This paper provides new results and insights for tracking an extended target object modeled with an Elliptic Random Hypersurface Model (RHM). An Elliptic RHM specifies the relative squared Mahalanobis distance of a measurement source to the center of the target object by means of a one-dimensional random scaling factor. It is shown that uniformly distributed measurement sources on an ellipse lead to a uniformly distributed squared scaling factor. Furthermore, a Bayesian inference mechanisms tailored to elliptic shapes is introduced, which is also suitable for scenarios with high measurement noise. Closed-form expressions for the measurement update in case of Gaussian and uniformly distributed squared scaling factors are derived.