Tracking extended targets aims to estimate the kinematic state and shape of the target of interest with a varying number of noisy detections received by a sensor. The key challenge in this problem stems from its nonlinearity and high dimensionality due to the target maneuver and model complexities. This paper presents a modified adaptive extended Kalman filter based on the random hypersurface model (RHM) to address this problem. First, the target maneuver is judged by using the input estimate (IE) chi-square detector. Then, the magnitude of the target maneuver is used to modify the prior of the shape parameters. Based on the prior information, we derive an extended Kalman filter for a closed-form recursive measurement update. The simulation and experimental results demonstrate the usefulness of the proposed method for tracking the maneuvering star-convex extended target.