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REVIEW 3 major objections 6 minor 46 references

The authors introduce NaviAIS, a scenario-level AIS dataset with vectorized lane priors, and NaviLane, a model that uses those priors alongside a macro-action decoder and consequence-aware ranking to outperform existing vessel trajectory pr

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · deepseek-v4-flash

2026-08-01 14:00 UTC pith:WLZ2U3C6

load-bearing objection Useful dataset, shaky model validation—the future-derived lane priors make the NaviLane comparison unfair, but the benchmark resource is still worth a serious look. the 3 major comments →

arxiv 2607.18887 v1 pith:WLZ2U3C6 submitted 2026-07-21 cs.AI

NaviAIS: A Scenario-Level Vessel Trajectory Prediction Dataset withVectorized Lane Priors and the NaviLane Forecasting Framework

classification cs.AI
keywords vessel trajectory predictionAIS datascenario-level datasetvectorized lane priorsmacro-action codebookworld modelmultimodal predictionmaritime navigation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims that vessel trajectory prediction improves materially when models are given structured navigational priors—lane centerlines, water/land polygons, and navigable masks—encoded jointly with vessel history. To support this, the authors release NaviAIS, a standardized scenario-level dataset that packages multi-vessel trajectories with vectorized maps and lane graphs, and propose NaviLane, a hierarchical macro-action framework that generates and ranks multimodal futures. On NaviAIS, NaviLane reports the best long-horizon errors, cutting FDE@10 from over 8.8 in the strongest baseline to 7.03, and also wins on multimodal coverage metrics. A sympathetic reader would care because this suggests that map-aware, consequence-aware forecasting, already standard in road autonomy, transfers to maritime AIS data and enables more plausible, safer vessel predictions for collision warning and route planning.

Core claim

Vessel trajectory prediction in complex waterways improves materially when the model can see structured navigational priors—lane centerlines, water/land polygons, navigable masks—encoded jointly with trajectory history. The paper's central claim is that NaviLane, built on trajectory–map joint encoding, a 128-entry macro-action codebook, residual refinement, and a world-model-based counterfactual risk selector, achieves the best ADE@10 (3.57), FDE@10 (7.03), and multimodal minADE@10 and minFDE@10 (2.61/4.85) on the new NaviAIS test set, outperforming kinematic, sequence-based, and multimodal baselines. In plain terms, conditioning future motion on waterway geometry and lane structure yields p

What carries the argument

The vectorized lane prior: lane centerlines, lane graphs, and water/land polygons extracted from public chart data and injected into each ego-centric scenario. NaviLane uses these priors in a joint trajectory–map encoder, then a discrete macro-action codebook (K_macro=128) partitions candidate futures into distinct navigation strategies, a residual refinement module corrects endpoint drift and curvature, and an Interaction World Model with Counterfactual Risk (CFR) scoring ranks candidates by closest-point-of-approach, collision risk, lane deviation, and heading consistency. The load-bearing mechanism is the coupling of map-aware encoding with hierarchical coarse-to-refined generation and co

Load-bearing premise

The evaluation assumes that NaviAIS's single-day splits and lane priors built from months after the scenario dates are representative and fair; if the priors leak future information or the chosen days are unrepresentative, the reported margins could shrink.

