  All-sky and directed continuous gravitational-wave searches look for signals
from unknown asymmetric rotating neutron stars. These searches do not take into
account the proper motion of the neutron star, assuming that the loss of
signal-to-noise ratio caused by this is negligible and that no biases in
parameter estimation are introduced. In this paper we study the effect that
proper motion has on continuous wave searches, and we show for what regions of
parameter space (frequency, proper motion, sky position) and observation times
this assumption may not be valid. We also calculate the relative uncertainty on
the proper motion parameter estimation that these searches can achieve.
