  In this study, we investigate the problem of tracking objects with unknown
shapes using three-dimensional (3D) point cloud data. We propose a Gaussian
process-based model to jointly estimate object kinematics, including position,
orientation and velocities, together with the shape of the object for online
and offline applications. We describe the unknown shape by a radial function in
3D, and induce a correlation structure via a Gaussian process. Furthermore, we
propose an efficient algorithm to reduce the computational complexity of
working with 3D data. This is accomplished by casting the tracking problem into
projection planes which are attached to the object's local frame. The resulting
algorithms can process 3D point cloud data and accomplish tracking of a dynamic
object. Furthermore, they provide analytical expressions for the representation
of the object shape in 3D, together with confidence intervals. The confidence
intervals, which quantify the uncertainty in the shape estimate, can later be
used for solving the gating and association problems inherent in object
tracking. The performance of the methods is demonstrated both on simulated and
real data. The results are compared with an existing random matrix model, which
is commonly used for extended object tracking in the literature.
