This paper is about tracking an extended object or a group target, which gives rise to a varying number of measurements from different measurement sources. For this purpose, the shape of the target is tracked in addition to its kinematics. The target extent is modeled with a new approach called Random Hypersurface Model (RHM) that assumes varying measurement sources to lie on scaled versions of the shape boundaries. In this paper, a star-convex RHM is introduced for tracking star-convex shape approximations of targets. Bayesian inference for star-convex RHM is performed by means of a Gaussian-assumed state estimator allowing for an efficient recursive closed-form measurement update. Simulations demonstrate the performance of this approach for typical extended object and group tracking scenarios.