The extended object tracking method under condition of now available probability framework requires the statistic information of the system measurement noise, however, most of the measurement noise is unknown but bounded in real object tracking systems, and the probability-based tracking methods are difficult to estimate the position and shape of the extended object accurately. For the above-mentioned reasons, an extended object tracking algorithm is proposed based on the set membership filter with unknown but bounded noise. The proposed algorithm expresses the unknown but bounded noise by using an enclosing ellipsoidal set and by using the set membership filter to calculate state set parameters. In the process of the estimation of the object shape, the Graham scan algorithm in convex hull computational geometry theory is used to calculate the minimum boundary matrix, including the maximum error of the object shape. To obtain the updated object shape matrix, the boundary parameters of Minkowski different are calculated by using the offset hypersurface and the affine transformation. The simulation results show that the estimation accuracy of the proposed algorithm under the UBB noise is prior to the Bayesian filters based on the traditional probability framework at the state and extent of the target.