  Of the current known pulsars, the Crab pulsar (B0531+21) is one of the most
promising sources of gravitational waves. The relatively large timing noise of
the Crab causes its phase evolution to depart from a simple spin-down model.
This effect needs to be taken in to account when performing time domain
searches for the Crab pulsar in order to avoid severely degrading the search
efficiency. The Jodrell Bank Crab pulsar ephemeris is examined to see if it can
be used for tracking the phase evolution of any gravitational wave signal from
the pulsar, and we present a method of heterodyning the data that takes account
of the phase wander. The possibility of obtaining physical information about
the pulsar from comparisons of the electromagnetically and a gravitationally
observed timing noise is discussed. Finally, additional problems caused by
pulsar glitches are discussed.
