A new polarisation amplitude bias reduction method
  Polarisation amplitude estimation is affected by a positive noise bias,
particularly important in regions with low signal-to-noise ratio (SNR). We
present a new approach to correct for this bias in the case there is additional
information about the polarisation angle. We develop the 'known-angle
estimator' that works in the special case when there is an independent and high
signal-to-noise ratio ($\gtrsim 2\sigma$) measurement of the polarisation
angle. It is derived for the general case where the uncertainties in the Q,U
Stokes parameters are not symmetric. This estimator completely corrects for the
polarisation bias if the polarisation angle is perfectly known. In the
realistic case, where the angle template has uncertainties, a small residual
bias remains, but that is shown to be much smaller that the one left by other
classical estimators. We also test our method with more realistic data, using
the noise properties of the three lower frequency maps of WMAP. In this case,
the known-angle estimator also produces better results than methods that do not
include the angle information. This estimator is therefore useful in the case
where the polarisation angle is expected to be constant over different data
sets with different SNR.
