Hybrid Machine Learning and Estimation-based Flight Trajectory Prediction in Terminal Airspace

For air traffic management, trajectory prediction plays an important role as the predicted trajectory information is used in crucial tasks for the safety and efficiency of air traffic operations, such as conflict detection and resolution, scheduling, and sequencing. In this paper, we propose a framework for trajectory prediction in terminal airspace by combining a machine learning-based method and a physics-based estimation method. A trajectory prediction model based on machine learning is trained from historical surveillance data to represent the collective behavior of a set of flight trajectories, from which the data-driven prediction can be obtained as the expected future behavior of an incoming flight. A physics-based estimation algorithm called Residual-Mean Interacting Multiple Models (RM-IMM) then incorporates the machine learning prediction as a pseudo-measurement to account for the current motion of the aircraft. The proposed framework is tested, with real air traffic surveillance data, by predicting the future state information of the flights for real-time air traffic control applications. The results show that the proposed framework produces a greatly improved prediction accuracy compared to the two existing machine learning-based algorithms.


I. INTRODUCTION
To accommodate the growing demand of air traffic, the modern Air Traffic Management (ATM) system becomes one of the most complex and vast systems. Among the operations in airspace which consists of en-route, terminal, and surface, terminal airspace operations have a higher impact on the entire ATM system's safety and efficiency due to the high traffic density and highly structured operational procedures, such as Standard Terminal Arrival Route (STAR) and Standard Instrument Departure (SID). According to the data published by Boeing [1], 65 percent of fatal accidents occur in terminal airspace, while it accounts for only 6 percent of the total flight time. Therefore, most research on decision support tools has focused on terminal airspace to help Air Traffic Controllers (ATC) who are responsible for the safety and efficiency in terminal airspace. The performance of decision support tools highly relies on the accuracy of trajectory prediction for ATC's tasks such as conflict detection and resolution, sequencing, and scheduling. In this regard, there have been extensive efforts in the development of trajectory prediction algorithms, which can be categorized as estimation-based methods and machine learning-based methods.
In estimation-based methods, the behaviors of aircraft are characterized based on the governing dynamics, and the aircraft's current states are propagated into the future timesteps based on the dynamics by using tools such as Kalman filtering or its variations. In [2], a trajectory prediction technique is proposed based on a stochastic differential equation that describes the aircraft's motion disturbed by wind, and the distribution of solutions to the stochastic differential equation is approximated as a Markov chain. In [3], the aircraft's dynamics is represented by using a stochastic linear hybrid system (SLHS). A hybrid estimation technique is combined with an intent inference algorithm for aircraft trajectory prediction. This approach has been extended in [4] by considering a state-dependent transition model to better represent the changes in flight modes, such as Constant Velocity (CV) and Coordinated Turn (CT) modes.
In [5], an online four-dimensional trajectory prediction technique is developed based on a point-mass model and aircraft performance data, along with a conformance monitoring and aircraft intent update process for more accurate trajectory prediction.
In machine learning-based methods, a trajectory pattern is identified as a set of flight trajectories with similar behaviors, from which a data-driven model is trained to represent the collective behavior of the trajectory pattern using machine learning techniques such as support vector regression [6], Gaussian Mixture Models (GMM) [7], [8], recurrent neural network [9], Long Short-Term Memory (LSTM) [10], [11], and hybrid deep learning [12]- [14]. With the trained model, the future trajectory is predicted as the expected behavior of the aircraft in the future timesteps, given a series of measurements observed until the current timestep. For specific operational conditions, several machine learning-based methods have been developed for trajectory prediction in enroute airspace [11], [13], [15]- [18] and terminal airspace [7], [8], [10], [12], [19]. Especially in terminal airspace, [8], [19] focused on the operations in extended terminal airspace (about 20 minutes or 100 nm from an airport) to predict the Estimated Time of Arrival (ETA) of arrival flights, while [7], [10] presented the prediction of aircraft's position in the airspace close to an airport (1 to 2.5 minutes from an airport), for both takeoff and landing. In [19], major trajectory patterns are first identified by using a clustering method and then the ETA for each pattern is learned based on a regression model. The ETA of an aircraft is obtained as a weighted sum of ETAs of individual trajectory patterns, where the weight is the probability of the aircraft following that specific trajectory pattern. In [7], a trajectory prediction is performed for 1 minute from an airport using a probabilistic trajectory model based on the GMM, which is also used in [8] for the extended terminal airspace, considering the different time horizons up to 100 nm from an airport. A deep learning-based approach is proposed in [10] based on LSTM for the prediction horizon of 1.5 minutes for takeoff and 2.5 minutes for landing. In [20], multi-aircraft trajectory prediction is proposed based on the social LSTM by effectively capturing the interaction between aircraft.
In the estimation-based methods, the expected future behaviors of an aircraft rely on the assumption that the aircraft follows its flight plan or an a priori known trajectory pattern. In this paper, such information is extracted from historical data by using machine learning techniques that can represent the collective behavior (or pattern) of the aircraft which operated in terminal airspace. Note that there could be some degree of errors in the trained model due to the assumed structure of the machine learning model, and the machine learning-based methods cannot explicitly account for the current motion of an aircraft. Hence, the machine learning model could generate inaccurate (possibly unfeasible) future states that violate the aircraft dynamics. To make up for it, we propose a flight trajectory prediction framework by combining the following two approaches: The collective behavior of a set of similar flight trajectories is represented as a machine learning model trained from historical data; and for the aircraft's observed states until the current timestep, the machine learning model is then used to generate the expected states in the future timesteps, which are fed into an estimation-based method that combines the expected states from the data with the propagated states from the current state into the future timesteps based on the aircraft dynamics. The framework of the proposed method is illustrated in Fig. 1 which consists of (i) data preparation by using a pattern identification framework, (ii) construction of a machine learning model with the identified trajectory patterns, and (iii) the hybrid trajectory prediction method that combines the machine learning-based method and the estimation-based method. The main contributions of this paper are as follows: is used for inferring the current dynamics of aircraft and estimating the future trajectory. To the best of our knowledge, it is the first work to combine a machine learning-based method and an estimation-based method to enhance aircraft trajectory prediction performance in complex terminal airspace. • The proposed method guarantees the real-time prediction of trajectory for 2 minutes look-ahead time, while the combined LSTM and RM-IMM method failed to predict in real-time. This prediction horizon is set by considering the response time of both Conflict Alerts (CAs) and Minimum Safe Altitude Warnings (MSAWs) in literature [22]. • The proposed trajectory prediction method generates a greatly improved prediction accuracy compared to the baseline algorithms such as LSTM.
For the rest of this paper, the data preparation procedure is presented in Section II, and the proposed framework for trajectory prediction is described in Section III, followed by the demonstration with the real data in Section IV. Concluding remarks are given in Section V.

