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SKETCH: Semantic Key-Point Conditioning for Long-Horizon Vessel Trajectory Prediction

Linyong Gan, Zimo Li, Wenxin Xu, Xingjian Li, Jianhua Z. Huang, Enmei Tu, Shuhang Chen

TL;DR

SKETCH introduces a semantic Next Key Point (NKP) conditioned framework for long-horizon vessel trajectory prediction, reformulating the problem as $p(Y|X)= \sum_Z p(Y|X,Z) p(Z|X)$ to separate global navigational intent from local dynamics. A three-stage learning pipeline combines conditional trajectory modeling, NKP embedding via contrastive learning, and integrated inference, with a retrieval-augmented, open-set NKP module to handle unseen targets. A decoder-only Transformer backbone (MiniMind) plus a physics-based short-horizon motion update enables coherent, efficient forecasting on large AIS datasets, achieving state-of-the-art results in long-duration predictions and robust generalization. The approach provides a general hierarchical modeling paradigm for long-horizon sequential tasks and offers a foundation for downstream maritime AI applications such as anomaly detection, route optimization, and multi-agent coordination.

Abstract

Accurate long-horizon vessel trajectory prediction remains challenging due to compounded uncertainty from complex navigation behaviors and environmental factors. Existing methods often struggle to maintain global directional consistency, leading to drifting or implausible trajectories when extrapolated over long time horizons. To address this issue, we propose a semantic-key-point-conditioned trajectory modeling framework, in which future trajectories are predicted by conditioning on a high-level Next Key Point (NKP) that captures navigational intent. This formulation decomposes long-horizon prediction into global semantic decision-making and local motion modeling, effectively restricting the support of future trajectories to semantically feasible subsets. To efficiently estimate the NKP prior from historical observations, we adopt a pretrain-finetune strategy. Extensive experiments on real-world AIS data demonstrate that the proposed method consistently outperforms state-of-the-art approaches, particularly for long travel durations, directional accuracy, and fine-grained trajectory prediction.

SKETCH: Semantic Key-Point Conditioning for Long-Horizon Vessel Trajectory Prediction

TL;DR

SKETCH introduces a semantic Next Key Point (NKP) conditioned framework for long-horizon vessel trajectory prediction, reformulating the problem as to separate global navigational intent from local dynamics. A three-stage learning pipeline combines conditional trajectory modeling, NKP embedding via contrastive learning, and integrated inference, with a retrieval-augmented, open-set NKP module to handle unseen targets. A decoder-only Transformer backbone (MiniMind) plus a physics-based short-horizon motion update enables coherent, efficient forecasting on large AIS datasets, achieving state-of-the-art results in long-duration predictions and robust generalization. The approach provides a general hierarchical modeling paradigm for long-horizon sequential tasks and offers a foundation for downstream maritime AI applications such as anomaly detection, route optimization, and multi-agent coordination.

Abstract

Accurate long-horizon vessel trajectory prediction remains challenging due to compounded uncertainty from complex navigation behaviors and environmental factors. Existing methods often struggle to maintain global directional consistency, leading to drifting or implausible trajectories when extrapolated over long time horizons. To address this issue, we propose a semantic-key-point-conditioned trajectory modeling framework, in which future trajectories are predicted by conditioning on a high-level Next Key Point (NKP) that captures navigational intent. This formulation decomposes long-horizon prediction into global semantic decision-making and local motion modeling, effectively restricting the support of future trajectories to semantically feasible subsets. To efficiently estimate the NKP prior from historical observations, we adopt a pretrain-finetune strategy. Extensive experiments on real-world AIS data demonstrate that the proposed method consistently outperforms state-of-the-art approaches, particularly for long travel durations, directional accuracy, and fine-grained trajectory prediction.
Paper Structure (43 sections, 4 theorems, 34 equations, 3 figures, 6 tables, 1 algorithm)

This paper contains 43 sections, 4 theorems, 34 equations, 3 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Decoder-only Transformer Trajectory Predictor
  4. Retrieval-Augmented Verification
  5. Contrastive Learning for Embedding Consistency
  6. Methodology
  7. Overview
  8. Semantic Next-Key-Point Modeling
  9. Multi-stage Learning for NKP-Trajectory Modeling
  10. Conditional Trajectory Modeling (blue)
  11. NKP Modeling (green)
  12. Integrated Inference
  13. Model Architecture and Physical Representation
  14. Evaluation Metrics
  15. Mean Squared Error of Position (MSEP).
  16. ...and 28 more sections

Key Result

Proposition 3.3

Under ass:linear_motion, given current coordinates $(lat_0, lon_0)$, the next position $(lat_1, lon_1)$ is given by where $R$ denotes the Earth’s radius.

Figures (3)

  • Figure 1: Overall Architecture. The inputs of AIS data go through Encoder 1 and MiniMind model 1 to be transformed into hidden state 1. The hidden state 1 will be sent into an MLP to predict the Next Key Point information. These coordinates will be sent to the encoder 2 to derive the hidden state 2. Then, hidden states 1 and 2 will be concatenated and passed through a dense layer, MiniMind model 2, and a decoder to obtain the predicted SOG and COG.
  • Figure 2: Key-Point Prediction Training Paradigm. Contrastive Learning is used to derive the hidden states of each trajectory, thereby decoupling the NKP information. To be more efficient, the two blocks trained previously are frozen and reused for fine-tuning.
  • Figure 3: from COG & SOG to latitude & longitude - dense. Purple and green points represent the next coordinates derived by the formula and ground truth, respectively. The fact that the purple and green dots are close enough indicates the practical validity of the formulation.

Theorems & Definitions (8)

  • Definition 3.1: Semantic Navigational Key Point (NKP)
  • Proposition 3.3: SOG/COG Coordinate Update
  • Lemma 1.1: Monotonicity of Conditional Entropy
  • proof
  • Lemma 1.2: Tower Property of Conditional Expectation
  • proof
  • Theorem 1.3: Bayes Risk Monotonicity
  • proof