As intelligent vehicles become increasingly computerized and networked, they gain more autonomous capabilities. However, they are also becoming more exposed to cyber-threats which are likely to be a more prominent concern. This paper proposes a cyber-attack detection method for autonomous vehicles based on secure estimation of vehicle states, with an example application under attacks in the vehicle localization system. To investigate the effects of vehicle model and estimator on the attack detection performance, different nonlinear vehicle dynamic models and estimation approaches are employed. The deviation between the measurement from the onboard sensors and the state estimation is monitored in real time. With the designed vehicle state estimator and preset threshold, the cyber-attack detection algorithm is further developed for autonomous vehicles, whose performance is tested in simulations where the vehicle localization system is assumed to be compromised during a double lane change maneuver. The test results demonstrate the feasibility and effectiveness of the proposed cyber-attack algorithm. In addition, the results illustrate the impacts of vehicle nonlinear characteristics on the cyber-attack detection performance. Beyond this, the effects of different vehicle models on the attack detection performance, as well as the selection of suitable filtering approaches for the attack detection, are also discussed.