## 1 Introduction  
The trajectory prediction (TP), as a core technique in air traffic studies, has been attracting more and more attention from all over the world. It is the foundation of performing many air traffic applications, such as traffic flow prediction and conflict detection [1; 2]. TP aims at predicting the flight trajectory in the near future based on its flight plan and motion patterns. As a part of our previous study, it was also applied to check the conformance of the flight trajectory [3], which ensures the safety of the flight operation. Machine learning-based algorithms were proposed to cope with the high stochasticity of the flight environment [4; 5; 6], typically a sequential regression task. In general, existing approaches can be summarized as the following categories:  
(a) Kinematics and dynamics-based approaches (KDAs): this type of approach divides the flight operation into different phases based on its flight profile, typically climb, cruise and descent [7; 8]. Considering the flight dynamics and aircraft performance constraints, several kinematics equations are built to illustrate the flight transition patterns for each phase [9], which are further solved to predict the flight trajectory. However, the KDA approach highly depends on the phase definition and fails to cope with the influence of the complicated and time-varying flight environment on kinematic and dynamic characteristics [10]. Consequently, the accuracy and stability of the prediction results failed to meet the requirements of air traffic research. (b) Filter-based approaches and its variations: the Kalman filter (KF) was first proposed to build the motion state transitions between two consecutive prediction instants [11]. Meanwhile, the correction rules were also proposed to build more accurate transition equations after receiving real-time observations (flight positions) [12; 13], which is expected to improve the finally prediction performance. In succession, some KF-based variations were proposed to improve the applicability for dealing with flight trajectories with heavy maneuverability [12; 13; 14; 15], such as climb, acceleration. Unfortunately, the representation of the transition patterns among flight motion states is always an obstacle for dealing with the drastic changes of the flight operation. (c) Machine learning-based approaches: the core idea of this type of approach is mining frequent transition patterns from historical trajectories [5; 16], which is further used to build the trajectory patterns of the predicted flights. In general, historical trajectories of a certain flight are proven to be feasible, safe and effective [4; 17]. Therefore, based on the learned transition patterns, a machine learning-based approach can obtain higher prediction accuracy than that of other hand-crafted models [18]. On one hand, some well-designed probabilistic model-based machine learning approaches were proposed to predict flight trajectory, such as the hidden Markov model [19; 20], Gaussian mixture model [21]. Gaussian process was also studied to check the conformance of flight trajectory in [22]. On the other hand, neural networks were also developed to predict flight trajectory by fitting the data distribution (i.e., flight transition patterns) from training samples automatically, such as deep neural networks (DNNs) [23; 24], recurrent neural networks (RNNs) [7; 25; 26], and long short-term memory block [27; 28; 29]. The machine learning-based approaches have recently been the most popular ones and obtained promising performance for many applications. It is clear that the learning mechanism is indispensable for dealing with the stochastic flight environment. In this work, we mainly focus on proposing a novel trajectory prediction approach that is able to illustrate the positional distribution integrally.