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The benchmarking of CO2 emissions serves as the foundation for the accurate assessment of the environmental impact of air traffic. To calculate the environmental benchmarks of arrival traffic flows with Point Merge System (PMS) patterns, this study proposes a 4D trajectory optimization method that combines data-driven and optimal control models. First, the predominant arrival routes of traffic flows are identified using the trajectory spectral clustering method, which provides the horizontal reference for 4D trajectory optimization. Second, an optimal control model for vertical profiles with point merging topology is established, with the objective of minimizing the fuel–time cost. Finally, considering the complex structure of the PMS, a flexible and adaptable genetic algorithm-based vertical profile nonlinear optimization model is created. The experimental results demonstrate that the proposed method is adaptable to variations in aircraft type and cost index parameters, enabling the generation of different 4D trajectories. The results also indicate an environmental efficiency gap of approximately 10% between the actual CO2 emissions of the arrival traffic flow example and the obtained benchmark. With this benchmark trajectory generation methodology, the environmental performance of PMSs and associated arrival aircraft scheduling designs can be assessed on the basis of reliable data.

Performing clustering analysis on a large amount of historical trajectory data can obtain information such as frequent flight patterns of aircraft and air traffic flow distribution, which can provide a reference for the revision of standard flight procedures and the optimization of the division of airspace sectors. At present, most trajectory clustering uses a single clustering algorithm. When other processing remains unchanged, it is difficult to improve the clustering effect by using a single clustering method. Therefore, this paper proposes a trajectory clustering ensemble method based on a similarity matrix. Firstly, a stacked autoencoder is used to learn a small number of features that are sufficiently representative of the trajectory and used as the input to the subsequent clustering algorithm. Secondly, each basis cluster is used to cluster the data set, and then a consistent similarity matrix is obtained by using the clustering results of each basis cluster. On this basis, using the deformation of the matrix as the distance matrix between trajectories, the agglomerative hierarchical clustering algorithm is used to ensemble the results of each basis cluster. Taking the Nanjing Lukou Airport terminal area as an example, the experimental results show that integrating multiple basis clusters eliminates the inherent randomness of a single clustering algorithm, and the trajectory clustering results are more robust.

Availability of different types of data and advances in data-driven techniques open the path to more detailed analyses of various phenomena. Here, we examine the insights that can be gained through the analysis of historical flight trajectories, using data mining techniques. The goal is to learn about usual (or nominal) choices airlines make in terms of routing, and their relation with aircraft types and operational flight costs. The clustering is applied to intra-European trajectories during one entire summer season, and a statistical test of independence is used to evaluate the relations between the variables of interest. Even though about half of all flights are less than 1000 km long, and mostly operated by one airline, along one trajectory, the analysis shows that, for longer flights, there exists a clear relation between the trajectory clusters and the operating airlines (in about 49% of city pairs) and/or the aircraft types (30%), and/or the flight costs (45%).

An airport’s terminal area is the bottleneck of the air transport system. Convective weather can seriously affect the normal flight status of arrival and departure flights. At present, pilots take different flight operation strategies to avoid convective weather based on onboard radar, visual information, adverse weather experience, etc. This paper studies trajectory clustering based on the OPTICS algorithm to obtain the arrival of typical flight routes in the terminal area. Based on weather information of the planned typical flight route and flight plan information, Random Forest (RF), K-nearest Neighbor KNN (KNN), and Support Vector Machines (SVM) algorithms were used for training and establishing the Arrival Flight Operation Strategy Prediction Model (AFOSPM). In this paper, case studies of historical arrival flights in the Guangzhou (ZGGG) and Wuhan (ZHHH) terminal area were carried out. The results show that trajectory clustering results based on the OPTICS algorithm can more accurately reflect the regular flight routes of arrival flights in a terminal area. Compared to KNN and SVM, the prediction accuracy of AFOSPM based on RF is better, reaching more than 88%. On this basis, six features—including 90% VIL, weather coverage, weather duration, planned route, max VIL, and planned Arrival Gate (AF)—were used as the input features for AFOSPM, which can effectively predict various arrival flight operation strategies. For the most frequently used arrival flight operation strategies under convective weather conditions—radar guidance, AF changing, and diversion strategy—the prediction accuracy of the ZGGG and ZHHH terminal areas can exceed 95%, 85%, and 80%, respectively.

