Modeling of extended objects based on support functions and extended Gaussian images for target tracking

This paper considers tracking of extended objects using the measurements of down-range and cross-range extent. This type of measurement can be naturally and intuitively expressed in terms of support functions. Based on support functions, we propose a general approach to model smooth shapes of objects. Another approach based on extended Gaussian image is proposed to model nonsmooth shapes such as polygons. Compared with existing approaches, a larger range of object shapes can be modeled by the proposed approaches, which have concise mathematical forms and favorable properties. Specifically for elliptical and rectangular objects, our approaches can be implemented easily utilizing simple parametric representations without the need to assume that the major axis of the object is parallel to its velocity vector. Based on these models, a Bayesian algorithm for extended object tracking is easily obtained, where the kinematic state and object extension can be jointly estimated effectively. The benefits of the proposed modeling approaches are illustrated by simulation results.