What would settle it

Run a controlled re-split of NaviAIS where lane priors are constructed only from AIS data before January 2024 and the test set spans many randomly sampled days instead of January 7. If NaviLane's ADE@10/FDE@10 margin over TPTrans and PECNet narrows to near zero, the central map-priors claim is not supported. A second, cheaper check: remove the vectorized lane inputs from NaviLane while keeping all other modules and measure the drop in ADE@10.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If correct, map-aware models will consistently beat sequence-only models for vessel forecasting, especially at horizons beyond a few minutes.
  • Macro-action codebooks produce multimodal candidates that are diverse yet interpretable, unlike latent-sampling baselines that over-disperse or collapse.
  • World-model consequence ranking improves top-1 selection, not just candidate coverage, which matters for downstream collision-warning systems.
  • A standardized scenario-level AIS dataset with vectorized priors enables fair cross-method comparison and reproducible environment-aware research.
  • The reported gains in MHE indicate predicted headings are more directionally consistent, suggesting the model learns physically plausible turning behavior.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Editorial: The dataset construction uses lane priors derived from AIS records collected months after the scenario dates; retraining with only time-consistent priors would test for temporal leakage and likely change the reported margins.
  • Editorial: The CFR energy terms (CPA, collision, map, land, heading) are largely rule-based; ablating them separately from the learned selector would quantify how much of the ranking gain is purely physical reasoning versus learned scoring.
  • Editorial: Because each split uses a single day, the benchmark may overstate robustness; resampling scenarios across many days and ports would reveal whether NaviLane's advantage holds across traffic regimes.
  • Editorial: The same trajectory–map joint encoding could transfer to inland waterways, canals, and autonomous surface vessels, where lane priors are weaker but water-land constraints are equally strong.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper introduces NaviAIS, a scenario-level AIS vessel trajectory prediction dataset that provides vectorized lane priors, raster/vector maps, and lane graphs, together with NaviLane, a hierarchical forecasting framework combining trajectory–map joint encoding, macro-action codebook generation, residual refinement, and a world-model-based counterfactual risk (CFR) evaluator for candidate ranking. The authors evaluate NaviLane on NaviAIS and report improvements over several baselines across single-modal and multimodal metrics (Tables II and III), attributing the gains to structured navigational priors, hierarchical multimodal generation, and consequence-aware evaluation. The dataset and code are publicly released. The central empirical claim, however, is undermined by a temporal inconsistency in the construction of map priors: priors are computed from AIS records from September–December 2024, while the scenario trajectories are from January 2024, so NaviLane has access to future-derived route statistics that the baselines lack.

Significance. If the evaluation setup were sound, NaviAIS would be a valuable resource for environment-aware vessel trajectory forecasting, and the NaviLane framework has several plausible design elements: the ablation study (Table IV) isolates contributions from the refinement module, world-CFR evaluator, and selector, and the release of code and data is a concrete reproducibility strength. However, the core claim that structured navigational priors improve prediction is not established because of the temporal leakage in prior construction. The benchmark also uses a single-day test split, and key ranking weights in the hybrid scoring function are unreported. These are load-bearing issues for the paper's headline conclusion.

