element (TLE) scenario with a 10-km baseline shows how the gains differ across the three modes: OUCA reduces the final three-dimensional error from 102.617 m to 10.102 m for the phase-only mode (90.2%), from 17.725 m to 6.253 m for the Doppler-only mode (64.7%), and from 56.232 m to 4.581 m for the phase+Doppler mode (91.9%). Second, once OUCA is applied, the phase+Doppler mode provides an effective joint solution across different orbit-quality conditions. Under high-precision orbit conditions, this mode retains the same centimeter-level positioning accuracy as the phase-only mode. Under TLE-grade orbit conditions, the phase+Doppler mode improves positioning accuracy compared with the Doppler-only mode.