  In this work we study the performance of linear multifilters for the
estimation of the amplitudes of the thermal and kinematic Sunyaev-Zel'dovich
effects. We show that when both effects are present, estimation of these
effects with standard matched multifilters is intrinsically biased. This bias
is due to the fact that both signals have basically the same spatial profile.
We find a new family of multifilters related to the matched multifilters that
cancel this systematic bias, hence we call them Unbiased Matched Multifilters.
We test the unbiased matched multifilters and compare them with the standard
matched multifilters using simulations that reproduce the future Planck
mission's observations. We find that in the case of the standard matched
multifilters the systematic bias in the estimation of the kinematic
Sunyaev-Zel'dovich effect can be very large, even greater than the statistical
error bars. Unbiased matched multifilters cancel effectively this kind of bias.
In concordance with other works in the literature, our results indicate that
the sensitivity and resolution of Planck will not be enough to give reliable
estimations of the kinematic Sunyaev-Zel'dovich of individual clusters.
However, since the estimation with the unbiased matched multifilters is not
intrinsically biased, it can be possible to use them to statistically study
peculiar velocities in large scales using large sets of clusters.
