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Two main factors, including regression accuracy and adversarial attack robustness, of six trajectory prediction models are measured in this paper using the traffic flow management system (TFMS) public dataset of fixed-wing aircraft trajectories in a specific route provided by the Federal Aviation Administration. Six data-driven regressors with their desired architectures, from basic conventional to advanced deep learning, are explored in terms of the accuracy and reliability of their predicted trajectories. The main contribution of the paper is that the existence of adversarial samples was characterized for an aircraft trajectory problem, which is recast as a regression task in this paper. In other words, although data-driven algorithms are currently the best regressors, it is shown that they can be attacked by adversarial samples. Adversarial samples are similar to training samples, however, they can cause finely trained regressors to make incorrect predictions, which poses a security concern for learning-based trajectory prediction algorithms. It is shown that although deep-learning-based algorithms (e.g., long short-term memory (LSTM)) have higher regression accuracy with respect to conventional classifiers (e.g., support vector regression (SVR)), they are more sensitive to crafted states, which can be carefully manipulated even to redirect their predicted states towards incorrect states. This fact poses a real security issue for aircraft as adversarial attacks can result in intentional and purposely designed collisions of built-in systems that can include any type of learning-based trajectory predictor.

Best paper award in the trajectory prediction track; International audience; Ground-based aircraft trajectory prediction is a major concern in air traffic control and management. A safe and efficient prediction is a prerequisite to the implementation of new automated tools. In current operations, trajectory prediction is computed using a physical model. It models the forces acting on the aircraft to predict the successive points of the future trajectory. Using such a model requires knowledge of the aircraft state (mass) and aircraft intent (thrust law, speed intent). Most of this information is not available to ground-based systems. Focusing on the climb phase, we train neural networks to predict some of the unknown point-mass model parameters. These unknown parameters are the mass and the speed intent. For each unknown parameter, our model predicts a Gaussian distribution. This predicted distribution is a predictive distribution: it is the distribution of possible unknown parameter values conditional to the observed past trajectory of the considered aircraft. Using this distribution, one can extract a predicted value and the uncertainty related to this specific prediction. Using a physical model like BADA, this distribution could be used to derive a probability distribution of possible future trajectory ([1]). This study relies on ADS-B data coming from The OpenSky Network. It contains the climbing segments of the year 2017 detected by this sensor network. The 11 most frequent aircraft types are studied. The obtained data set contains millions of climbing segments from all over the world. Using this data, we show that despite having an RMSE slightly larger than previously tested methods, the predicted uncertainty allows us to reduce the size of prediction intervals while keeping the same coverage probability. Furthermore, we show that the trajectories with a similar predicted uncertainty have an observed RMSE close to the predicted one. The data set and the machine learning code are publicly available.

International audience; Ground-based aircraft trajectory prediction is a major concern in air traffic control and management. Focusing on the climb phase, we predict some of the unknown point-mass model parameters. These unknown parameters are the mass and the speed intent. This speed intent is parameterized by three values (cas 1 , cas 2 , $M$ ). These missing parameters might be useful to predict the future trajectory of a climbing aircraft. In this work, an ensemble of neural networks uses the observed past trajectory of the considered aircraft as input and predicts a Gaussian Mixture Model (GMM) modeling the joint distribution of (mass, cas 1 , cas 2 , $M$ ). Ideally, this predicted distribution will be close to a conditional distribution: the distribution of possible (mass, cas 1 , cas 2 , $M$ ) values given the observed past trajectory of the considered aircraft. This study relies on ADS-B data coming from The OpenSky Network. It contains the climbing segments of the year 2017 detected by this sensor network. The obtained data set contains millions of climbing segments from all over the world. Using this data, we show that using the proposed predictive model instead of a regression model brings almost as much information as using a regression model instead of a simple mean. The data set and the machine learning code are publicly available.

