  We present a first-stage study of the effect of using knowledge from
electromagnetic (EM) observations in the gravitational wave (GW) data analysis
of Galactic binaries that are predicted to be observed by the new Laser
Interferometer Space Antenna in the low-frequency range, $10^{-4}
\mathrm{Hz}<f<1 \mathrm{Hz}$. In particular, we examine the extent to which the
accuracy of GW parameter estimation improves if we use available information
from EM data. We do this by investigating whether correlations exist between
the GW parameters that describe these binaries and whether some of these
parameters are also available from EM observations. We used verification
binaries, which are known as the guaranteed sources for eLISA and will test the
functioning of the instrument. We find that of the seven parameters that
characterise such a binary, only a few are correlated. The most useful result
is the strong correlation between amplitude and inclination, which can be used
to constrain the parameter uncertainty in amplitude by making use of the
constraint of inclination from EM measurements. The improvement can be up to a
factor of $\sim6.5$, but depends on the signal-to-noise ratio of the source
data. Moreover, we find that this strong correlation depends on the
inclination. For mildly face-on binaries ($\iota \lesssim 45^{\circ}$), EM data
on inclination can improve the estimate of the GW amplitude by a significant
factor. However, for edge-on binaries ($\iota \sim 90^{\circ}$), the
inclination can be determined accurately from GW data alone, thus GW data can
be used to select systems that will likely be eclipsing binaries for EM
follow-up.
