  A moment approach for orbit determinations of astrometric binaries from
astrometric observations alone has been recently studied for a low
signal-to-noise ratio (Iwama et al. 2013, PASJ, 65, 2). With avoiding a direct
use of the time-consuming Kepler equation, temporal information is taken into
account to increase the accuracy of statistical moments. As numerical tests,
100 realizations are done and the mean and the standard deviation are also
evaluated. For a semi-major axis, the difference between the mean of the
recovered values and the true value decreases to less than a tenth in the case
of $10000$ observed points. Therefore, the present moment approach works better
than the previous one for the orbit determinations when one has a number of the
observed points. The present approach is thus applicable to Cyg X-1.