II. DATA PREPARATION
The air traffic surveillance data used in this paper are collected from the Automatic Dependent Surveillance-Broadcast (ADS-B) system. The dataset provides the aircraft's states, such as timestamp, position (longitude, latitude, altitude), and speed (horizontal and vertical) for each flight trajectory. In this paper, we consider the arrival and departure flights around the major airport in South Korea, Incheon International Airport (ICN), from January to August in 2019. The flight trajectories during a single month (January 2019) are shown in Fig. 2. During the period of January to August 2019, the number of arrival and departure trajectories are identified as 130,110 and 138,999, respectively. The track points of each trajectory are recorded every minute but with some missing or repeated timestamps. The trajectories with heavily missing points are excluded from the dataset and repeated points are removed. After performing data cleaning, the trajectories recorded within 60 nm from the airport are considered as flights in the entire terminal airspace of ICN. To handle the trajectories more effectively and efficiently, the trajectories with similar behaviors are grouped together by using the trajectory pattern identification algorithm that we developed [23]. Based on this framework, firstly, the dissimilarity between trajectories is computed using Dynamic Time Warping (DTW) [24] and Euclidean distance. Then, trajectories are being linked using the Ward's linkage method [25] and a dendrogram can be built. The dendrogram allows us to choose the number of trajectory patterns that we want. The number of trajectory pattern is chosen such that all trajectories within one pattern share the same set of waypoints.
As an illustrative example, the resultant trajectory patterns, a set of the trajectories arriving at and departing from ICN along two specific routes, are presented in Fig. 3. The arrival flights pass through a fix at the east of ICN, called KARBU, which is the entry fix to the arrival route, and then approach from the southeast direction for landing (i.e., landing at Runway 33L/R or 34). Conversely, the departure flights take off from Runway 15L/R and pass through a fix at the east of ICN, called EGOBA, which is the last fix of the departure route. For the use of the data in the downstream step of the proposed trajectory prediction framework, the flight trajectories are resampled to have the same sampling time (∆t) and normalized between 0 and 1 in order to be fed into machine learning models. The normalization is computed as: where X is a flight trajectory data, max and min indicate the maximum and the minimum value of the sample, respectively, andX is the normalized data. VOLUME 4, 2016

