  The vector Apodizing Phase Plate (vAPP) is a pupil plane coronagraph that
suppresses starlight by forming a dark hole in its point spread function (PSF).
The unconventional and non-axisymmetrical PSF arising from the phase
modification applied by this coronagraph presents a special challenge to
post-processing techniques. We aim to implement a recently developed
post-processing algorithm, temporal reference analysis of planets (TRAP) on
vAPP coronagraphic data. The property of TRAP that uses non-local training
pixels, combined with the unconventional PSF of vAPP, allows for more
flexibility than previous spatial algorithms in selecting reference pixels to
model systematic noise. Datasets from two types of vAPPs are analysed: a double
grating-vAPP (dgvAPP360) that produces a single symmetric PSF and a
grating-vAPP (gvAPP180) that produces two D-shaped PSFs. We explore how to
choose reference pixels to build temporal systematic noise models in TRAP for
them. We then compare the performance of TRAP with previously implemented
algorithms that produced the best signal-to-noise ratio (S/N) in companion
detections in these datasets. We find that the systematic noise between the two
D-shaped PSFs is not as temporally associated as expected. Conversely, there is
still a significant number of systematic noise sources that are shared by the
dark hole and the bright side in the same PSF. We should choose reference
pixels from the same PSF when reducing the dgvAPP360 dataset or the gvAPP180
dataset with TRAP. In these datasets, TRAP achieves results consistent with
previous best detections, with an improved S/N for the gvAPP180 dataset.
