  WASP-33b is a retrograde hot Jupiter with a period of 1.2 days orbiting
around a rapidly rotating and pulsating A-type star. A previous study found
that the transit chord of WASP-33b had changed slightly from 2008 to 2014 based
on Doppler tomographic measurements. They attributed the change to orbital
precession caused by the non-zero oblateness of the host star and the
misaligned orbit. We aim to confirm and more precisely model the precession
behavior using additional Doppler tomographic data of WASP-33b obtained with
the High Dispersion Spectrograph on the 8.2m Subaru telescope in 2011, as well
as the datasets used in the previous study. Using equations of a long-term
orbital precession, we constrain the stellar gravitational quadrupole moment
$J_{2}=(9.14\pm 0.51)\times 10^{-5}$ and the angle between the stellar spin
axis and the line of sight $i_{\star}=96^{+10}_{-14}$ deg. These values update
that the host star is more spherical and viewed more equator than the previous
study. We also estimate that the precession period is $\sim$840 years. We also
find that the precession amplitude of WASP-33b is $\sim$67 deg and WASP-33b
transits in front of the host star for only $\sim$20\% of the whole precession
period.
