Source-linked AI summary
TempTPI: Informer-Based trajectory prediction for maritime vessels
Kevin Ferneding, Veronika Lietavcova, Aleksandra M. Blachowiak, Peder Heiselberg
TL;DR
Long-horizon maritime trajectory prediction must address both Transformer attention cost and declining forecasting accuracy. TempTPI combines temporal cyclic encoding with an Informer encoder and outperforms TPTrans across prediction windows, including a roughly 55% improvement at five hours. Its predictions can still violate water boundaries, and seasonal-variation capability remains under investigation.
Problem
Accurate long-term vessel trajectory prediction is needed for maritime safety and coordination, while long-sequence Transformers face quadratic self-attention costs and forecasting challenges.
Method
TempTPI combines a temporal encoder for cyclic vessel-behavior patterns with an Informer encoder using ProbSparse self-attention.
Results
TempTPI consistently improves over TPTrans across prediction lengths, with a roughly 55% improvement over TPTrans at five hours.
Takeaways & Limitations
The results support TempTPI as a promising foundation for long-term maritime trajectory forecasting and logistics applications.
Takeaways & Limitations
Predicted trajectories sometimes violate water boundaries, and the full potential for capturing seasonal variations remains to be investigated.
Abstract
from arXiv · showhide
Accurate long-term trajectory prediction for maritime vessels is essential for safety and logistical efficiency. While deep learning models, particularly Transformers, have shown promise in processing Automatic Identification System (AIS) data, they often struggle with the quadratic computational complexity of self-attention and the loss of accuracy over extended forecasting horizons. This study proposes TempTPI, a novel prediction framework that integrates an Informer-based encoder with a multi-channel temporal encoding mechanism. The Informer architecture leverages a ProbSparse self-attention mechanism to reduce computational overhead and focus on the most significant dependencies, while the temporal encoder utilizes Fourier-like frequency expansions to capture cyclic patterns (hourly, daily, and seasonal) in vessel behavior. We evaluate our model against the state-of-the-art TPTrans architecture using AIS data from Danish waters. Experimental results demonstrate that TempTPI consistently outperforms existing methods across prediction windows of 1 to 5 hours. Notably, at a 5-hour horizon, the proposed model achieves a 55% improvement in Mean Squared Error (MSE), offering a robust solution for long-range maritime situational awareness.
I. INTRODUCTION
Maritime trajectory prediction supports safer, more efficient vessel coordination, but AIS data quality and long-sequence Transformer costs complicate accurate long-horizon forecasting. TempTPI is motivated by these operational, data, and computational challenges.
- High-accuracy vessel trajectories can support reliable coordination in increasingly complex maritime traffic.
- AIS provides real-time vessel status and extensive historical data, including static identity and dynamic movement information.
- AIS trajectories require preprocessing because shared or spoofed identifiers, signal dropouts, and physically implausible transmissions create heterogeneous data quality.
- Vessel traffic exhibits seasonal patterns, motivating a dataset selection focused on commercial maritime activity.
- Vanilla Transformer self-attention has quadratic cost for long input sequences, motivating architectures designed for long-horizon forecasting.
- Informer-based forecasting uses sparse attention for efficient long-sequence processing and has shown stable long-range behavior across benchmark datasets.
A. Data Processing
AIS trajectories are filtered, ordered, deduplicated, and segmented to remove invalid records and isolate temporally coherent vessel tracks.
- Preprocessing removes out-of-region messages and retains vessels with valid MMSI identifiers and acceptable mobile classes.
- For each vessel, records are timestamp-ordered, duplicates are removed, and physically implausible tracks are excluded using duration, speed, and track-length criteria.
- Trajectories are segmented when consecutive AIS messages are separated by more than 15 minutes.
B. Model Architecture
TempTPI extends TPTrans with temporal input encoding and an Informer encoder, combining cyclic time features with efficient sparse-attention sequence processing for latitude and longitude prediction.
- TempTPI adds a temporal input encoding and Informer encoder to the TPTrans architecture.
- The temporal encoder targets seasonal vessel-behavior variation by representing hour-of-day, day-of-week, and month-of-year cycles.
- Fourier-like frequency expansions generate sine and cosine features across frequencies k = 1, .., K for each cyclic feature.
- Temporal projections are combined with normal data projections before positional encoding.
- ProbSparse self-attention evaluates only O(log LQ) dot-products for each query instead of the standard O(LQ).
- Informer distilling compresses sequences through convolution and pooling, while its generative decoder predicts the full horizon in one step.
C. Model Training
Training compares TempTPI with TPInform and TPTrans through controlled training settings and ablations over temporal context, prediction horizon, data volume, and stride.
- TempTPI, TPInform, and TPTrans were evaluated, with TPInform omitted from final results after consistently underperforming TempTPI.
- Models used PyTorch, Adam optimization, a 1e−4 learning rate, batch size 32, up to 200 epochs, and a 70%/20%/10% train-validation-test split.
- The first ablation block varied historical input windows of 240, 360, and 480 minutes while holding the dataset and 30-minute stride fixed.
- TempTPI performs significantly worse at the smallest sample size, indicating a larger data requirement than TPTrans in that experiment.
III. RESULTS
Across prediction lengths, TempTPI reduces loss relative to TPTrans, with more accurate long-horizon trajectory samples and generally stable training behavior. The model performs better overall, although some predictions still violate water boundaries.
- 55% improvement in MSE at a 5-hour prediction length is achieved by TempTPI over TPTrans.
- TempTPI consistently improves loss over TPTrans across the evaluated prediction lengths after adding the temporal encoder to the Informer-based architecture.
- After approximately 50 epochs, TempTPI performs better than TPTrans and shows a longer, more stable learning curve for 5-hour prediction.
- TempTPI predictions navigate narrow pathways such as the Øresund and Great Belt straits relatively well, but sometimes violate water boundaries.
- The proposed model shows a significant reduction in test loss for very long predictions compared with TPTrans.
IV. DISCUSSION
The discussion presents TempTPI as a promising architecture for long-term maritime trajectory prediction, while identifying limited temporal and geographic coverage and unresolved land-boundary errors. Broader seasonal and regional validation, along with improved land avoidance, remain future directions.
- TempTPI combines an Informer-based encoder with temporal encoding and yields significantly better results than a transformer-based model.
- The dataset covered traffic for only two weeks in a single month, limiting representation of seasonal variation.
- The study investigated only Denmark, leaving performance across other maritime domains unassessed.
- A land-punishment experiment destabilized training and reduced overall performance, so it was excluded from the paper.
- The architecture provides a promising foundation for long-term prediction, but its full potential for capturing seasonal variations remains unresolved.