major comments (3)
  1. [IV-A, dataset construction] Temporal leakage in lane-prior construction. The paper states that 'AIS records from September to December 2024 were used to compute aggregated navigational priors, including lane density, route patterns, and waterway attributes,' while the scenario samples are from January 1/4/7, 2024. Since NaviLane is the only evaluated method that consumes these priors, its consistent advantage in Tables II and III may reflect access to route statistics from after the prediction period rather than the intrinsic value of map-aware modeling. This directly affects the abstract and conclusion claim that structured navigational priors are beneficial. To support this claim, the priors must be recomputed from data strictly preceding January 2024, or the authors must provide evidence (e.g., a control experiment using only pre-January data) that the later-period priors do not alter the ranking.
  2. [IV-A, train/validation/test splits] The evaluation uses single days per split (Jan 1/4/7, 2024). A one-day test set of 1,000 scenarios cannot capture the seasonal, weather, traffic, and geographic variability that a deployed system would encounter, and it makes the reported margins potentially specific to those days. The dataset's claimed multi-scenario coverage (open sea, inland river, lake) is not actually reflected in the evaluation. I recommend constructing splits from multiple days or reporting results on several test days to support the generalizability statements in the conclusion.
  3. [III-C, Eqs. (18), (20), (22)] The final ranking and therefore the headline results depend on six energy weights λ1–λ6 in Eq. (18) and four fusion weights α, β, γ, δ in Eqs. (20) and (22). None of these values are reported, no sensitivity analysis is given, and the selection procedure is not described. Since the consequence-aware evaluator is a key claimed contribution, the unreported fitted weights prevent reproduction of the ranking and make it impossible to assess whether the reported top-1/top-6 results are robust or finely tuned. This is a load-bearing issue for the claimed advantage of the scoring/reranking mechanism.
minor comments (6)
  1. [Table II] LSTM achieves a lower ADE@3 (1.06) than the proposed model (1.18). The text says NaviLane achieves the best on 'most metrics,' which is accurate, but it would be clearer to explicitly acknowledge this exception.
  2. [Eq. (7)] The definition of velocity v_{k,t} = y_{k,t} - y_{k,t-1} is not specified for t=1. Please state the boundary handling.
  3. [Section IV-A] Training details are sparse: the paper mentions 30 epochs, batch size 16, and A100 GPUs, but does not report training time, parameter count, or optimizer settings. Adding these would aid reproducibility.
  4. [Fig. 2] Some module labels in the figure (e.g., 'World Model', 'CFR Selector') are not all explicitly referenced in the text of Section III; ensure each component is described and connected to the equations.
  5. [Tables II and III] The units for displacement metrics (100 m per unit) are stated only in the text of Section IV-A. Please restate this in table captions to avoid misreading.
  6. [References] The code and dataset URLs are given in the Data Availability section; consider adding a citation or availability note in the abstract or introduction for discoverability.

Circularity Check

0 steps flagged

No circularity by construction; the evaluation is empirical with a held-out test split. The temporal mismatch in lane-prior construction is a validity concern, not a circular step.

full rationale

The paper's central claim is empirical: NaviLane outperforms baselines on NaviAIS. Nothing in the method definitions or equations makes the predicted trajectories equal to the inputs. The map and lane priors are inputs to the encoder, not outputs; the final score s_k is a weighted combination of learned scores, prior probabilities, and energy terms, and the selected Y* is argmax over generated candidates, not a restatement of the priors. No load-bearing self-citation appears in the reference list, and no uniqueness theorem or ansatz is imported from the authors' prior work. The notable temporal mismatch — aggregated lane priors from Sep–Dec 2024 used for scenarios in Jan 2024 — is a legitimate external-validity / benchmark-construction concern that could inflate NaviLane's apparent advantage because only NaviLane consumes these priors, but it is not an identity between the prediction and its inputs by construction, so it does not constitute circularity under the defined patterns. The comparison protocol is also self-administered (authors chose baselines and unreported weights λ1–λ6, α, β, γ, δ), which is a reproducibility concern, not a circular derivation.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

No new physical entities or forces are introduced; the modeling constructs such as macro-action anchors, CFR scores, and the world model are architectural choices rather than new claims about the world. The central numerical claims depend on several undisclosed scalar parameters and on the adequacy of map-derived lane priors.

free parameters (4)
  • Energy weights λ1..λ6
    Eq. (18) combines CPA collision, instantaneous collision, dynamic, map, land, and heading terms; the values are not reported and are likely tuned on NaviAIS validation.
  • Score fusion weights α, β, γ, δ
    Eqs. (20)-(22) combine prior score, learned selector score, normalized energy, and rerank score; no values or sensitivity analysis are given.
  • Distance thresholds d_safe and d_col
    Eqs. (16)-(17) define collision risk using safe and collision distances; the values are not reported and directly affect the CFR ranking.
  • Macro-action codebook size K_macro = 128 = 128
    Table V shows sensitivity, but the final choice is made on the authors' own benchmark and is not independently justified.
axioms (4)
  • domain assumption OSM waterway and NOAA ENC line/area features accurately represent navigable lanes in the study areas.
    Sec. IV-A: OSM waterways are used as the global backbone and NOAA features are fused into lane geometries; errors here propagate into all map-based penalties and lane priors.
  • domain assumption Cleaned AIS trajectories are reliable ground truth for vessel motion, and the selected single-day splits are representative.
    Sec. IV-A: training uses Jan 1, validation Jan 4, test Jan 7, 2024; no evidence is given that these days cover typical traffic conditions.
  • ad hoc to paper Map priors computed from September-December 2024 are static and do not leak future information into January 2024 scenarios.
    Sec. IV-A states these statistics serve only as static map priors, but the future-to-past temporal ordering is not discussed as a leakage or validity issue.
  • domain assumption The world model predicts neighboring-vessel futures accurately enough for CFR ranking.
    Eq. (14) predicts neighbor trajectories that are used in Eqs. (16)-(17) to compute risk; no error analysis of the world model is provided.

