  The simple assumption of an instantaneous reionization of the Universe may
bias estimates of cosmological parameters. In this paper a model-independent
principal component method for the reionization history is applied to give
constraints on the cosmological parameters from recent Planck 2015 data. We
find that the Universe are not completely reionized at redshifts $z \ge 8.5$ at
95% CL. Both the reionization optical depth and the matter fluctuation
amplitude are higher than but consistent with those obtained in the standard
instantaneous reionization scheme. The high estimated value of the matter
fluctuation amplitude strengthens the tension between Planck CMB observations
and some astrophysical data, such as cluster counts and weak lensing. The
tension can significantly be relieved if the neutrino masses are allowed to
vary. Thanks to a high scalar spectral index, the low-scale spontaneously
broken SUSY inflationary model can fit the data well, which is marginally
disfavored at 95% CL in the Planck analysis.
