Citations
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file = {/home/lars/Zotero/storage/WKKE4DRU/an-intuitive-explanation-of-lstm-a035eb6ab42c.html}
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}
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@article{harrisArrayProgrammingNumPy2020,
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title = {Array Programming with {{NumPy}}},
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author = {Harris, Charles R. and Millman, K. Jarrod and van der Walt, St{\'e}fan J. and Gommers, Ralf and Virtanen, Pauli and Cournapeau, David and Wieser, Eric and Taylor, Julian and Berg, Sebastian and Smith, Nathaniel J. and Kern, Robert and Picus, Matti and Hoyer, Stephan and van Kerkwijk, Marten H. and Brett, Matthew and Haldane, Allan and del R{\'i}o, Jaime Fern{\'a}ndez and Wiebe, Mark and Peterson, Pearu and {G{\'e}rard-Marchant}, Pierre and Sheppard, Kevin and Reddy, Tyler and Weckesser, Warren and Abbasi, Hameer and Gohlke, Christoph and Oliphant, Travis E.},
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year = 2020,
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month = sep,
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journal = {Nature},
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volume = {585},
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number = {7825},
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pages = {357--362},
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publisher = {{Springer Science and Business Media LLC}},
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doi = {10.1038/s41586-020-2649-2}
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}
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@article{hunterMatplotlib2DGraphics2007,
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title = {Matplotlib: {{A 2D}} Graphics Environment},
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author = {Hunter, J. D.},
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year = 2007,
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journal = {Computing in Science \& Engineering},
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volume = {9},
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number = {3},
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pages = {90--95},
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publisher = {IEEE COMPUTER SOC},
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doi = {10.1109/MCSE.2007.55},
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abstract = {Matplotlib is a 2D graphics package used for Python for application development, interactive scripting, and publication-quality image generation across user interfaces and operating systems.}
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}
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@misc{nntikz,
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title = {{{NNTikZ}}: {{TikZ}} Diagrams for Deep Learning and Neural Networks},
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author = {Love, Fraser},
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@@ -60,6 +86,24 @@
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publisher = {GitHub}
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}
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@misc{paszkePyTorchImperativeStyle2019,
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title = {{{PyTorch}}: {{An Imperative Style}}, {{High-Performance Deep Learning Library}}},
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shorttitle = {{{PyTorch}}},
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author = {Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen, Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca and Desmaison, Alban and K{\"o}pf, Andreas and Yang, Edward and DeVito, Zach and Raison, Martin and Tejani, Alykhan and Chilamkurthy, Sasank and Steiner, Benoit and Fang, Lu and Bai, Junjie and Chintala, Soumith},
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year = 2019,
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month = dec,
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number = {arXiv:1912.01703},
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eprint = {1912.01703},
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primaryclass = {cs},
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publisher = {arXiv},
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doi = {10.48550/arXiv.1912.01703},
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urldate = {2025-12-18},
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abstract = {Deep learning frameworks have often focused on either usability or speed, but not both. PyTorch is a machine learning library that shows that these two goals are in fact compatible: it provides an imperative and Pythonic programming style that supports code as a model, makes debugging easy and is consistent with other popular scientific computing libraries, while remaining efficient and supporting hardware accelerators such as GPUs. In this paper, we detail the principles that drove the implementation of PyTorch and how they are reflected in its architecture. We emphasize that every aspect of PyTorch is a regular Python program under the full control of its user. We also explain how the careful and pragmatic implementation of the key components of its runtime enables them to work together to achieve compelling performance. We demonstrate the efficiency of individual subsystems, as well as the overall speed of PyTorch on several common benchmarks.},
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archiveprefix = {arXiv},
