David Gianazza

High Confidence Intervals Applied to Aircraft Altitude Prediction

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.

Optimization of air traffic control sector configurations using tree search methods and genetic algorithms

The paper describes two classical tree search algorithms and a genetic algorithm for the Air Traffic Flow Management process that take as input the traffic flows and build optimal sector configurations considering the airspace capacity constraints and also the maximum number of control positions that can be manned at each time of the day. This optimization is made in a realistic context, using the airspace description data, the traffic data, the number of available control positions, and the sector capacities of the French ATC centers.

Machine Learning and Mass Estimation Methods for Ground-Based Aircraft Climb Prediction

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 squares 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, in which the mass is considered 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 base of aircraft data (BADA) reference mass or the two state-of-the-art mass estimation methods. In these experiments, nine different aircraft types are considered. When compared with the baseline method (respectively, 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.

Wind parameters extraction from aircraft trajectories

When supervising aircraft, air traffic controllers need to know the current wind magnitude and direction since they impact every flying vessel. The wind may accelerate or slow down an aircraft, depending on its relative direction to the wind. Considering several aircraft flying in the same geographical area, one can observe how the ground speed depends on the direction followed by the aircraft. If a sufficient amount of trajectory data is available, approximately sinusoidal shapes emerge when plotting the ground speeds. These patterns characterize the wind in the observed area. After visualizing this phenomenon on recorded radar data, we propose an analytical method based on a least squares approximation to retrieve the wind direction and magnitude from the trajectories of several aircraft flying in different directions. After some preliminary tests for which the use of the algorithm is discussed, we propose an interactive procedure to extract the wind from trajectory data. In this procedure, a human operator selects appropriate subsets of radar data, performs automatic and/or manual curve fitting to extract the wind, and validates the resulting wind estimates. The operators can also assess the wind stability in time, and validate or invalidate their previous choices concerning the time interval used to filter the input data. The wind resulting from the least squares approximation is compared with two other sources - the wind data provided by Meteo-France and the wind computed from on-board aircraft parameters - showing the good performance of our algorithm. The interactive procedure received positive feedback from air traffic controllers, which is reported in this paper.

Separating air traffic flows by allocating 3D-trajectories

This paper introduces two algorithms which allocate optimal separated 3D-trajectories to the main traffic flows. The first approach is a 1 vs. n strategy which applies an A* algorithm iteratively to each flow. The second is a global approach using a genetic algorithm, applied to a population of trajectory sets. The algorithms are first tried on a toy problem, and then applied to real traffic data, using operational aircraft performances. The cumulated costs of the trajectory deviations are used to compare the two algorithms.

Finding and proving the optimum: cooperative stochastic and deterministic search

In this article, we introduce a global cooperative approach between an Interval Branch and Bound Algorithm and an Evolutionary Algorithm, that takes advantage of both methods to optimize a function for which an inclusion function can be expressed. The Branch and Bound algorithm deletes whole blocks of the search space whereas the Evolutionary Algorithm looks for the optimum in the remaining space and sends to the IBBA the best evaluation found in order to improve its Bound. The two algorithms run independently and update common information through shared memory. The cooperative algorithm prevents premature and local convergence of the evolutionary algorithm, while speeding up the convergence of the branch and bound algorithm. Moreover, the result found is the proved global optimum. In part 1, a short background is introduced. Part 2.1 describes the basic Interval Branch and Bound Algorithm and part 2.2 the Evolutionary Algorithm. Part 3 introduces the cooperative algorithm and part 4 gives the results of the algorithms on benchmark functions. The last part concludes and gives suggestions of avenues of further research.

Metaheuristics for Air Traffic Management

Air Traffic Management involves many different services such as Airspace Management, Air Traffic Flow Management and Air Traffic Control. Many optimization problems arise from these topics and they generally involve different kinds of variables, constraints, uncertainties. Metaheuristics are often good candidates to solve these problems. The book models various complex Air Traffic Management problems such as airport taxiing, departure slot allocation, en route conflict resolution, airspace and route design. The authors detail the operational context and state of art for each problem. They introduce different approaches using metaheuristics to solve these problems and when possible, compare their performances to existing approaches

Applications to Air Traffic Management

Air traffic management (ATM) is an endless source of challenging optimization problems. Before discussing applications of metaheuristics to these problems, let us describe an ATM system in a few words, so that readers who are not familiar with such systems can understand the problems being addressed in this chapter. Between the moment passengers board an aircraft and the moment they arrive at their destination, a flight goes through several phases: push back at the gate, taxiing between the gate and the runway threshold, takeoff and initial climb following a Standard instrument departure (SID) procedure, cruise, final descent following standard terminal arrival route (STAR), landing on the runway, and taxiing to the gate. During each phase, the flight is handled by several air traffic control organizations: airport ground control, approach and terminal control, en-route control. These control organizations provide services that ensure safe and efficient conduct of flights, from departure to arrival.