III. METHODOLOGY
In this section, we present the proposed algorithm for trajectory prediction in terminal airspace, that is, the hybrid machine learning and estimation-based trajectory prediction method. Two machine learning-based prediction methods are firstly explained as baseline algorithms: (i) conventional Gaussian Mixture Model (GMM) and (ii) Long Short-Term Memory (LSTM) which is a widely used deep learning method for time-series data. A Stochastic Linear Hybrid System (SLHS) is introduced and then the proposed hybrid approach for trajectory prediction is presented by combining a machine learning model and an estimation method.

1) GMM-based Trajectory Prediction Method
Each trajectory pattern has similar property along the spatial dimension, however, there exists some degree of variability in not only the spatial but also temporal dimensions. To capture such variability in each trajectory pattern, we use a GMM [26], that is, the probability distribution of datapoints can be modeled as a mixture of multiple Gaussian distributions. In the air traffic surveillance data, a flight trajectory is given in the form of a temporal sequence: where x t is the aircraft's position (longitude and latitude in the horizontal dimension and altitude in the vertical dimension) at timestep t ∈ [0, 1, · · · , T ] and T is the final timestep. The set of N flight trajectories is used to train a GMM whose Probability Density Function (PDF) is given as: where N (X|µ k , Σ k ) is the PDF of the multivariate Gaussian distribution with the mean µ k and the covariance Σ k , and For learning the GMM, we use the Expectation-Maximization (EM) algorithm which finds a maximum-likelihood fit for the given data. The number of Gaussian components, K, is a design parameter for balancing between underfitting (with a smaller K, which leads to a large training error) and overfitting (with a larger K, which leads to a large test error), which can be determined by using the criterion such as Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) [27], or by investigating the performance measure such as the prediction error.
For a new incoming flight observed up to the current timestep, the learned GMM corresponding to a trajectory pattern can generate its future trajectory for a given time horizon. We define a prediction time, T p , as the timestep when the prediction is performed (or the current timestep) and a prediction horizon, T h , as the duration of the future timesteps during which the future trajectory is predicted (T p + T h ≤ T ). Let each trajectory be partitioned as the past part X P = [x 0 , x 1 , · · · , x Tp ] T and the future part Similarly, the mean and the covariance of a Gaussian component are partitioned as: For a new incoming flight, X P new , its posterior probability for the k-th Gaussian component, k ∈ [1, · · · , K], is computed as:w The conditional mean and covariance of X F new with respect to the k-th Gaussian component are then given as: Finally, the PDF of X F new conditioned on X P new is obtained as: which yields the total conditional mean (or the predicted trajectory) as: For the illustration, we demonstrate two prediction examples as shown in Fig. 4. Given the number of Gaussian components of K = 10 and 10 past measurements (black star), the GMM computes the means from the posterior distribution (lime) and predicts the future states (red) of the aircraft using Eqs. (6) and (9).

2) LSTM-based Trajectory Prediction Method
In order to effectively process temporal sequential data in Eq. (2) using deep learning, the Recurrent Neural Network (RNN) [29], or its variant, called Long Short-Term Memory (LSTM) [30], has been widely used in flight trajectory prediction [10]- [13], [15], [31] to utilize its power in memorizing the information in the previous timesteps. To generate a one-step ahead prediction using LSTM by taking all the previous measurements, the input time-series and output time-series are constructed with a one-step shift, that is, for each trajectory, the input and output are given as {x t } T −1 t=0 and {y t } T −1 t=0 where y t = x t+1 , respectively. The structure of LSTM is shown in Fig. 5 where x t is an input element andŷ t is a predicted output element at timestep t. In the computation ofŷ t , the temporal dependency of the input elements in the previous timesteps, from 0 to t − 1, can be incorporated by the hidden state h t−1 and the memory cell c t−1 . At timestep t, the memory cell c t is first updated as: wherec t is the pseudo-memory cell at timestep t to update the new information from x t , which is fused with the memory cell at the previous timestep, c t−1 , to obtain the memory cell at timestep t, c t . The information flow is controlled by the forget gate, Γ f ∈ [0, 1] (for the past information, c t−1 ), and the update gate, Γ u ∈ [0, 1] (for the new information,c t ). These gates including the output gate, Γ o ∈ [0, 1], are given as: for (·) ∈ {f, u, o} where σ (·) is the sigmoid activation function and the parameters W 's and b's are the weight and bias parameters, respectively. The hidden state, h t , and the predicted output, y t , are then computed as: where tanh (·) is the hyperbolic tangent function and g y is the activation function such as hyper-tangent or sigmoid. The parameters W 's and b's are obtained by minimizing the error between the actual and predicted output elements, i.e., In order to improve the performance and get the best results, multiple LSTM layers with 512 units are stacked, followed by a few fully-connected layers with the Rectified Linear Unit (ReLU) activation function to reduce the dimension. The number of epochs and batch size varied with different trajectory patterns.