pith-pipeline@v1.3.0-alltime-deepseek · 14433 in / 12689 out tokens · 111026 ms · 2026-08-01T14:00:49.552267+00:00 · methodology

0 comments
read the original abstract

Vessel trajectory prediction in complex maritime environments is essential for traffic management, collision warning, route planning, and autonomous navigation. Although AIS-based learning methods have progressed rapidly, existing datasets are often released as raw message streams or irregular time series, with inconsistent sampling rates, noisy observations, heterogeneous coordinate systems, and non-unified scenario protocols. Most public AIS resources also lack structured representations of navigational lanes, waterway geometry, and navigable-region constraints, limiting reproducible, environment-aware forecasting. To address this, we introduce NaviAIS, a standardized scenario-level AIS dataset for vessel trajectory prediction. It organizes multi-vessel historical-future trajectories within unified temporal windows and local coordinate systems, and provides rasterized navigable maps, vectorized lane priors, lane graphs, and structured map representations. Compared with existing datasets, it jointly supports vectorized lanes, multi-scenario coverage, vectorized maps, open accessibility, and processed trajectories. Built on this dataset, we propose NaviLane, a hierarchical macro-action framework for map-aware prediction. NaviLane first performs trajectory-map joint encoding for a unified scene representation, then uses a discrete macro-action codebook to generate multimodal candidates coarse-to-refined. A residual refinement module improves local geometric and dynamical consistency, and a world-model-based consequence-aware evaluator ranks candidates by interaction risk and environmental feasibility. Experiments show NaviLane outperforms representative baselines in both single-modal and multimodal settings, confirming the value of structured navigational priors, hierarchical multimodal generation, and consequence-aware evaluation.

Figures

Figures reproduced from arXiv: 2607.18887 by Hongchen Luo, Jiao Wang, Liqi Qu, Longyue Fu, Yuan Gui.

Figure 1
Figure 1. Figure 1: This figure illustrates the multi-layer structure of a single navigation [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Framework overview: The proposed NaviLane first encodes historical vessel trajectories, vectorized lane polylines, and rasterized map priors, and [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: CFR Selector [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of dataset scenarios. First show raster maps, vector maps, navigable-channel vectors, and AIS vessel trajectories for narrow inland [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visualization of local navigable channels. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of trajectory prediction results of different methods in inland waterways. (a), (i): NaviLane (top-1); (b), (j): NaviLane (top-6); (c), (k): [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Visualization of trajectory prediction results of different methods in ports and coastal areas. (a), (i): NaviLane (top-1); (b), (j): NaviLane (top-6); (c), [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

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Reference graph

Works this paper leans on

46 extracted references · 2 linked inside Pith

  1. [1]

    Ragan: A generative adversarial network for risk-aware trajectory prediction in multi-ship encounter situations,

    C. Jia, J. Ma, X. Yang, and X. Lv, “Ragan: A generative adversarial network for risk-aware trajectory prediction in multi-ship encounter situations,”Ocean Engineering, vol. 289, p. 116188, 2023

  2. [2]

