  High-precision transit photometry supplies ideal opportunities for detecting
new exoplanets and characterizing their physical properties, which usually
encode valuable information for unveiling the planetary structure, atmosphere
and dynamical history. We present revised properties of three transiting
systems (i.e., HAT-P-13, HAT-P-16 and WASP-32) through analyzing TESS
photometry and ground-based transit observations, which were obtained at the 1m
and 2.4m telescopes of Yunnan Observatories, China, and the 1.2m telescope of
Hamburg Observatory, Germany, as well as the data in the literature. During
modelling the transit light curves, Gaussian process is employed to account for
the potential systematic errors. Through comprehensive timing analysis, we find
that both HAT-P-13b and HAT-P-16b show significant timing variations (TTVs)
that can be explained by apsidal precession. TTVs of WASP-32b may be led by a
decaying orbit due to tidal dissipation or apsidal precession. However, the
current observations can not rule out the origins of three systems' TTVs from
gravitational perturbations of close planetary companions conclusively.
