In the domain of sequence modelling, Recurrent Neural Networks (RNN) have been capable of achieving impressive results in a variety of application areas including visual question answering, part-of-speech tagging and machine translation. However this success in modelling short term dependencies has not successfully transitioned to application areas such as trajectory prediction, which require capturing both short term and long term relationships. In this paper, we propose a Tree Memory Network (TMN) for modelling long term and short term relationships in sequence-to-sequence mapping problems. The proposed network architecture is composed of an input module, controller and a memory module. In contrast to related literature, which models the memory as a sequence of historical states, we model the memory as a recursive tree structure. This structure more effectively captures temporal dependencies across both short term and long term sequences using its hierarchical structure. We demonstrate the effectiveness and flexibility of the proposed TMN in two practical problems, aircraft trajectory modelling and pedestrian trajectory modelling in a surveillance setting, and in both cases we outperform the current state-of-the-art. Furthermore, we perform an in depth analysis on the evolution of the memory module content over time and provide visual evidence on how the proposed TMN is able to map both long term and short term relationships efficiently via a hierarchical structure.
Approaches such as utilise probability models on aircraft dynamics in order to generate predictions on their future motion. They purely rely on the assumptions made on the dynamics of the aircraft, without using any historical information, which contributes to its main drawback. In @cite_33 , @cite_46 , @cite_14 researchers treated aircraft trajectory prediction as a machine learning problem, in which they train the model using historical trajectory data together with weather observations. Most recently @cite_7 proposed an approach that considered trajectories as a set of 4 dimensional data cubes, together with weather parameters. Initially they performed time series clustering on data for segmentation and then learnt a HMM on top of each cluster. Still due to the uncertainty with weather observations, these trajectory prediction approaches become inefficient.
@cite_46 @cite_14 @cite_33 @cite_7
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A machine learning approach to trajectory prediction for sequencing and merging of traffic following fixed arrival routes is described and evaluated using actual aircraft trajectory and meteorological data. In the approach a model is trained using historic data to make arrival time predictions. Model inputs are the aircraft type, aircraft ground speed and altitude at the start of the arrival route, surface wind, and altitude winds. A stepwise regression method is used to systematically determine the inputs and functions of inputs that are included in the prediction model based on their explanatory power. For the evaluation of the approach a 45 NM fixed arrival route was used that ends at the runway. Traffic performed a continuous descent operation. At a prediction horizon of 45 NM the model explained 63 of the observed variance in the arrival time. The mean absolute time error was 18 s. Finally, the prediction model was used to determine the required initial spacing interval between aircraft for continuous descent operation and examine the impact on runway throughput and conflicts. Using the prediction model, throughput increased by up to 4 aircraft per hour compared to a constant initial spacing. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004. This paper presents an approach to predict future motion of a moving object based on its past movement. This approach is capable of learning object movement in an open environment, which is one of the limitions in some prior works. The proposed approach exploits the similarities of short-term movement behaviors by modeling a trajectory as concatenation of short segments. These short segments are assumed to be noisy realizations of latent segments. The transitions between the underlying latent segments are assumed to follow a Markov model. This predictive model was applied to two real-world applications and yielded favorable performance on both tasks. At the heart of Air Traffic Management (ATM) lies the Decision Support Systems (DST) that rely upon accurate trajectory prediction to determine how the airspace will look like in the future to make better decisions and advisories. Dealing with airspace that is prone to congestion due to environmental factors still remains the challenge especially when a deterministic approach is used in the trajectory prediction process. In this paper, we describe a novel stochastic trajectory prediction approach for ATM that can be used for more efficient and realistic flight planning and to assist airspace flow management, potentially resulting in higher safety, capacity, and efficiency commensurate with fuel savings thereby reducing emissions for a better environment. Our approach considers airspace as a 3D grid network, where each grid point is a location of a weather observation. We hypothetically build cubes around these grid points, so the entire airspace can be considered as a set of cubes. Each cube is defined by its centroid, the original grid point, and associated weather parameters that remain homogeneous within the cube during a period of time. Then, we align raw trajectories to a set of cube centroids which are basically fixed 3D positions independent of trajectory data. This creates a new form of trajectories which are 4D joint cubes, where each cube is a segment that is associated with not only spatio-temporal attributes but also with weather parameters. Next, we exploit machine learning techniques to train inference models from historical data and apply a stochastic model, a Hidden Markov Model (HMM), to predict trajectories taking environmental uncertainties into account. During the process, we apply time series clustering to generate input observations from an excessive set of weather parameters to feed into the Viterbi algorithm. Our experiments use a real trajectory dataset with pertaining weather observations and demonstrate the effectiveness of our approach to the trajectory prediction process for ATM.