The increasing intrusion of non-cooperative unmanned aerial vehicles (UAVs) into restricted zones poses significant security risks, demanding accurate trajectory prediction to enable effective countermeasures such as capture missions. Traditional Extended Kalman Filter (EKF) methods exhibit limitations by typically modeling complex time-varying disturbances (e.g., aerodynamic effects, evasion maneuvers) simplistically as Gaussian noise, introducing estimation bias. To address this limitation, this study proposes a Disturbance observer with EKF (DEKF) method. A state-disturbance coupled dynamic model is first established to explicitly decouple aerodynamic disturbances from autonomous maneuvers. Subsequently, a cascaded architecture integrating a nonlinear disturbance observer (NDO) with the EKF is designed, facilitating real-time disturbance tracking and joint state optimization utilizing solely position measurements. Stability analysis, grounded in stochastic system theory, derives convergence bounds for the state estimation error. Experimental results in UAV pursuit-evasion scenarios demonstrate that DEKF significantly outperforms the standard EKF, reducing position Root Mean Square Error (RMSE) by 68.5% and velocity RMSE by 32.9%. Furthermore, DEKF maintains robust performance under strong disturbances and low signal-to-noise ratio conditions, exhibiting minimal lag during target maneuvers. By tightly integrating physical modeling with robust estimation, DEKF provides a high-precision trajectory prediction solution for counter-UAV capture tasks, offering considerable application potential in critical domains such as airport security.