    Ais data-driven ship trajectory prediction modelling and analysis based on machine learning and deep learning methods,

    H. Li, H. Jiao, and Z. Yang, “Ais data-driven ship trajectory prediction modelling and analysis based on machine learning and deep learning methods,”Transportation Research Part E: Logistics and Transportation Review, vol. 175, p. 103152, 2023

  3. [3]

    How big data enriches maritime research–a critical review of automatic identification system (ais) data applications,

    D. Yang, L. Wu, S. Wang, H. Jia, and K. X. Li, “How big data enriches maritime research–a critical review of automatic identification system (ais) data applications,”Transport reviews, vol. 39, no. 6, pp. 755–773, 2019

  4. [4]

    The open maritime traffic analysis dataset,

    M. Masek, C. P. Lam, T. Rybicki, J. Snell, D. Wheat, L. Kelly, C. Smith- Ganderet al., “The open maritime traffic analysis dataset,” 2021

  5. [5]

    Dataset of ocean vessel traffic in the north sea,

    R. Meyer, W. Kleynhans, M. Portier, J. Beja, and L. Tyberghein, “Dataset of ocean vessel traffic in the north sea,”Data in brief, vol. 51, p. 109746, 2023

  6. [6]

    Unified multimodal vessel trajectory prediction with explainable navigation intention,

    R. Zhang, C. Li, K. Liu, C. Wang, B. Zheng, and H. Jiang, “Unified multimodal vessel trajectory prediction with explainable navigation intention,”IEEE Transactions on Intelligent Transportation Systems, vol. 27, no. 1, pp. 258–269, 2025

  7. [7]

    Tptrans: Vessel trajectory prediction model based on transformer using ais data,

    W. Wang, W. Xiong, X. Ouyang, and L. Chen, “Tptrans: Vessel trajectory prediction model based on transformer using ais data,”ISPRS International Journal of Geo-Information, vol. 13, no. 11, p. 400, 2024

  8. [8]

    Ais in maritime research,

    M. Svanberg, V . Sant´en, A. H ¨orteborn, H. Holm, and C. Finnsg ˚ard, “Ais in maritime research,”Marine Policy, vol. 106, p. 103520, 2019

  9. [9]

    Literature review and future prospects on vessel movement data usage including ais-focusing on logistics, shipping, shipbuilding, environment, and cruise fields,

    Y . Wada, R. Shibasaki, H. Kosaka, D. Watanabe, H. Ito, K. Tsubota, T. Aratani, T. Izumiyama, and R. Iwasa, “Literature review and future prospects on vessel movement data usage including ais-focusing on logistics, shipping, shipbuilding, environment, and cruise fields,”Journal of the Japan Society of Naval Architects and Ocean Engineers, vol. 34, 2021

  10. [10]

    Harnessing the power of machine learning for ais data-driven maritime research: A comprehensive review,

    Y . Yang, Y . Liu, G. Li, Z. Zhang, and Y . Liu, “Harnessing the power of machine learning for ais data-driven maritime research: A comprehensive review,”Transportation research part E: logistics and transportation review, vol. 183, p. 103426, 2024

  11. [11]

    Vessel trajectory prediction with recurrent neural networks: An evaluation of datasets, features, and architectures,

    I. Slaughter, J. L. Charla, M. Siderius, and J. Lipor, “Vessel trajectory prediction with recurrent neural networks: An evaluation of datasets, features, and architectures,”Journal of Ocean Engineering and Science, vol. 10, no. 2, pp. 229–238, 2025

  12. [12]

    Vessel trajectory prediction based on ais data: dual-path spatial–temporal attention net- work with multi-attribute information,

    F. Huang, Z. Liu, X. Li, F. Mou, P. Li, and Z. Fan, “Vessel trajectory prediction based on ais data: dual-path spatial–temporal attention net- work with multi-attribute information,”Journal of Marine Science and Engineering, vol. 12, no. 11, p. 2031, 2024