International audience; Ground-based aircraft trajectory prediction is a major concern in air traffic control and management. A safe and efficient prediction is a prerequisite to the implementation of new automated tools. In current operations, trajectory prediction is computed using a physical model. It models the forces acting on the aircraft to predict the successive points of the future trajectory. Using such a model requires knowledge of the aircraft state (mass) and aircraft intent (thrust law, speed intent). Most of this information is not available to ground-based systems. This paper focuses on the climb phase. We improve the trajectory prediction accuracy by predicting some of the unknown point-mass model parameters. These unknown parameters are the mass and the speed intent. This study relies on ADS-B data coming from The OpenSky Network. It contains the climbing segments of the year 2017 detected by this sensor network. The 11 most frequent aircraft types are studied. The obtained data set contains millions of climbing segments from all over the world. The climbing segments are not filtered according to their altitude. Predictive models returning the missing parameters are learned from this data set, using a Machine Learning method. The trained models are tested on the two last months of the year and compared with a baseline method (BADA used with the mean parameters computed on the first ten months). Compared with this baseline, the Machine Learning approach reduce the RMSE on the altitude by 48 % on average on a 10 minutes horizon prediction. The RMSE on the speed is reduced by 25 % on average. The trajectory prediction is also improved for small climbing segments. Using only information available before the considered aircraft takeoff , the Machine Learning method can predict the unknown parameters, reducing the RMSE on the altitude by 25 % on average. The data set and the Machine Learning code are publicly available.

This paper describes the application of high-confidence-interval prediction methods to the aircraft trajectory prediction problem, more specifically to the altitude prediction during climb. We are interested in methods for finding two-sided intervals that contain, with a specified confidence, at least a desired proportion of the conditional distribution of the response variable. This paper introduces two-sided Bonferroni-quantile confidence intervals, which is a new method for obtaining high-confidence two-sided intervals in quantile regression. This paper also uses the Bonferroni inequality to propose a new method for obtaining tolerance intervals in least squares regression. The latter has the advantages of being reliable, fast, and easy to calculate. We compare physical point-mass models to the introduced models on an air traffic management data set composed of traffic at major French airports. Experimental results show that the proposed interval prediction models perform significantly better than the conventional point-mass model currently used in most trajectory predictors. When comparing with a recent state-of-the-art point-mass model with adaptive mass estimation, the proposed methods give altitude intervals that are slightly wider but more reliable.

International audience; Predicting aircraft trajectories is a key element in the detection and resolution of air traffic conflicts. In this paper, we focus on the ground-based prediction of final descents toward the destination airport. Several Machine Learning methods – ridge regression, neural networks, and gradient-boosting machine – are applied to the prediction of descents toward Toulouse airport (France), and compared with a baseline method relying on the Eurocontrol Base of Aircraft Data (BADA). Using a dataset of 15,802 Mode-S radar trajectories of 11 different aircraft types, we build models which predict the total descent length from the cruise altitude to a given final altitude. Our results show that the Machine Learning methods improve the root mean square error on the predicted descent length of at least 20 % for the ridge regression, and up to 24 % for the gradient-boosting machine, when compared with the baseline BADA method.

International audience; In this paper, we apply Machine Learning methods to improve the aircraft climb prediction in the context of ground-based applications. Mass is a key parameter for climb prediction. As it is considered a competitive parameter by many airlines, it is currently not available to ground-based trajectory predictors. Consequently, most predictors today use a reference mass that may be different from the actual aircraft mass. In previous papers, we have introduced a least square method to estimate the mass from past trajectory points, using the physical model of the aircraft. Another mass estimation method, based on an adaptive mechanism, has also been proposed by Schultz et. al. We now introduce a new approach, where the mass is considered as the response variable of a prediction model that is learned from a set of example trajectories. This Machine Learning approach is compared with the results obtained when using the BADA (Base of Aircraft Data) reference mass or the two state-of-the-art mass estimation methods. In these experiments, 9 different aircraft types are considered. When compared with the baseline method (resp. the mass estimation methods), the Machine Learning approach reduces the RMSE (Root Mean Square Error) on the predicted altitude by at least 58 % (resp. 27 %) when assuming the speed profile to be known, and by at least 29 % (resp. 17 %) when using the BADA speed profile except for the aircraft types E145 and F100. For these types, the observed speed profile is far from the BADA speed profile.

