GEO-Based VLBI for Deep Space Navigation: Time-Position Error Modeling and Performance Analysis

Radiometric interferometry, implemented through ground-based Very Long Baseline Interferometry (VLBI) and Delta Differential One-Way Ranging (Delta-DOR), is a powerful technique for angular spacecraft navigation. The previously proposed concept of Radiometric Interferometry Navigation using Geostationary Earth Orbit (GEO) Satellites (RINGS) replaces terrestrial stations with GEO satellites, so that its basic measurement unit is a single GEO-GEO interferometric baseline. This paper analyzes the two main practical error sources of this two-station sensor: residual relative clock misalignment between the satellites and uncertainty in their positions. Analytical models map both into angular error and show that the timing-induced path error is divided by the long GEO-GEO baseline. The timing chain is evaluated, including Global Navigation Satellite System (GNSS) synchronization, passive hydrogen maser (PHM) clocks, two-way inter-satellite time transfer, and relativistic corrections, and a Monte Carlo framework propagates clock and position errors through a dual-frequency angle-of-arrival estimator. For a GEO-GEO baseline of about 84,000 km, residual timing errors of 10 ps and 100 ps contribute about 0.05 nrad and 0.5 nrad of angular scatter, whereas GEO position uncertainty contributes about 17 nrad per meter per axis and is the dominant error driver; for the 120◦ three-GEO baseline these values are about 15% larger. A Sagnac-type term biases the uncorrected two-way clock estimate by about 1.25 μs and must be computed from the GEO states. Theoretical analysis supported by simulation shows that nanoradian-level angular precision is attainable with sub-meter GEO position knowledge and PHM-class timing. This is the statistical precision floor of the sensor, not its absolute accuracy after calibration.