B. HYBRID PREDICTION METHOD 1) Estimation-based Trajectory Prediction Method
To accurately account for the aircraft's motion in terminal airspace, which involves frequent changes of flight modes, e.g., from straight flight to turning or from altitude hold to altitude change, the aircraft's dynamics is modeled as a Stochastic Linear Hybrid System (SLHS) [28], [32], in which the discrete dynamics describes the transitions in the flight modes and the continuous dynamics represents how the aircraft's continuous states (such as position and speed) evolve along time in each mode. For each discrete state, or mode, q(t) ∈ Q := {1, . . . , n d } where n d is the total number of modes, the SLHS model is given by: where at given timestep t, ξ(t) ∈ R l is the continuous state, ζ(t) ∈ R p is the measurement, and ω q(t) (t) and υ(t) are the process noise and the measurement noise, assumed to be zero-mean white Gaussian noises with the covariances Q q(t) (t) and R(t), respectively. The system matrices A q(t) , E q(t) and C q(t) are with proper dimensions for each mode q(t). The discrete dynamics is represented by a constant mode transition probability matrix where π ij is the constant mode transition probability from mode i to mode j and i∈Q π ij = 1 for j ∈ Q. With the SLHS model, we use an estimation algorithm called Residual-Mean Interacting Multiple Models (RM-IMM) [21] which works as shown in Fig. 6. Suppose that Z t = {ζ(0), ζ(1), · · · , ζ(t)} is the measurement sequence up to timestep t and let Pr [·|·] denote a conditional probability density function. At timestep t, assume that we have the followings for all the modes i ∈ Q: • The probabilities of the discrete state (or mode probability), α i (t) := Pr [q (t) = i|Z t ]; and • A continuous state estimateξ i (t) with its covariance P i (t) conditioned on the measurement Z t and the event q (t) = i By taking the data-driven pseudo measurement with its covariance as input, ζ(t+1) =z(t+1) and R(t+1) =R(t+1), the mode-conditioned continuous state estimates and mode probabilities are updated as follows: • In each discrete state (or mode) j ∈ Q, the modeconditioned continuous state estimateξ j (t + 1) and its covariance P j (t + 1) are updated by a mode-matched Kalman filter: whereξ 0j (t) is the initial condition of the state estimate, K j (t + 1) is the Kalman filter gain, and ν j (t + 1) is the innovation computed by Kalman filter j. P j (t + 1|t) is the covariance of the state estimate at timestep t + 1 before the measurement update. • The mode probability α j (t + 1) is updated based on the Bayesian rule for all j ∈ Q: where m(t+1) is a normalization constant and Λ j (t+1) is the likelihood function of mode j computed with the residual and its covariance by Kalman filter j.