  13. [13]

    G-trans: A hierarchical approach to vessel trajectory prediction with gru-based transformer,

    H. Xue, S. Wang, M. Xia, and S. Guo, “G-trans: A hierarchical approach to vessel trajectory prediction with gru-based transformer,” Ocean Engineering, vol. 300, p. 117431, 2024

  14. [14]

    Higher- order relational reasoning for pedestrian trajectory prediction,

    S. Kim, H.-g. Chi, H. Lim, K. Ramani, J. Kim, and S. Kim, “Higher- order relational reasoning for pedestrian trajectory prediction,” inPro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024, pp. 15 251–15 260

  15. [15]

    Socialmoif: Multi-order intention fusion for pedestrian trajectory pre- diction,

    K. Chen, X. Zhao, Y . Huang, G. Fang, X. Song, R. Wang, and Z. Wang, “Socialmoif: Multi-order intention fusion for pedestrian trajectory pre- diction,” inProceedings of the Computer Vision and Pattern Recognition Conference, 2025, pp. 22 465–22 475

  16. [16]

    Vessel trajectory prediction based on spatio-temporal graph convolutional network for complex and crowded sea areas,

    S. Wang, Y . Li, H. Xing, and Z. Zhang, “Vessel trajectory prediction based on spatio-temporal graph convolutional network for complex and crowded sea areas,”Ocean Engineering, vol. 298, p. 117232, 2024

  17. [17]

    Deep learning framework for vessel trajectory prediction using auxiliary tasks and convolutional networks,

    Y . Shin, N. Kim, H. Lee, S. Y . In, M. Hansen, and Y . Yoon, “Deep learning framework for vessel trajectory prediction using auxiliary tasks and convolutional networks,”Engineering Applications of Artificial Intelligence, vol. 132, p. 107936, 2024

  18. [18]

    Large scale interactive motion forecasting for autonomous driving: The waymo open motion dataset,

    S. Ettinger, S. Cheng, B. Caine, C. Liu, H. Zhao, S. Pradhan, Y . Chai, B. Sapp, C. R. Qi, Y . Zhouet al., “Large scale interactive motion forecasting for autonomous driving: The waymo open motion dataset,” inProceedings of the IEEE/CVF international conference on computer vision, 2021, pp. 9710–9719

  19. [19]

    Argoverse 2: Next generation datasets for self-driving perception and forecasting,

    B. Wilson, W. Qi, T. Agarwal, J. Lambert, J. Singh, S. Khandelwal, B. Pan, R. Kumar, A. Hartnett, J. K. Ponteset al., “Argoverse 2: Next generation datasets for self-driving perception and forecasting,”arXiv preprint arXiv:2301.00493, 2023

  20. [20]

    Toward multimodal vessel trajectory prediction by modeling the distribution of modes,

    S. Guo, H. Zhang, and Y . Guo, “Toward multimodal vessel trajectory prediction by modeling the distribution of modes,”Ocean Engineering, vol. 282, p. 115020, 2023

  21. [21]

    Uncertainty-aware ship trajectory prediction via spatio-temporal graph transformer,

    J. Gong, H. Li, H. Jiao, and Z. Yang, “Uncertainty-aware ship trajectory prediction via spatio-temporal graph transformer,”Transportation Re- search Part E: Logistics and Transportation Review, vol. 203, p. 104315, 2025

  22. [22]

    Vessel trajectory prediction using vessel influence long short-term memory with uncertainty estimation,

    Z. Guo, H. Qiang, and X. Peng, “Vessel trajectory prediction using vessel influence long short-term memory with uncertainty estimation,”Journal of Marine Science and Engineering, vol. 13, no. 2, p. 353, 2025

  23. [23]

    Comprehensive analysis of automatic identification system (ais) data in regard to vessel movement prediction,

    P. Last, C. Bahlke, M. Hering-Bertram, and L. Linsen, “Comprehensive analysis of automatic identification system (ais) data in regard to vessel movement prediction,”The Journal of Navigation, vol. 67, no. 5, pp. 791–809, 2014

  24. [24]

    How can automatic identification system (ais) data be used for maritime spatial planning?