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keywords = {Computer Science - Machine Learning,Computer Science - Mathematical Software,Statistics - Machine Learning},
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file = {/home/lars/Zotero/storage/SAGV7FKX/Paszke et al. - 2019 - PyTorch An Imperative Style, High-Performance Deep Learning Library.pdf;/home/lars/Zotero/storage/P3AZNUD7/1912.html}
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}
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@article{riahimaneshAnalysisVulnerabilitiesAttacks2017,
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title = {Analysis of Vulnerabilities, Attacks, Countermeasures and Overall Risk of the {{Automatic Dependent Surveillance-Broadcast}} ({{ADS-B}}) System},
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author = {Riahi Manesh, Mohsen and Kaabouch, Naima},
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@@ -107,6 +151,20 @@
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file = {/home/lars/Zotero/storage/5SHHA862/Shi et al. - 2018 - LSTM-based Flight Trajectory Prediction.pdf}
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}
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@misc{teamPandasdevPandasPandas2025,
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title = {Pandas-Dev/Pandas: {{Pandas}}},
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shorttitle = {Pandas-Dev/Pandas},
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author = {pandas development {team}, The},
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year = 2025,
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month = sep,
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doi = {10.5281/zenodo.17229934},
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urldate = {2025-10-16},
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abstract = {Pandas is a powerful data structures for data analysis, time series, and statistics.},
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howpublished = {Zenodo},
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keywords = {data science,python},
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file = {/home/lars/Zotero/storage/QV289HHN/17229934.html}
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}
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@misc{zhangPhasedFlightTrajectory2022,
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title = {Phased {{Flight Trajectory Prediction}} with {{Deep Learning}}},
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author = {Zhang, Kai and Chen, Bowen},
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+13
-1
@@ -1,4 +1,4 @@
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\begin{thebibliography}{8}
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\begin{thebibliography}{12}
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\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi
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\expandafter\ifx\csname bibnamefont\endcsname\relax
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\def\bibnamefont#1{#1}\fi
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@@ -36,4 +36,16 @@
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\bibitem[{102()}]{102GatedRecurrent}
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\emph{\bibinfo{title}{10.2. {{Gated Recurrent Units}} ({{GRU}}) --- {{Dive}} into {{Deep Learning}} 1.0.3 documentation}}, \bibinfo{howpublished}{https://d2l.ai/chapter\_recurrent-modern/gru.html}.
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\bibitem[{\citenamefont{Paszke et~al.}(2019)\citenamefont{Paszke, Gross, Massa, Lerer, Bradbury, Chanan, Killeen, Lin, Gimelshein, Antiga et~al.}}]{paszkePyTorchImperativeStyle2019}
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\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Paszke}}, \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Gross}}, \bibinfo{author}{\bibfnamefont{F.}~\bibnamefont{Massa}}, \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Lerer}}, \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Bradbury}}, \bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{Chanan}}, \bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{Killeen}}, \bibinfo{author}{\bibfnamefont{Z.}~\bibnamefont{Lin}}, \bibinfo{author}{\bibfnamefont{N.}~\bibnamefont{Gimelshein}}, \bibinfo{author}{\bibfnamefont{L.}~\bibnamefont{Antiga}}, \bibnamefont{et~al.}, \emph{\bibinfo{title}{{{PyTorch}}: {{An Imperative Style}}, {{High-Performance Deep Learning Library}}}} (\bibinfo{year}{2019}), \eprint{1912.01703}.
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\bibitem[{\citenamefont{Harris et~al.}(2020)\citenamefont{Harris, Millman, van~der Walt, Gommers, Virtanen, Cournapeau, Wieser, Taylor, Berg, Smith et~al.}}]{harrisArrayProgrammingNumPy2020}
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\bibinfo{author}{\bibfnamefont{C.~R.} \bibnamefont{Harris}}, \bibinfo{author}{\bibfnamefont{K.~J.} \bibnamefont{Millman}}, \bibinfo{author}{\bibfnamefont{S.~J.} \bibnamefont{van~der Walt}}, \bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Gommers}}, \bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Virtanen}}, \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Cournapeau}}, \bibinfo{author}{\bibfnamefont{E.}~\bibnamefont{Wieser}}, \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Taylor}}, \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Berg}}, \bibinfo{author}{\bibfnamefont{N.~J.} \bibnamefont{Smith}}, \bibnamefont{et~al.}, \bibinfo{journal}{Nature} \textbf{\bibinfo{volume}{585}}, \bibinfo{pages}{357} (\bibinfo{year}{2020}).