2) Integration of Machine Learning-based and Estimation-based Methods
In order to integrate the machine learning model and the estimation algorithm, we propose to use the machine learning prediction as a pseudo measurement for an estimation-based prediction using RM-IMM, to account for the expected future behavior as well as the current motion of an aircraft. As shown in Fig. 7, the trained model first generates a pseudo measurement by taking the previous measurements up to timestep t. The estimation algorithm (RM-IMM) propagates the current state through the aircraft dynamics and then corrects the propagated state by using the pseudo measurement. Note that the input and output of the estimation-based method are given in a stochastic form, i.e., the PDF of the data-driven pseudo measurement, N z(t + 1),R(t + 1) , as input and the PDF of the (posterior) prediction, N ẑ(t + 1),R(t + 1) , as output. Since this information can be readily provided by the learned GMM using Eq. (8), the incorporation of the GMM-based predicted measurement and RM-IMM can be achieved without additional integration processes. However, the LSTM-based method works in a deterministic manner, that is, it takes a sequence of points, x 0 , · · · , x t , and generates a pseudo measurement,z(t + 1).
To address the mismatch in the format of the input and output, we integrate the LSTM model and RM-IMM as follows: • From the output of RM-IMM given as a PDF at timestep t, N ẑ(t),R(t) , a set of points are sampled. Each sampled point is then fed into the LSTM-based prediction method to obtain an output point at timestep t + 1. • The set of output points from the LSTM-based prediction method are fitted into a Gaussian PDF, N z(t + 1),R(t + 1) , to be used as an input to RM-IMM.
Therefore, it is concluded that the proposed hybrid trajectory prediction approach can be applicable to conventional machine learning (GMM) as well as deep learning (LSTM), that is, hybrid GMM and RM-IMM and hybrid LSTM and RM-IMM are made available.
However, since the trajectory prediction should be achieved in an online fashion from the application perspective, the computational efficiency of the algorithm is crucial. We run four prediction algorithms on a computer with Intel Core i7-9750H CPU, 16 GB RAM, and NVIDIA GeForce RTX 2060 GPU under a Windows system. The computation time of predicting the flight trajectory for 2 minutes lookahead time is measured as shown in Table 1. The computation time of the LSTM-based hybrid method is significantly larger than that of the other algorithms due to the numerically intensive sampling process, which means it is unable to meet the requirement for real-time applications. For this reason, the GMM, LSTM model, and GMM-based hybrid method are used to perform experimental tests and validation in the next section.

IV. EXPERIMENTAL RESULTS
To test and demonstrate the methodology described in Section III with the processed data in Section II, we compare and analyze three trajectory prediction methods by using historical ADS-B data in this section. The dataset has a total of 269,109 trajectories, which include 130,110 arrivals and 138,999 departures. The dataset for both GMM and LSTM is divided into a training dataset and a test dataset with the ratio 8:2, and 20% of the training dataset for LSTM is used as a validation dataset.

A. PERFORMANCE METRICS
To measure the performance of the trajectory prediction methods in detail, we introduce four metrics that are widely used in trajectory prediction [33]- [35]. The horizontal error (HE) measures the difference between the actual and expected locations of an aircraft in the horizontal dimension. The along-track error (ATE) and cross-track error (CTE) measure the parallel and perpendicular difference to the actual course between the aircraft's actual and predicted positions. The vertical error (VE) represents the altitude error in the vertical dimension. These metrics can also be computed by using Root Mean Square Error (RMSE) which is given by where n is the number of data points. P t represents the trajectory predicted by a model and R t denotes the actual trajectory at timestep t. Since RMSE is always non-negative, the smaller the values of each metric, the closer the prediction is to the actual value, which means that the model's prediction is more accurate.

