  The Random Hypersurface Model (RHM) is introduced that allows for estimating
a shape approximation of an extended object in addition to its kinematic state.
An RHM represents the spatial extent by means of randomly scaled versions of
the shape boundary. In doing so, the shape parameters and the measurements are
related via a measurement equation that serves as the basis for a Gaussian
state estimator. Specific estimators are derived for elliptic and star-convex
shapes.
