This paper addresses the problem of spatiotemporal wind velocity field estimation for air traffic management applications. Using data obtained from aircraft, the eastward and northward components of the wind velocity field inside a specific air space are calculated as functions of time. Both short-term wind velocity field forecasting and wind velocity field reconstruction are performed. Wind velocity data are indirectly obtained from the states of the aircraft flying in the relevant airspace, which are broadcast by the ADS-B and Mode-S aircraft surveillance systems. The wind velocity field is estimated by combining two data-driven techniques: the polynomial chaos expansion and the Gaussian process regression. The former approximates the global behavior of the wind velocity field, whereas the latter approximates the local behavior. The eastward and northward wind components of the wind velocity field must be estimated, which causes the problem to be a multiple-output problem. This method enables the estimation of the wind velocity field at any spatiotemporal location using wind velocity observations from any spatiotemporal location, eliminating the need for spatial and temporal grids. Moreover, since the method proposed in this article allows for the probability distributions of the estimates to be computed, it causes the computation of the confidence intervals to be possible. Furthermore, since the method presented in this paper allows for data assimilation, it can be used online to continuously update the wind velocity field estimation. The method is tested on different wind scenarios and different training-test data configurations, by means of which the consistency between the results of the wind velocity field forecasting and the wind velocity field reconstruction is checked. Finally, the ERA5 meteorological reanalysis data of the European Centre for Medium-Range Weather Forecasts are used to validate the proposed technique. The results show that the method is able to reliably estimate the wind velocity field from aircraft-derived data.

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Wind velocity field knowledge is crucial for the future air traffic management paradigm and is key in many applications, such as aircraft performance studies. This paper addresses the problem of spatio-temporal windc velocity field estimation. The north and east wind components within a given air space are estimated as a function of time. Both wind velocity field reconstruction in space for a past or present time instant and short-term prediction are performed. Wind data are obtained indirectly from the states of the aircraft broadcast by the Mode-S and ADS-B aircraft surveillance systems. The Gaussian process regression method, which is a flexible and universal estimator, is employed to solve both problems. Under general conditions, the method is statistically consistent, meaning that the method converges to the ground truth when increasingly more data are available, which is especially interesting, since aircraft data availability is expected to grow in the future through the deployment of the European System-Wide Information Management. Besides estimation, the Gaussian process regression method provides the probability distribution of any particular estimate, allowing confidence intervals to be computed. Moreover, the spatial modelling is performed using raw data without relying on grids and estimation can be performed at any spatio-temporal location. Furthermore, since the training phase of the method described in this paper is fast, requiring less than 5 minutes on a standard desktop computer, it can be used online to continuously track the state of the wind velocity field, thus allowing for data assimilation. In the case study presented in this paper, the Gaussian process regression method is tested on different days with different wind intensities. The available data set is split into several training and testing data sets, which are used to check the consistency of the results of wind velocity field reconstruction and prediction. Finally, the Gaussian process regression method is validated using the European Centre for Medium-Range Weather Forecasts ERA5 meteorological reanalysis data. The obtained results show that Gaussian process regression can be used to reliably estimate the wind velocity field from aircraft derived data.@en

This work addresses the problem of vertical wind profile online estimation at a given location. Specifically, the north and east components of the wind are continuously estimated as functions of time and altitude at two waypoints used for landing on the Adolfo Suarez Madrid-Barajas airport. A continuous nowcast of the wind profile is performed in which wind observations are derived from the aircraft states and assimilated into the model. It is well known that wind is one of the utmost contributors to uncertainties in the current and future paradigm of Air Traffic Management. Accurate wind information is key in continuous climb and descent operations, spacing, four dimensional trajectory-based operations, and aircraft performance studies, among others. In this work, wind data are obtained indirectly from the aircraft’s states broadcast by the Mode S and ADS-B aircraft surveillance systems. The Gaussian process regression is adapted to this framework and used to solve the problem. The presented method allows to construct a complete vector wind profile at any specific position that is continuous in time and altitude; namely, there is no need for grid points and time discretisation. The Gaussian process regression is a very flexible estimator which is statistically consistent under general conditions, meaning that it converges to the underground truth when more and more data are dispensed. In addition, the Gaussian process regression approach provides the whole probability distribution of any particular estimation, allowing confidence intervals to be computed naturally. In the case study presented in this paper, in which the wind is constantly estimated, the Gaussian process regression model is iteratively updated every 15 min to capture possible changes in the wind behaviour and give an estimation of the wind profile every half a minute. The method has been validated using a test dataset, achieving a reduction of 50% of the prediction uncertainty in comparison to a baseline model. Moreover, two popular wind profile estimators based on the Kalman filter are also implemented for the sake of comparison. The Kalman filter outperforms the baseline model, but it does not outperform the Gaussian process regression with errors higher by around 35%, in comparison. The obtained results show that the Gaussian process regression of aircraft-derived data reliably nowcast the wind state, which is key in Air Traffic Management.

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Accurate wind information is crucial in air traffic management, for instance, to improve trajectory predictability and precision in controlled time of arrival. Nowadays, air traffic management relies on Numerical Weather Prediction, which usually has a low resolution and low update rate. A potential approach for improving the resolution and accuracy of the weather predictions consist in using airborne aircraft as meteorological sensors. Aircraft surveillance systems such as ADS-B and Mode S, transmit data related to weather conditions, automatically or in response to interrogation by air traffic control surveillance radars. In this paper, three different methods for constructing wind profiles from surveillance data have been applied and a comparison between them carried out. The first two methods being modifications of the Kalman filter have been referred to as the Adapted Kalman Filter and Smooth Adapted Kalman Filter. The third one is based on Gaussian process regression. The Kalman filter based methods are able to assimilate nearby data in a straightforward way and update the wind speed estimation in real time. Gaussian process regression is a very flexible and general regression model that can smoothly interpolate in space and extrapolate in time. These three methods have been validated using a test data set, achieving a 50% reduction of the prediction uncertainty in comparison with a baseline model. In addition, the Gaussian process methodology has been applied to reconstruct and forecast the wind field. @en