  The goal of motion tomography is to recover a description of a vector flow
field using information on the trajectory of a sensing unit. In this paper, we
develop a predictor corrector algorithm designed to recover vector flow fields
from trajectory data with the use of occupation kernels developed by Rosenfeld
et al.. Specifically, we use the occupation kernels as an adaptive basis; that
is, the trajectories defining our occupation kernels are iteratively updated to
improve the estimation on the next stage. Initial estimates are established,
then under mild assumptions, such as relatively straight trajectories,
convergence is proven using the Contraction Mapping Theorem. We then compare to
the established method by Chang et al. by defining a set of error metrics. We
found that for simulated data, which provides a ground truth, our method offers
a marked improvement and that for a real-world example we have similar results
to the established method.