International audience; In this paper, we apply Machine Learning methods to improve the aircraft climb prediction in the context of groundbased applications. Mass and speed intent are key parameters for climb prediction. As they are considered as competitive parameters by many airlines, they are currently not available to groundbased trajectory predictors. Consequently, most predictors today use reference parameters that may be quite different from the actual ones. In our most recent paper ([1]), we have demonstrated that Machine Learning techniques provide a mass estimation significantly more precise than two state-of-the-art mass estimation methods. In this paper, we apply similar techniques to the speed intent. We first build a set of examples by adjusting CAS/Mach speed profile to each climb trajectory in our database. Then, using the adjusted values (ccas; cM) in this database, we learn a model able to predict the (cas;M) values of a new trajectory, using its past points as input. We apply this technique to actual Mode-C radar data and we consider 9 different aircraft types. When compared with the reference speed profiles provided by BADA, the reduction of the speed RMSE ranges from 36 % to 79 %, depending on the aircraft type. Using the predicted mass and speed profile, BADA is used to compute the predicted future trajectory with a 10 minute horizon. When compared with BADA used with the reference parameters, the reduction of the future altitude RMSE ranges from 45 % to 87 %.

International audience; This paper focuses on the estimation of the aircraft mass in ground-based applications. Mass is a key parameter for climb prediction. It is currently not available to groundbased trajectory predictors because it is considered a competitive parameter by many airlines. There is hope that the aircraft mass might become widely available someday, but in the meantime it is possible to estimate an equivalent mass from the data already available, assuming the thrust to be known (maximum or reduced climb thrust for example). In a previous paper ([1]), two mass estimation methods were compared using simulated data. In this paper, we compare these two mass estimation methods using Mode-C radar data. Both methods estimate the aircraft mass by fitting the modeled energy rate (i.e. the power of the forces acting on the aircraft) with the energy rate observed at several points of the past trajectory. The first method, proposed by Schultz et al. ([2]), dynamically adjusts the weight parameter so as to fit the energy rate, using an adaptive sensitivity parameter to weight each observation. The second method, introduced in one of our previous publications ([1]), estimates the mass by minimizing the quadratic error on the observed energy rate, taking advantage of the polynomial expression of the modeled power when using the BADA model. The actual mass is unavailable in our radar data. However, we can use the estimated mass to compute a trajectory prediction. This prediction is then compared to the actual trajectory giving us some insight on the accuracy of the estimated mass. We have compared the obtained predictions with the ones obtained using the BADA reference mass. The root mean square error on the predicted altitude is reduced by 45 % using the least squares method. With the adaptive method this error is divided by two.

