The paper presents an analysis of a nonlinear filtering problem corresponding to tracking of an extended target whose shape is modelled by an ellipse. The measurements of target extent are assumed to be available in addition to the usual positional measurements. Using Cramer-Rao bounds we establish the best achievable error performance for this highly nonlinear problem. The theoretical bounds are used to examine the performance as a function of measurement accuracy, observer-target geometry and prior knowledge of shape parameters. Finally an extended Kalman filter (KF) and an unscented KF are developed for this application and their performance (consistency and RMS error) are examined.