Air traffic trajectory optimization is a complex, multidimensional and non-linear optimization problem and requires a firm focus on the essential criteria. The criteria cover operational, economical, environmental, political, and social factors and differ from continent to continent. Since air traffic is a transcontinental transport system, the criteria may also change during a single flight. Historic flight track data allow observation and assess real flights, to extract essential criteria and to derive optimization strategies to increase air traffic efficiency. Real flight track data from the Chinese and European air traffic show significant differences in the routing structure in both regions. For that reason, reference trajectories of historic ADS-B 24-h air traffic data in China and Europe have been extracted and analyzed regarding horizontal flight efficiency and the most restrictive criteria of trajectory optimization. We found that prohibited areas might be the most powerful reason to describe deviations from the great circle distance in the Chinese air traffic system. Atmospheric conditions, network requirements, aircraft types and flight planning procedures are similar in China and Europe and only have a minor impact on flight efficiency during the cruise phase. In a multi-criteria trajectory optimization of the extracted reference trajectories considering the weather, operational constraints and prohibited areas, we found that flown ground distances could be reduced by 255 km in the Chinese airspace and 2.3 km in the European airspace. The resultant reference trajectories can be used for further analysis to increase the efficiency of continental air traffic flows.

The aircraft trajectory clustering analysis in the terminal airspace is conducive to determining the representative route structure of the arrival and departure trajectory and extracting their typical patterns, which is important for air traffic management such as airspace structure optimization, trajectory planning, and trajectory prediction. However, the current clustering methods perform poorly due to the large flight traffic, high density, and complex airspace structure in the terminal airspace. In recent years, the continuous development of Deep Learning has demonstrated its powerful ability to extract internal potential features of large dataset. Therefore, this paper mainly tries a deep trajectory clustering method based on deep autoencoder (DAE). To this end, this paper proposes a trajectory clustering method based on deep autoencoder (DAE) and Gaussian mixture model (GMM) to mine the prevailing traffic flow patterns in the terminal airspace. The DAE is trained to extract feature representations from historical high-dimensional trajectory data. Subsequently, the output of DAE is input into GMM for clustering. This paper takes the terminal airspace of Guangzhou Baiyun International Airport in China as a case to verify the proposed method. Through the direct visualization and dimensionality reduction visualization of the clustering results, it is found that the traffic flow patterns identified by the clustering method in this paper are intuitive and separable.

The current airspace route system consists mainly of pre-defined routes with a low number of intersections to facilitate air traffic controllers to oversee the traffic. Our aim is a method to create an artificial and reliable route network based on planned or as-flown trajectories. The application possibilities of the resulting network are manifold, reaching from the assessment of new air traffic management (ATM) strategies or historical data to a basis for simulation systems. Trajectories are defined as sequences of common points at intersections with other trajectories. All common points of a traffic sample are clustered, and, after further optimization, the cluster centers are used as nodes in the new main-flow network. To build almost-realistic flight trajectories based on this network, additional parameters such as speed and altitude are added to the nodes and the possibility to take detours into account to avoid congested areas is introduced. As optimization criteria, the trajectory length and the structural complexity of the main-flow system are used. Based on these criteria, we develop a new cost function for the optimization process. In addition, we show how different traffic situations are covered by the network. To illustrate the capabilities of our approach, traffic is exemplarily divided into separate classes and class-dependent parameters are assigned. Applied to two real traffic scenarios, the approach was able to emulate the underlying route systems with a difference in median trajectory length of 0.2%, resp. 0.5% compared to the original routes.