    M. Le Tixerant, D. Le Guyader, F. Gourmelon, and B. Queffelec, “How can automatic identification system (ais) data be used for maritime spatial planning?”Ocean & Coastal Management, vol. 166, pp. 18–30, 2018

  25. [25]

    Hierarchical game-theoretic planning for autonomous vehicles,

    J. F. Fisac, E. Bronstein, E. Stefansson, D. Sadigh, S. S. Sastry, and A. D. Dragan, “Hierarchical game-theoretic planning for autonomous vehicles,” in2019 International conference on robotics and automation (ICRA). IEEE, 2019, pp. 9590–9596

  26. [26]

    Gameformer: Game-theoretic modeling and learning of transformer-based interactive prediction and planning for autonomous driving,

    Z. Huang, H. Liu, and C. Lv, “Gameformer: Game-theoretic modeling and learning of transformer-based interactive prediction and planning for autonomous driving,” inProceedings of the IEEE/CVF International Conference on Computer Vision, 2023, pp. 3903–3913

  27. [27]

    Nashformer: Leveraging local nash equilibria for semantically diverse trajectory prediction,

    J. Lidard, O. So, Y . Zhang, J. DeCastro, X. Cui, X. Huang, Y .-L. Kuo, J. Leonard, A. Balachandran, N. Leonardet al., “Nashformer: Leveraging local nash equilibria for semantically diverse trajectory prediction,”arXiv preprint arXiv:2305.17600, 2023

  28. [28]

    Ship trajectory reconstruction from ais sensory data via data quality control and prediction,

    X. Chen, J. Ling, Y . Yang, H. Zheng, P. Xiong, O. Postolache, and Y . Xiong, “Ship trajectory reconstruction from ais sensory data via data quality control and prediction,”Mathematical Problems in Engineering, vol. 2020, no. 1, p. 7191296, 2020

  29. [29]

    Aisclean: Ais data-driven vessel trajectory reconstruction under uncertain conditions,

    M. Liang, J. Su, R. W. Liu, and J. S. L. Lam, “Aisclean: Ais data-driven vessel trajectory reconstruction under uncertain conditions,”Ocean Engineering, vol. 306, p. 117987, 2024

  30. [30]

    Ship trajectories pre-processing based on ais data,

    L. Zhao, G. Shi, and J. Yang, “Ship trajectories pre-processing based on ais data,”The Journal of Navigation, vol. 71, no. 5, pp. 1210–1230, 2018

  31. [31]

    Marine trajectory reconstruc- tion method based on navigation state recognition and bi-directional kinematic interpolation,

    Y . Liu, Z. Shi, B. Fu, H. Xu, and H. Wu, “Marine trajectory reconstruc- tion method based on navigation state recognition and bi-directional kinematic interpolation,”Journal of Marine Science and Engineering, vol. 12, no. 12, p. 2164, 2024

  32. [32]

    Unsupervised knowledge discovery framework: From ais data processing to maritime traffic networks generating,

    Z. Guo, H. Qiang, S. Xie, and X. Peng, “Unsupervised knowledge discovery framework: From ais data processing to maritime traffic networks generating,”Applied Ocean Research, vol. 146, p. 103924, 2024

  33. [33]

    Reconstructing trajec- tories and extracting shipping routes between ports based on ais data,

    Z. Yan, G. Yang, R. He, K. Shi, and H. Yang, “Reconstructing trajec- tories and extracting shipping routes between ports based on ais data,” Applied Ocean Research, vol. 161, p. 104709, 2025

  34. [34]