Ground-based aircraft trajectory prediction is a critical issue for air traffic management. A safe and efficient prediction is a prerequisite for the implementation of automated tools that detect and solve conflicts between trajectories. In this scope, this work proposes two non-parametric interval prediction methods in the regression context. These methods are designed to predict intervals that contain at least a desired proportion of the conditional distribution of the response value (referred to predictive intervals). Firstly, we consider the problem of the estimation of a probability distribution with a small sample size. Based on the probabilistic interpretation of the possibility theory, we describe possibility distributions that encode different kinds of statistical interval. Then, we propose a statistical test to verify the reliability of an interval prediction model. We also introduce two measures for comparing different interval prediction models giving intervals that have different sizes and coverage. Starting from our work on statistical intervals (and the associated possibility distribution), we present a pair of methods to find two-sided predictive intervals for non-parametric least squares regression without the non-biased prediction and the error homoscedasticity assumptions. Our predictive intervals are built by using tolerance intervals on prediction errors in the query point neighborhood. The query point neighborhood is obtained with a fixed or variable size neighborhood selection method. We finally obtain a method that finds in most cases the smallest reliable predictive interval model of a dataset. The proposed interval prediction methods are compared with other well-known interval prediction methods both at the theoretical and the practical level. An evaluation is performed with nine benchmark datasets. They are tested on their reliability, efficiency, precision and tightness of their obtained envelope. These experiments show that our methods are more reliable, effective and precise than their competitors. The final chapter describes the application of our method to an aircraft trajectory prediction problem in the climb phase and we compare the results with those obtained with the state of the art algorithms and with physical models.; La prédiction de trajectoires d'avions à partir des données disponibles au sol est un problème critique pour le contrôle aérien. Une prédiction fiable et efficace est un prérequis pour l'implémentation d'outils automatiques pour la détection et la résolution de conflits entre les trajectoires. Dans ce contexte, nous proposons de nouvelles méthodes non paramétriques pour la prédiction d'intervalle contenant une proportion attendue des données avec un haut niveau de confiance. Dans un premier temps, nous traitons le problème de l'estimation d'une distribution de probabilité à partir d'un petit échantillon. En considérant l'interprétation des distributions de possibilité comme une famille de distributions de probabilité, nous décrivons un ensemble de distributions de possibilité qui résument différents types d'intervalles statistiques. Ensuite, nous proposons un cadre de travail pour vérifier si un modèle, construit à partir de données, respecte les propriétés de recouvrement requises par les intervalles de prédiction. Nous introduisons aussi deux mesures pour comparer des modèles de prédiction d'intervalle qui ont des tailles moyennes et des taux de recouvrement différents. A partir de nos travaux sur les intervalles statistiques (et leurs distributions de possibilité associés), nous présentons une nouvelle méthode pour induire des intervalles de prédictions bornés pour des méthodes de régression des moindres carrés non paramétriques sans assumer que la prédiction est non biaisée et que les erreurs sont homoscédastiques. Nos intervalles de prédiction sont construits en utilisant des intervalles de tolérances sur les erreurs dans le voisinage du point à prédire. Pour cela, nous décrivons une méthode de sélection de voisinage à taille fixe ou de voisinage à taille variable dépendant de la quantité d'informations autour du point. Nous obtenons un algorithme qui induit, dans la majorité des cas, les intervalles de prédiction fiables les plus petits possibles. Les méthodes que nous proposons sont comparées avec les méthodes les plus connues au niveau théorique et au niveau pratique. Une évaluation est effectuée sur neuf bases de données. La taille, l'efficacité, la fiabilité et la précision des intervalles prédits sont comparés. Ces expérimentations montrent que nos approches sont significativement plus précises et fiables que les autres. Enfin nous appliquons nos méthodes au problème de la prédiction de trajectoires d'avions et nous comparons les résultats avec ceux des méthodes classiques et des modèles physiques.

