Relative Time, Frequency, and RF-Phase Offset Estimation Between Two Undisciplined Ground Receivers from Uncooperative LEO Downlinks: Identifiability, Bounds, and Error Budgets

The coherent post-processing of distributed sensors requires spatially separated receivers to be referred to a common time, frequency, and radio-frequency (RF) phase. We study whether these relative offsets between two fixed ground receivers with independent, undisciplined clocks can be estimated from undecoded downlinks of uncooperative low-Earth-orbit (LEO) satellites. We derive a common-transmit-epoch cross-ambiguity observable, show that the delay–Doppler–scale search collapses to two dimensions for a single-reference receiver, establish identifiability conditions, and connect orbit, atmosphere, receiver-position, hardware, and clock-wander models to a two-noisy-channel equivalent Fisher information. In a parametric study over 100 random pass geometries, with ten satellites in 30 min, two-line-element-class ephemerides, and 10ps differential-delay noise per satellite per 10s epoch, the median clock-offset bound at a 2GHz carrier is 32ps with orbit errors alone and 62ps with all modeled error sources, differential ionospheric delay dominating; at the Ku band, where 240MHz downlinks exist and this delay noise corresponds to about 59dB-Hz per receiver, the all-source bound is about 40ps. These values hold for clock pairs with a relative flicker floor below about 3×10−14. Orbit priors of about 100m bring the orbit-limited bound to about 10ps, and the fixed-ambiguity carrier phase with a calibrated antenna brings the all-source bound to about 18ps. The RF-phase accuracy is set by the calibration of the direction-independent differential antenna phase. A semi-synthetic replay of a recorded Starlink direct-to-cell capture exercises the processing chain on a recorded waveform.