  On large angular scales, CMB polarization depends mostly on the evolution of
the ionization level of the IGM during reionization. In order to avoid biasing
parameter estimates, an accurate and model independent approach to reionization
is needed when analyzing high precision data, like those expected from the
Planck experiment. In this paper we consider two recently proposed methods of
fitting for reionization and we discuss their respective advantages. We test
both methods by performing a MonteCarlo Markov Chain analysis of simulated
Planck data, assuming different fiducial reionization histories. We take into
account both temperature and polarization data up to high multipoles, and we
fit for both reionization and non reionization parameters. We find that while a
wrong assumption on reionization may bias \tau_e, A_s and r by 1-3 standard
deviations, other parameters, in particular n_s, are not significantly biased.
The additional reionization parameters introduced by considering the model
independent methods do not affect the accuracy of the estimates of the main
cosmological parameters, the biggest degradation being of order ~ 15% for
\tau_e. Finally, we show that neglecting Helium contribution in the analysis
increases the bias on \tau_e, r and A_s even when a general fitting approach to
reionization is assumed.
