Probabilistic Maritime Trajectory Prediction in Complex Scenarios Using Deep Learning

Kristian Aalling Sørensen*, Peder Heiselberg, Henning Heiselberg

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Maritime activity is expected to increase, and therefore also the need for maritime surveillance and safety. Most ships are obligated to identify themselves with a transponder system like the Automatic Identification System (AIS) and ships that do not, intentionally or unintentionally, are referred to as dark ships and must be observed by other means. Knowing the future location of ships can not only help with ship/ship collision avoidance, but also with determining the identity of these dark ships found in, e.g., satellite images. However, predicting the future location of ships is inherently probabilistic and the variety of possible routes is almost limitless. We therefore introduce a Bidirectional Long-Short-Term-Memory Mixture Density Network (BLSTM-MDN) deep learning model capable of characterising the underlying distribution of ship trajectories. It is consequently possible to predict a probabilistic future location as opposed to a deterministic location. AIS data from 3631 different cargo ships are acquired from a region west of Norway spanning 320,000 sqkm. Our implemented BLSTM-MDN model characterizes the conditional probability of the target, conditioned on an input trajectory using an 11-dimensional Gaussian distribution and by inferring a single target from the distribution, we can predict several probable trajectories from the same input trajectory with a test Negative Log Likelihood loss of -9.96 corresponding to a mean distance error of 2.53 km 50 min into the future. We compare our model to both a standard BLSTM and a state-of-the-art multi-headed self-attention BLSTM model and the BLSTM-MDN performs similarly to the two deterministic deep learning models on straight trajectories, but produced better results in complex scenarios.
Original languageEnglish
Article number2058
Issue number5
Number of pages21
Publication statusPublished - 2022


  • Automatic Identification System (AIS)
  • Deep learning
  • Trajectory prediction
  • Mixture Density Network (MDN)
  • Long Short Term Memory (LSTM)
  • Maritime Situational Awareness (MSA)


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