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\bibitem[{\citenamefont{pandas~development {team}}(2025)}]{teamPandasdevPandasPandas2025}
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\bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{pandas~development {team}}}, \emph{\bibinfo{title}{Pandas-dev/pandas: {{Pandas}}}}, \bibinfo{howpublished}{Zenodo} (\bibinfo{year}{2025}).
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\bibitem[{\citenamefont{Hunter}(2007)}]{hunterMatplotlib2DGraphics2007}
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\bibinfo{author}{\bibfnamefont{J.~D.} \bibnamefont{Hunter}}, \bibinfo{journal}{Computing in Science \& Engineering} \textbf{\bibinfo{volume}{9}}, \bibinfo{pages}{90} (\bibinfo{year}{2007}).
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\end{thebibliography}
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A second C++ program is used to filter the structured CSV data on the actual trajectories between airports as mentioned above. This program reads the CSV file, applies the trajectory filtering criteria, and outputs a new CSV file containing only the relevant trajectories. This two-step approach allows for efficient handling of the large ADS-B dataset while ensuring that only pertinent data is retained for model training.
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\subsubsection{Model Implementation and Training}
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The RNN model for aircraft trajectory prediction is implemented using the PyTorch deep learning framework, which provides a flexible and efficient platform for building and training neural networks. The model architecture, including the input multilayer perceptrons (I-MLPs), RNN layers (LSTM or GRU), and readout layer, is defined as a custom PyTorch module. The training process involves defining a suitable optimizer, such as Adam or RMSprop, to update the model parameters based on the computed loss. The Haversine distance-loss function is implemented as a separate module to ensure modularity and ease of integration with the training loop. The training loop iterates over the training dataset, feeding batches of input sequences into the model, computing the loss, and performing backpropagation to update the model weights. To monitor the model's performance, we track metrics such as the average loss on after each epoch.
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The RNN model for aircraft trajectory prediction is implemented using the PyTorch deep learning framework \cite{paszkePyTorchImperativeStyle2019}, which provides a flexible and efficient platform for building and training neural networks. The model architecture, including the input multilayer perceptrons (I-MLPs), RNN layers (LSTM or GRU), and readout layer, is defined as a custom PyTorch module. The training process involves defining a suitable optimizer, such as Adam or RMSprop, to update the model parameters based on the computed loss. The Haversine distance-loss function is implemented as a separate module to ensure modularity and ease of integration with the training loop. The training loop iterates over the training dataset, feeding batches of input sequences into the model, computing the loss, and performing backpropagation to update the model weights. To monitor the model's performance, we track metrics such as the average loss on after each epoch.
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For preprocessing and postprocessing tasks, we utilize libraries such as NumPy and Pandas for efficient data manipulation and analysis. Matplotlib is employed for visualizing the training progress and evaluating the model's predictions against ground truth trajectories. The entire implementation is structured in a modular fashion, allowing for easy experimentation with different model configurations, hyperparameters, and input feature sets.
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For preprocessing and postprocessing tasks, we utilize libraries such as NumPy \cite{harrisArrayProgrammingNumPy2020} and Pandas \cite{teamPandasdevPandasPandas2025} for efficient data manipulation and analysis. Matplotlib\cite{hunterMatplotlib2DGraphics2007} is employed for visualizing the training progress and evaluating the model's predictions against ground truth trajectories. The entire implementation is structured in a modular fashion, allowing for easy experimentation with different model configurations, hyperparameters, and input feature sets.
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All source code for data fetching, parsing, preprocessing, model implementation, training, and evaluation is made publicly available on GitHub at \url{https://github.uio.no/larsbog/aiRtrafficNN} to facilitate reproducibility and further research in the field of aircraft trajectory prediction using deep learning techniques.
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