Tracking Arbitrarily Shaped Extended Objects Using Gaussian Processes

In this paper, we consider the problem of tracking dynamic objects with unknown shapes using point cloud measurements generated by sensors such as lidars and radars. Specifically, our objective is to extend the Gaussian process-based extended object tracking (GPEOT) framework to encompass a broader class of objects. The derivation of the existing GPEOT algorithms is based on the assumption that the object of interest is star-convex. This assumption enables the modeling of the object’s extent through a radial distance function, which is described by a Gaussian process (GP). To enhance the flexibility of the resulting trackers, we propose the utilization of a potential function to indicate the unknown object extent. This approach enables the representation of objects with arbitrary shapes, including those that are non-convex and composed of disconnected components. Closely following the original formulation of GPEOT, the potential function is then modeled by a GP, which systematically accounts for the intrinsic spatial correlation of the extent. Furthermore, we develop a state-space model that incorporates both kinematic variables and an approximate description of the underlying GP model. The state vector can be estimated via a standard Bayesian technique, leading to an EOT algorithm. Through simulation experiments, we demonstrate the suggested method can satisfactorily estimate the kinematic variables of the objects while simultaneously learning their complex shapes.