Estimating Accurate Relative Spacecraft Angular Position from Deep Space Network Very Long Baseline Interferometry Phases Using X-Band Telemetry or Differential One-Way Ranging Tones

At present spacecraft angular position with the Deep Space Network (DSN) is determined using group delay estimates from very long baseline interferometry (VLBI) phase measurements employing differential one-way ranging (DOR) tones. Group delay measurements require high signal-to-noise ratio (SNR) to provide modest angular position accuracy. On the other hand, VLBI phases with modest SNR can be used to determine the position of a spacecraft with high accuracy, except for the interferometer interference fringe cycle ambiguity, which can be resolved using multiple baselines, requiring several antenna stations as is done, for example, using the Very Long Baseline Array (VLBA) (e.g, the VLBA has 10 antenna stations). As an alternative to this approach, here we propose estimating the position of a spacecraft to half-a-fringe-cycle accuracy using time variations between measured and calculated phases, using DSN VLBI baseline(s), as the Earth rotates (i.e., estimate position offset from the difference between observed and calculated phases for different spatial frequency (U, V ) values). Combining the fringe location of the target with the phase information allows for estimate of spacecraft angular position to a high accuracy.