    Learning lane graph representations for motion forecasting,

    M. Liang, B. Yang, R. Hu, Y . Chen, R. Liao, S. Feng, and R. Urtasun, “Learning lane graph representations for motion forecasting,” inEuro- pean Conference on Computer Vision. Springer, 2020, pp. 541–556

  35. [35]

    Vectornet: Encoding hd maps and agent dynamics from vectorized rep- resentation,

    J. Gao, C. Sun, H. Zhao, Y . Shen, D. Anguelov, C. Li, and C. Schmid, “Vectornet: Encoding hd maps and agent dynamics from vectorized rep- resentation,” inProceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2020, pp. 11 525–11 533

  36. [36]

    Pretram: Self-supervised pre-training via connecting trajectory and map,

    C. Xu, T. Li, C. Tang, L. Sun, K. Keutzer, M. Tomizuka, A. Fathi, and W. Zhan, “Pretram: Self-supervised pre-training via connecting trajectory and map,” inEuropean Conference on Computer Vision. Springer, 2022, pp. 34–50

  37. [37]

    Covernet: Multimodal behavior prediction using trajectory sets,

    T. Phan-Minh, E. C. Grigore, F. A. Boulton, O. Beijbom, and E. M. Wolff, “Covernet: Multimodal behavior prediction using trajectory sets,” inProceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2020, pp. 14 074–14 083

  38. [38]

    Tnt: Target-driven trajectory prediction,

    H. Zhao, J. Gao, T. Lan, C. Sun, B. Sapp, B. Varadarajan, Y . Shen, Y . Shen, Y . Chai, C. Schmidet al., “Tnt: Target-driven trajectory prediction,” inConference on robot learning. PMLR, 2021, pp. 895– 904

  39. [39]

    Long short-term memory,

    A. Graves, “Long short-term memory,”Supervised sequence labelling with recurrent neural networks, pp. 37–45, 2012

  40. [40]

    Comparison and evaluation of advanced motion models for vehicle tracking,

    R. Schubert, E. Richter, and G. Wanielik, “Comparison and evaluation of advanced motion models for vehicle tracking,” in2008 11th interna- tional conference on information fusion. IEEE, 2008, pp. 1–6

  41. [41]

    Real time trajectory prediction for col- lision risk estimation between vehicles,

    S. Ammoun and F. Nashashibi, “Real time trajectory prediction for col- lision risk estimation between vehicles,” in2009 IEEE 5Th international conference on intelligent computer communication and processing. IEEE, 2009, pp. 417–422. 12

  42. [42]

    Cooperative path prediction in vehicular environments,

    P. Lytrivis, G. Thomaidis, and A. Amditis, “Cooperative path prediction in vehicular environments,” in2008 11th international IEEE conference on intelligent transportation systems. IEEE, 2008, pp. 803–808

  43. [43]

    Attention is all you need,

    A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, “Attention is all you need,”Advances in neural information processing systems, vol. 30, 2017

  44. [44]

    A transformer network with sparse aug- mented data representation and cross entropy loss for ais-based vessel trajectory prediction,

    D. Nguyen and R. Fablet, “A transformer network with sparse aug- mented data representation and cross entropy loss for ais-based vessel trajectory prediction,”IEEE Access, vol. 12, pp. 21 596–21 609, 2024

  45. [45]

    It is not the journey but the destination: Endpoint conditioned trajectory prediction,

    K. Mangalam, H. Girase, S. Agarwal, K.-H. Lee, E. Adeli, J. Malik, and A. Gaidon, “It is not the journey but the destination: Endpoint conditioned trajectory prediction,” inEuropean conference on computer vision. Springer, 2020, pp. 759–776

  46. [46]

    Aisformer for long-term vessel trajectory prediction,

    Q. Yu, X. Yin, X. Geng, S. Chen, and J. Yang, “Aisformer for long-term vessel trajectory prediction,”Ocean Engineering, vol. 340, p. 122098, 2025