AUTHOR=Chen Chih-Wei , Huang Hsin-Hsiung 

TITLE=Unsupervised vessel trajectory reconstruction

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=9

YEAR=2023

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2023.1124091

DOI=10.3389/fams.2023.1124091

ISSN=2297-4687

ABSTRACT=<p>A trajectory is a sequence of observations in time and space, for examples, the path formed by maritime vessels, orbital debris, or aircraft. It is important to track and reconstruct vessel trajectories using the Automated Identification System (AIS) data in real-world applications for maritime navigation safety. In this project, we use the National Science Foundation (NSF)'s Algorithms for Threat Detection program (ATD) 2019 Challenge AIS data to develop novel trajectory reconstruction method. Given a sequence of <italic>N</italic> unlabeled timestamped observations <inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="-tex-caligraphic">X</mml:mi></mml:mrow><mml:mtext> </mml:mtext><mml:mo>=</mml:mo><mml:mtext> </mml:mtext><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mstyle mathvariant="bold"><mml:mtext>x</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mstyle mathvariant="bold"><mml:mtext>x</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mstyle mathvariant="bold"><mml:mtext>x</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula>, the goal is to track trajectories by clustering the AIS points with predicted positions using the information from the true trajectories <inline-formula><mml:math id="M2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="-tex-caligraphic">X</mml:mi></mml:mrow></mml:math></inline-formula>. It is a natural way to connect the observed point <bold>x</bold><sub>î</sub> with the closest point that is estimated by using the location, time, speed, and angle information from a set of the points under consideration <bold>x</bold><sub><italic>i</italic></sub> ∀ <italic>i</italic> ∈ {1, 2, …, <italic>N</italic>}. The introduced method is an unsupervised clustering-based method that does not train a supervised model which may incur a significant computational cost, so it leads to a real-time, reliable, and accurate trajectory reconstruction method. Our experimental results show that the proposed method successfully clusters vessel trajectories.</p>