  In this work, we study how to infer the orbit of a supermassive black hole
binary (SMBHB) by time-dependent measurements with Very Long Baseline
Interferometry (VLBI), such as the Event Horizon Telescope (EHT). Assuming a
point-like luminosity image model, we show that with multiple years of
observations by EHT, it is possible to recover the SMBHB orbital parameters --
eccentricity, (rescaled) semi-major axis, orbital frequency, and orbital angles
-- from their time-varying visibilities even if the binaries orbital period is
a few times longer than the duration of observation. Together with the future
gravitational wave detections of resolved sources of SMBHBs with Pulsar Timing
Array, and/or the detections of optical-band light curves, we will be able to
further measure the individual mass of the binary, and also determine the
Hubble constant if the total mass of the binary is measured through the light
curves of the two black holes or by alternative methods.
