  Tracking the motions of transient jets launched by low-mass X-ray binaries
(LMXBs) is critical for determining the moment of jet ejection, and identifying
any corresponding signatures in the accretion flow. However, these jets are
often highly variable and can travel across the resolution element of an image
within a single observation, violating a fundamental assumption of aperture
synthesis. We present a novel approach in which we directly fit a single
time-dependent model to the full set of interferometer visibilities, where we
explicitly parameterise the motion and flux density variability of the emission
components, to minimise the number of free parameters in the fit, while
leveraging information from the full observation. This technique allows us to
detect and characterize faint, fast-moving sources, for which the standard time
binning technique is inadequate. We validate our technique with synthetic
observations, before applying it to three Very Long Baseline Array (VLBA)
observations of the black hole candidate LMXB MAXI J1803-298 during its 2021
outburst. We measured the proper motion of a discrete jet component to be
$1.37\pm0.14$ mas/hr, and thus we infer an ejection date of MJD
$59348.08_{-0.06}^{+0.05}$, which occurs just after the peak of a radio flare
observed by the Australia Telescope Compact Array (ATCA) and the Atacama Large
Millimeter/Sub-Millimeter Array (ALMA), while MAXI J1803-298 was in the
intermediate state. Further development of these new VLBI analysis techniques
will lead to more precise measurements of jet ejection dates, which, combined
with dense, simultaneous multi-wavelength monitoring, will allow for clearer
identification of jet ejection signatures in the accretion flow.
