This paper presents methods for vehicle state estimation and prediction for autonomous driving. A roundabout is chosen to apply the methods and illustrate the results as autonomous vehicles have difficulty in handling roundabouts. State estimation based on the unscented Kalman filter (UKF) is introduced first with application to a roundabout. The microscopic traffic simulator SUMO is used to generate realistic traffic in the roundabout for the simulation experiments. Change point detection based driving behavior prediction using a multi policy approach is then introduced and evaluated for the round intersection example. Finally, these methods are combined for vehicle trajectory estimation based on UKF and policy prediction and demonstrated using the roundabout example.