Hypersonic Hight vehicles have important strategic value in aerospace confrontation. However, the rapidly developing interception technologies and complex disturbance in adversarial environments pose great challenges to the design of evasion strategies for such vehicles. Aiming at the pursuit-evasion game problem of hypersonic Hight vehicles under three types of sensor measurement errors, namely relative distance, longitudinal line-of-sight angle and lateral line-of-sight angle, this paper proposes a dual-layer anti-disturbance game-based evasion control framework. First, based on the motion equations of both the attacker and defender, a relative kinematic model and a zero-sum differential game model are established, and the above measurement errors are modeled and characterized. Second, at the control layer, an anti-disturbance control algorithm based on a nonlinear adaptive observer is designed to compensate for the influence of measurement errors on the system. Then, at the game decision-making layer, a performance index function for the pursuit-evasion vehicles is developed. The optimal evasion strategy is derived by solving the corresponding Hamilton-Jacobi-Isaacs (HJI) equation, and adaptive dynamic programming is adopted to approximate the optimal strategy using a critic neural network. Finally, multi-scenario numerical simulations and Monte Carlo simulations are carried out to verify the effectiveness and robustness of the proposed method. The sensitivity of evasion performance to the three types of measurement errors is analyzed. The results demonstrate that the proposed method can effectively improve the evasion performance of hypersonic vehicles under measurement errors.