This work investigates the application of Gaussian processes to capturing the probability distribution of a set of aircraft trajectories from historical measurement data. To achieve this, all data are assumed to be generated from a probabilistic model that takes the shape of a Gaussian process. The approach to Gaussian process modelling used here is based on a linear expansion of trajectory data into set of basis functions that may be parametrized by a multivariate Gaussian distribution.The parameters are learned through maximum likelihood estimation. The resulting probabilistic model can be used for both modelling the dispersion of trajectories along the common flightpath and for generating new samples that are similar to the historical data. The performance of this approach is evaluated using three trajectory datasets; toy trajectories generated from a Gaussian distribution, sounding rocket trajectories that are generated by a stochastic rocket flight simulator and aircraft trajectories on a given departure path from Dallas Fort Worth airport, as measured by ground-based radar. The results indicate that the maximum deviation between the probabilistic model and test data obtained for the three data sets are respectively 4.9%, 7.6% and 13.1%.
Technological developments in the last decade have shifted challenges in traffic flow management from obtaining and storing data, to analysing and presenting the enormous amount of available trajectory data in a comprehensible manner. This paper introduces a novel approach to visualising air-traffic, shifting the focus from displaying traffic density, towards directly visualising the flight corridors used by air-traffic. Such an approach is suitable for visualising air-traffic in three dimensions, which is particularly helpful in the vicinity of an airport where the air-traffic often changes level. Furthermore, the approach is data-driven, allowing the comparison of multiple trajectory datasets in order to identify changes in traffic corridors related to changing air-traffic and weather conditions. Finally, by using the probabilistic nature of the approach, it is possible to quantify the air-traffic complexity in terms of the traffic structure. The results presented in this paper show the approach applied to a trajectory dataset as measured by ground-radar near Denver airport (DEN
Take-off and landing are the periods of a flight where aircraft are most vulnerable to a ground based rocket attack by terrorists. While aircraft approach and depart from airports on pre-defined flight paths, there is a degree of uncertainty in the trajectory of each individual aircraft. Capturing and characterizing these deviations is important for accurate strategic planning for the defence of airports against terrorist attack. A methodology is demonstrated whereby approach and departure trajectories to a given airport are characterized statistically from historical data. It uses a two-step process of first clustering to extract the common trend, and then modelling uncertainty using Gaussian Processes (GPs). Furthermore it is shown that this approach can be used to either select probabilistic regions of airspace where trajectories are likely and -if required -can automatically generate a set of representative trajectories, or select key trajectories that are both likely and critically vulnerable. An evaluation of the methodology is demonstrated on an example data-set collected by the ground radar at an airport. The evaluation indicates that 99.8% of the calculated footprint underestimates less than 5% when replacing the original trajectory data with a set of representative trajectories.
Teetool is a Python package which models and visualises motion patterns found in two-and three-dimensional trajectory data. It models the trajectories as a Gaussian process and uses the mean and covariance of the trajectory data to produce a confidence region, an area (or volume) through which a given percentage of trajectories travel. The confidence region is useful in obtaining an understanding of, or quantifying, dispersion in trajectory data. Furthermore, by modelling the trajectories as a Gaussian process, missing data can be recovered and noisy measurements can be corrected. Teetool is available as a Python package on GitHub, and includes Jupyter Notebooks, showing examples for two-and three-dimensional trajectory data.
Predicting the flight-path of an unguided rocket can help overcome unnecessary risks. Avoiding residential areas or a car-park can improve the safety of launching a rocket significantly. Furthermore, an accurate landing site prediction facilitates recovery. This paper introduces a six-degrees-of-freedom flight simulator for large unguided model rockets that can fly to altitudes of up to 13 km and then return to earth by parachute. The open-source software package assists the user with the design of rockets, and its simulation core models both the rocket flight and the parachute descent in stochastic wind conditions. Furthermore, the uncertainty in the input variables propagates through the model via a Monte Carlo wrapper, simulating a range of possible flight conditions. The resulting trajectories are captured as a Gaussian process, which assists in the statistical assessment of the flight conditions in the face of uncertainties, such as changes in wind conditions, failure to deploy the parachute, and variations in thrust. This approach also facilitates concise presentation of such uncertainties via visualisation of trajectory ensembles.
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