Ground-based aircraft trajectory prediction is a critical issue for air traffic management. A safe and efficient prediction is a prerequisite for the implementation of automated tools that detect and solve conflicts between trajectories. In this scope, this work proposes two non-parametric interval prediction methods in the regression context. These methods are designed to predict intervals that contain at least a desired proportion of the conditional distribution of the response value (referred to predictive intervals). Firstly, we consider the problem of the estimation of a probability distribution with a small sample size. Based on the probabilistic interpretation of the possibility theory, we describe possibility distributions that encode different kinds of statistical interval. Then, we propose a statistical test to verify the reliability of an interval prediction model. We also introduce two measures for comparing different interval prediction models giving intervals that have different sizes and coverage. Starting from our work on statistical intervals (and the associated possibility distribution), we present a pair of methods to find two-sided predictive intervals for non-parametric least squares regression without the non-biased prediction and the error homoscedasticity assumptions. Our predictive intervals are built by using tolerance intervals on prediction errors in the query point neighborhood. The query point neighborhood is obtained with a fixed or variable size neighborhood selection method. We finally obtain a method that finds in most cases the smallest reliable predictive interval model of a dataset. The proposed interval prediction methods are compared with other well-known interval prediction methods both at the theoretical and the practical level. An evaluation is performed with nine benchmark datasets. They are tested on their reliability, efficiency, precision and tightness of their obtained envelope. These experiments show that our methods are more reliable, effective and precise than their competitors. The final chapter describes the application of our method to an aircraft trajectory prediction problem in the climb phase and we compare the results with those obtained with the state of the art algorithms and with physical models., La prédiction de trajectoires d'avions à partir des données disponibles au sol est un problème critique pour le contrôle aérien. Une prédiction fiable et efficace est un prérequis pour l'implémentation d'outils automatiques pour la détection et la résolution de conflits entre les trajectoires. Dans ce contexte, nous proposons de nouvelles méthodes non paramétriques pour la prédiction d'intervalle contenant une proportion attendue des données avec un haut niveau de confiance. Dans un premier temps, nous traitons le problème de l'estimation d'une distribution de probabilité à partir d'un petit échantillon. En considérant l'interprétation des distributions de possibilité comme une famille de distributions de probabilité, nous décrivons un ensemble de distributions de possibilité qui résument différents types d'intervalles statistiques. Ensuite, nous proposons un cadre de travail pour vérifier si un modèle, construit à partir de données, respecte les propriétés de recouvrement requises par les intervalles de prédiction. Nous introduisons aussi deux mesures pour comparer des modèles de prédiction d'intervalle qui ont des tailles moyennes et des taux de recouvrement différents. A partir de nos travaux sur les intervalles statistiques (et leurs distributions de possibilité associés), nous présentons une nouvelle méthode pour induire des intervalles de prédictions bornés pour des méthodes de régression des moindres carrés non paramétriques sans assumer que la prédiction est non biaisée et que les erreurs sont homoscédastiques. Nos intervalles de prédiction sont construits en utilisant des intervalles de tolérances sur les erreurs dans le voisinage du point à prédire. Pour cela, nous décrivons une méthode de sélection de voisinage à taille fixe ou de voisinage à taille variable dépendant de la quantité d'informations autour du point. Nous obtenons un algorithme qui induit, dans la majorité des cas, les intervalles de prédiction fiables les plus petits possibles. Les méthodes que nous proposons sont comparées avec les méthodes les plus connues au niveau théorique et au niveau pratique. Une évaluation est effectuée sur neuf bases de données. La taille, l'efficacité, la fiabilité et la précision des intervalles prédits sont comparés. Ces expérimentations montrent que nos approches sont significativement plus précises et fiables que les autres. Enfin nous appliquons nos méthodes au problème de la prédiction de trajectoires d'avions et nous comparons les résultats avec ceux des méthodes classiques et des modèles physiques.

International audience; Ground-based aircraft trajectory prediction is a major concern in air traffic control and management. A safe and efficient prediction is a prerequisite to the implementation of automated tools that detect and solve conflicts between trajectories. This paper focuses on the climb phase, because predictions are much less accurate in this phase than in the cruising phase. Trajectory prediction usually relies on a point-mass model of the forces acting on the aircraft to predict the successive points of the future trajectory. The longitudinal acceleration and climb rate are determined by an equation relating the modeled power of the forces to the kinetic and potential energy rate. Using such a model requires knowledge of the aircraft state (mass, current thrust setting, position, velocity, etc.), atmospheric conditions (wind, temperature) and aircraft intent (thrust law, speed intent). Most of this information is not available to ground-based systems. In this paper, we improve the trajectory prediction accuracy by learning some of the unknown point-mass model parameters from past observations. These unknown parameters, mass and thrust, are adjusted by fitting the modeled specific power to the observed energy rate. The thrust law is learned from historical data, and the mass is estimated on past trajectory points. The adjusted parameters are not meant to be exact, however they are designed so as to improve the energy rate prediction. The performances of the proposed method are compared with the results of standard model-based methods relying on the Eurocontrol Base of Aircraft DAta (BADA), using two months of radar track records and weather data.

