  The conventional approach to high-precision narrow-angle astrometry using a
long baseline interferometer is to directly measure the fringe packet
separation of a target and a nearby reference star. This is done by means of a
technique known as phase-referencing which requires a network of dual beam
combiners and laser metrology systems. Using an alternative approach that does
not rely on phase-referencing, the narrow-angle astrometry of several closed
binary stars (with separation less than 2$"$), as described in this paper, was
carried out by observing the fringe packet crossing event of the binary
systems. Such an event occurs twice every sidereal day when the line joining
the two stars of the binary is is perpendicular to the projected baseline of
the interferometer. Observation of these events is well suited for an
interferometer in Antarctica. Proof of concept observations were carried out at
the Sydney University Stellar Interferometer (SUSI) with targets selected
according to its geographical location. Narrow-angle astrometry using this
indirect approach has achieved sub-100 micro-arcsecond precision.