B. COMPARATIVE ANALYSIS
The literature [22] has shown that the median response time (i.e., the time between the activation of an alert and the issue of a control instruction) following a Conflict Alerts (CAs) and a Minimum Safe Altitude Warnings (MSAWs) are 88 seconds and 38 seconds, respectively. In this regard, the 2-minutes-ahead prediction could help ATC's situational awareness that is important for safe and efficient air traffic operations. In the experimental tests, the predictions of each method are performed over the horizon of 24 timesteps (120 seconds with the time interval ∆t = 5 seconds). For the illustration, we first present representative trajectories for the arrivals and the departures around ICN. Figure  8 presents a total of 4 prediction results of two arrivals (a, b) and two departures (c, d). The actual and the predicted trajectories in the horizontal dimension and in the vertical dimension are plotted in the left and the right, respectively. As can be seen from Fig. 8 (a1 -d1), the horizontal prediction of the three methods shows the same trend with the actual trajectory, but the predicted trajectory of the LSTM model deviates significantly, especially in the heading, from the actual trajectory compared with the other two methods. In Fig. 8 (a2 -d2), compared with the actual altitude, the predicted trajectory points of the LSTM model have large fluctuations at some timesteps. For all the plots in Fig. 8, it VOLUME 4, 2016   can generally be seen that the trajectories predicted by the proposed hybrid method are closest to the actual trajectory, with the smallest error, followed by GMM and LSTM.
To evaluate the performance of the proposed hybrid trajectory prediction method, the four metrics of HE, ATE, CTE, and VE discussed in Section IV-A are first computed based on the predicted trajectories of arrival aircraft and ground truth. For the illustration, the histograms of the metrics are presented in Fig. 9. The HE histogram of the proposed method is skewed to the left and the ATE, CTE, and VE histograms are concentrated on around zero, which means the proposed method outperforms the other methods in terms of the given evaluation metrics.
We carried out the extensive trajectory prediction tests with all the available test dataset for the quantitative evaluation of the proposed method, and the RMSE of HE, ATE, CTE, and VE is used to measure prediction accuracy. The RMSE is computed using Eq. (25) and the results of arrival  and departure flights are presented in Table 2 and Table 3, respectively. The comparison shows that the prediction errors, HE, ATE, CTE, and VE, of the proposed hybrid method for arrival flights are reduced by 46.8%, 48.6%, 24.2%, and 1.2% compared to the prediction errors of GMM on average and by 76.0%, 77.4%, 65.0%, and 55.8% compared to the prediction errors of the LSTM model on average. Similarly, the prediction errors of the hybrid method for departure flights also show significant performance improvements, that is, huge error reduction compared to the other two baseline algorithms, like the arrivals. Therefore, based on these quantitative analysis results, it is concluded that our hybrid trajectory prediction method outperforms the GMM and the LSTM model for the given time horizon.
In other words, the experimental results show that the GMM, as well as the proposed hybrid method, can predict the future position of the aircraft trajectories more accurately than the LSTM model in general. Interestingly, as shown in Fig. 10, while the LSTM model performs similarly to the hybrid trajectory prediction method and better than the GMM for one or two-step prediction (corresponding to 5 or 10 seconds), it is quickly outperformed by the other two methods as the prediction time grows. This is because for LSTM, as discussed in Section III-A2, only the future position in onestep ahead can be predicted at a time, to achieve real-time prediction. For a look-ahead time of 2 minutes, the LSTM model needs to be implemented multiple times, each time with a new one-step prediction appended to the original data. Therefore, the error from each step's prediction propagates, which causes the performance of the LSTM model to be worse than the proposed hybrid method and the GMM in multi-step trajectory prediction.
The prediction errors of the hybrid method are lower than those of GMM in general. The difference is attributed to the current dynamics (or flight mode) of the aircraft that is explicitly incorporated into the hybrid method, while the GMM generates future predictions based only on the learned model and past measurements. For the illustration, the prediction example by a single GMM that shows poor performance is presented in Fig. 11. The predicted trajectory of the GMM begins to slow down and turn as soon as the prediction starts, even though the aircraft maintains the Constant Velocity (CV) mode. This sudden change in the aircraft's motion cannot be explained by its dynamics because the current motion of the aircraft follows the CV mode with a high probability. Due to the interaction between the GMM and RM-IMM in Fig. 7, the pseudo measurement from the GMM has been corrected by RM-IMM step by step, and thus the prediction is kept closer to the ground truth, while the prediction by a single GMM significantly deviates from the ground truth after five steps. Therefore, we conclude that the proposed hybrid machine learning and an estimation-based method can contribute to enhancing the prediction accuracy by facilitating the benefits of both methods.

V. CONCLUSION
In this paper, we proposed a framework for trajectory prediction in terminal airspace by combining a machine learningbased method and estimation-based method to enhance the prediction accuracy. The collective behavior of a trajectory pattern was represented as a machine learning model that is based on Gaussian Mixture Model (GMM), whose output serves as a pseudo measurement for an estimation-based prediction method, Residual-Mean Interacting Multiple Models (RM-IMM). The proposed method was tested and demonstrated with real air traffic surveillance data for the operations in the terminal airspace around Incheon International Airport (ICN) in South Korea. A total of 269,109 trajectories are considered in the experiments and the four metrics, horizontal error, along-track error, cross-track error, and vertical error, are used to measure the trajectory prediction errors. The quantitative comparison showed that the proposed method yields better accuracy than the GMM and LSTM model, which means the proposed method could help enhance ATC's situational awareness that is important for the safety and efficiency of air traffic operations in terminal airspace.
However, the proposed method has the following limitations: (i) It considers 2 minutes look-ahead time based on the literature [22]. However, this work can be extended to longer prediction times; (ii) Reliability of data-driven trajectory prediction is not considered in this paper even though adversarial attack could induce the proposed method to generate incorrect predictions; and (iii) It used only surveillance data since other features such as meteorological data (i.e., wind speed and direction) and operational information are not included in the Automatic Dependent Surveillance-Broadcast (ADS-B) data. Therefore, in future work, these limitations will be further studied to achieve more accurate and reliable trajectory prediction for longer look-ahead times. In addition, we will enhance the prediction performance, which could be improved by performing a further clustering along the temporal dimension.