International audience; This paper focuses on the estimation of the aircraft mass in ground-based applications. Mass is a key parameter for climb prediction. It is currently not available to groundbased trajectory predictors because it is considered a competitive parameter by many airlines. There is hope that the aircraft mass might become widely available someday, but in the meantime it is possible to estimate an equivalent mass from the data already available, assuming the thrust to be known (maximum or reduced climb thrust for example). In this paper, we compare the performances of two mass estimation methods proposed in recent publications. Both methods estimate the aircraft mass by fitting the modeled energy rate (i.e. the power of the forces acting on the aircraft) with the energy rate observed at several points of the past trajectory. The first method, proposed by Schultz et al. ([1]), dynamically adjusts the weight parameter so as to fit the energy rate, using an adaptive sensitivity parameter to weight each observation. The second method, introduced in one of our previous publications ([2]), estimates the mass by minimizing the quadratic error on the observed energy rate, taking advantage of the polynomial expression of the modeled power when using the BADA model. The robustness of both methods to the observation errors is assessed, using simulated data with various distributions of the noise added to the observed state variables. The results show that both methods are able to find mass estimates that are very close to the "actual" mass, with slightly better performances for the least squares method.

International audience; Ground-based aircraft trajectory prediction is a critical issue for air traffic management. A safe and efficient prediction is a prerequisite for the implementation of automated tools that detect and solve conflicts between trajectories. Moreover, regarding the safety constraints, it could be more reasonable to predict intervals rather than precise aircraft positions . In this paper, a standard point-mass model and statistical regression method is used to predict the altitude of climbing aircraft. In addition to the standard linear regression model, two common non-linear regression methods, neural networks and Loess are used. A dataset is extracted from two months of radar and meteorological recordings, and several potential explanatory variables are computed for every sampled climb segment. A Principal Component Analysis allows us to reduce the dimensionality of the problems, using only a subset of principal components as input to the regression methods. The prediction models are scored by performing a 10-fold cross-validation. Statistical regression results method appears promising. The experiment part shows that the proposed regression models are much more efficient than the standard point-mass model. The prediction intervals obtained by our methods have the advantage of being more reliable and narrower than those found by point-mass model.

Ground-based aircraft trajectory prediction is a major concern in air traffic control and management. A safe and efficient prediction is a prerequisite to the implementation of automated tools that detect and solve conflicts between trajectories. This paper focuses on the climb phase, because predictions are much less accurate in this phase than in the cruising phase. Trajectory prediction usually relies on a point-mass model of the forces acting on the aircraft to predict the successive points of the future trajectory. The longitudinal acceleration and climb rate are determined by an equation relating the modeled power of the forces to the kinetic and potential energy rate. Using such a model requires knowledge of the aircraft state (mass, current thrust setting, position, velocity, etc.), atmospheric conditions (wind, temperature) and aircraft intent (thrust law, speed intent). Most of this information is not available to ground-based systems. In this paper, we improve the trajectory prediction accuracy by learning an unknown point-mass model parameter from past observations. This unknown parameter, the mass, is adjusted by fitting the modeled specific power to the observed energy rate. Two methods addressing this issue has been recently published. In this paper, we describe an improvement of the mass estimation method presented in one of them. Using a set of trajectories, the robustness of the two methods is compared by adding a noise on the observed variables.

In the mainframe of a project for the autonomous determination of best aircraft flight paths to avoid in-flight conflicts, SELEX Sistemi Integrati S.p.A. developed a bi-dimensional, i.e. altitude and distance, aircraft trajectory prediction tool that was enough accurate to support Air Traffic Management requirements with minimum processing load. Indeed, it is expected that this tool should be called hundreds of time per second by the main Air Traffic Management system in order to select best trajectories. The Aerospace System Group at the Department of Aerospace Engineering of the Università di Napoli “Federico II was funded by SELEX Sistemi Integrati S.p.A to provide support for this project by means of proper selection of aircraft dynamics models that could be adequate to meet the above mentioned requirements. Some project constraints were assigned to the system so that it would be adequate for real-time operation of conflict resolution routines. It must be capable to accurately track the performance status of aircrafts during all typical transport aircraft flight phases such as takeoff, climb, cruise, descent, and landing. Regarding the aircraft dynamics representation, the system was based on a customized version of the Total Energy Model that turned out as an efficient point-mass model. Moreover, the tool had to be easily upgradable in case new aircrafts were added in the airspace. For this reason, the Base of Aircraft Data developed by EUROCONTROL was adopted as reference. The paper describes tool architecture and results of performances compared to other assessed non real-time Trajectory Prediction software systems.