This paper addresses the problem of tracking extended objects. Examples of extended objects are ships and a convoy of vehicles. Such kind of objects have particularities which pose challenges in front of methods considering the extended object as a single point. Measurements of the object extent can be used for estimating size parameters of the object, whose shape is modeled by an ellipse. This paper proposes a solution to the extended object tracking problem by mixture Kalman filtering. The system model is formulated in a conditional dynamic linear (CDL) form. Based on the specifics of the task, two latent indicator variables are proposed, characterising the mode of maneuvering and size type, respectively. The developed Mixture Kalman filter is validated and evaluated by computer simulation.