Trajectory Prediction Uncertainty Research Articles

Robust aircraft conflict resolution under trajectory prediction uncertainty

In air traffic control, aircraft velocity may be perturbed due to weather effects or measurements errors and affect trajectory prediction. We address the aircraft conflict resolution problem in the presence of such perturbations. We consider polyhedral uncertainty sets on aircraft velocity, develop a budgeted robust optimization approach and show that it is amenable to mixed-integer optimization. Numerical experiments reveal that perturbations of the order of 5% on aircraft velocities can be accounted for without significantly impacting performance.

Assessing the prediction uncertainty in a route optimization model for autonomous maritime logistics

AbstractUnmanned operations and automation in modern industry create complex everyday problems, which require algorithmic thinking and creativity. Development of risk assessment methods is critical for the future of this business segment. To provide decision support for the management of an autonomous emission control boat, we begin by proposing a k‐Nearest‐Neighbours (k‐NN)‐based trajectory prediction method. This is employed in a bi‐objective routing problem of finding a Hamiltonian circuit in a dynamic network defined by predicted locations of ships over time. The objectives are maximizing the number of measurement tasks to be done and minimizing the corresponding total travel distance of the emission control boat. To evaluate the impact of trajectory prediction uncertainty on Pareto‐optimal itineraries, we propose a risk measure in a mean‐risk framework. The risk is defined based on an expected shortfall when implementation of an efficient itinerary under the predicted trajectories needs rescheduling based on realized trajectories. The risk measure helps the decision maker to evaluate choice alternatives among efficient itineraries under predicted trajectories and to make a balanced risk‐adjusted decision. We show how historical data is employed in integer linear programming for the estimation of such risk measure. Empirical results demonstrate such estimation.

Interdependent Uncertainty Handling in Trajectory Prediction

The concept of 4D trajectory management relies on the prediction of aircraft trajectories in time and space. Due to changes in atmospheric conditions and complexity of the air traffic itself, the reliable prediction of system states is an ongoing challenge. The emerging uncertainties have to be modeled properly and considered in decision support tools for efficient air traffic flow management. Therefore, the subjacent causes for uncertainties, their effects on the aircraft trajectory and their dependencies to each other must be understood in detail. Besides the atmospheric conditions as the main external cause, the aircraft itself induces uncertainties to its trajectory. In this study, a cause-and-effect model is introduced, which deals with multiple interdependent uncertainties with different stochastic behavior and their impact on trajectory prediction. The approach is applied to typical uncertainties in trajectory prediction, such as the actual take-off mass, non-constant true air speeds, and uncertain weather conditions. The continuous climb profiles of those disturbed trajectories are successfully predicted. In general, our approach is applicable to all sources of quantifiable interdependent uncertainties. Therewith, ground-based trajectory prediction can be improved and a successful implementation of trajectory-based operations in the European air traffic system can be advanced.

Stochastic Optimal Control for Ground-Based Metering Operations

Trajectory-based operations is a NextGen program concept that uses trajectory prediction, scheduling tools, and improved methods for trajectory management to improve the capacity and efficiency of the National Airspace System. Metering operations are one element of trajectory-based operations and involve the sequencing and scheduling of aircraft to flow-constrained points or meter points. Aircraft trajectories are managed to the schedule to ensure aircraft-to-aircraft spacing across the meter point. Automation tools are being developed to support air traffic controller tasks in managing aircraft trajectories to meet scheduled times of arrival at the meter points. Uncertainties in trajectory prediction, such as those related to wind-forecast and aircraft-modeling errors, pose a significant challenge in the design of automation for trajectory management. This paper proposes a framework for exploring and designing metering strategies in the presence of trajectory uncertainties, in which tradeoffs between the costs of interventions and the costs of precisely meeting a scheduled time of arrival are quantified. A ground-based metering operation is formulated as a discrete-time, finite-horizon Markov decision process from which different control strategies for meeting a scheduled time of arrival can be explored. Simulation results demonstrate the opportunities for exploring control laws in a quantitative manner and the feasibility of designing optimal control laws given the trajectory uncertainties.

Aircraft Trajectory Planning Under Uncertainty by Light Propagation

In the SESAR framework (Single European Sky ATM Research), the need to increase the air traffic capacity motivated the 4D (space + time) aircraft trajectory planning. This paper deals with an important Air Traffic Management (ATM) problem that consists in generating sets of 4D conflict-free trajectories (the tactical planning problem). The Light Propagation Algorithm (LPA) was introduced in [1] to deal with this problem. LPA has recently been shown to manage successfully a full day of traffic over the French airspace, removing all conflicts while satisfying ATM constraints.In this paper, we adapt the LPA to take into account uncertainties in trajectory prediction. We introduce and test a new algorithm called u/LPA (LPA under uncertainty) on the same day of traffic. For some situations, uncertainties reduce so much the search space that the standard algorithm cannot guarantee conflict free situation. As a consequence, one must include some time constraints for few trajectories (so-called RTA points: Real Time of Arrival constraints) in order to remove the remaining conflicts. The goal of RTA points is to impose an aircraft to be at a specified position at some given time. This results into a new optimization formulation of the tactical trajectory planning problem involving the decision as to where/when RTA points should be imposed. In order to solve this new problem, here we are content with a simple heuristic that yields encouraging results.