## 1 Introduction
It is observed that the method outperforms the widely used long short-term memory network, Markov, weighted Markov, support-vector machine, and Kalman filter models [15]. [PERSON] et al. proposed a 4D trajectory prediction model based on the backpropagation (BP) neural network. The results indicated that the predicted 4D trajectory is close to the real flight data, the time error at the crossing point is no more than 1 min, and the altitude error at the crossing point is no more than 50 m [16]. [PERSON] et al. developed a probabilistic horizontal interdependency measure between aircraft supported by machine learning algorithms, addressing time separations at crossing points [17]. In contrast to traditional civil aircraft or fixed-wing unmanned aerial vehicles (UAV), rotary-wing drones have high stability during vertical take-off and landing, hovering, and horizontal movement [18]. Due to the characteristics of strong maneuverability, high flexibility, and the changeable range of activities of rotary-wing drones, their intentions are not easy to capture, and their trajectories are more difficult to predict [19]. It is recognized that non-cooperative drones pose several safety and privacy concerns to the public [20]. Research has been conducted to identify target intent [21], some of which was conducted under the conditions of uncertain or incomplete information [22]. Existing trajectory prediction models for drones include models based on equations of kinematics and dynamics, such as the model predictive control model subject to aerodynamic disturbances [23], the motion-based trajectory paradigm shift that improves Flight Management System compatibility with tactical operations [8], the algorithm for the estimation, filtering, and prediction of the trajectories of light aircraft and gliders using interacting multiple model filters [24], and machine learning methods based on historic trajectory data, such as recurrent neural networks (RNNs), long short-term memory (LSTM), gated recurrent unit (GRU), and their various improved algorithms [25]. In the authors' previous research, a novel procedure based on the bidirectional gated recurrent unit (D-GRU) method has been proposed for intention recognition and the short-term trajectory prediction of quadrotors [26]. When a non-cooperative drone invades the prohibited zone of an airport or the protected area of a manned aircraft, it may collide with the manned aircraft that is taking off or landing near the airport [27]. To ensure the safe, orderly, and efficient operation of an aircraft in low-altitude airspace, it is necessary to obtain the accurate trajectory prediction results of manned aircraft and drones in order to provide technical support for abnormal behavior detection, conflict warning, and flight situation awareness. At present, the research on collision risk mainly focuses on the collision risk between manned aircraft or between drones, whereas there are a few works concentrated on the collision probability of intruding drones to manned aircraft. For example, a probabilistic model based on the stochastic kinematic model was developed to implement the collision risk evaluation. The cases covering different drones' initial positions, positions updates, and different collision zones are simulated and analyzed using the proposed collision-course based model [28]. A 3D Monte Carlo unmanned aircraft system (UAS) positional distribution model, based on flight dynamics of the UAS, was developed to help assess the risk posed by the UAS to aircraft operating inside the aerodrome. The 3D model was also used to carry out simulations that could help determine the buffer airspace needed for cooperative UASs operating inside the aerodrome [29]. Although few studies have been conducted with regard to the collision risk between manned aircraft and drones, most were based on kinematic models and simulation analysis under hypothetical assumptions.