Vessel Trajectory Prediction

Anticipation of vessel trajectories is an essential task when navigating at sea. This applies to both human navigators and autonomous surface vessels. Trajectory forecasting enables sub-routines such as collision avoidance to assess the situation and react accordingly in time. This paper investigates Transformer and Performer models for trajectory prediction of surface vessels in confined waters. Using widely available position data from the Automatic Identification System (AIS), candidate models are trained and evaluated. Historical information on how other vessels have moved in the local area surrounding each agent is conveyed using positional heat maps. The heat maps are generated using Kernel Density Estimation (KDE) and encoded with a Convolutional Neural Network (CNN) before entering the Transformer models. The models are trained with quantile loss to efficiently obtain a model-aware prediction interval, as this is crucial for timely collision avoidance. The proposed model architectures are shown to greatly outperform previous work while the inclusion of local heat maps enables the prediction of vessel movement that is not otherwise indicated from the previous positions.

Reported gains in vessel-trajectory prediction from Automatic Identification System (AIS) data are credited to new architectures, but the evaluation protocol is rarely measured as a source of error reduction. We build a leakage-aware protocol with vessel-, time- and region-disjoint splits and apply it to two corpora with different traffic: 31 days of Danish national AIS traffic and 30 days of US Gulf coast traffic off Houston and Galveston. On both, we audit TrAISformer, GATransformer, and controlled AISFormer-inspired reconstructions. Three protocol effects appear in both corpora. First, TrAISformer's best-of-16 oracle decoder lowers error by a factor of 2.1-3.2 relative to greedy decoding. Second, a split that shares vessels lowers its greedy error by 23-25% at one hour, against 2% or less for a compact 0.43 M-parameter encoder. Third, a region-disjoint split raises TrAISformer's one-hour error from 2.2 to 24.6 km on the US corpus, because 99.9% of the test contexts fall in longitude bins never seen in training; the encoder built on local offsets is unaffected by this. Architectural mechanisms matter less: GATransformer's graph attention gives no measurable benefit on either corpus, while its waterway feature is worth 12-22%. The effect of a time-disjoint split is not stable across corpora (13% versus 2%). We release the splits and code.

To address the challenges of behavioral multimodality, limited semantic utilization, and long-term error accumulation in vessel trajectory prediction, this paper proposes M3-Former, a multimodal trajectory prediction framework enhanced by large language models (LLMs). The proposed framework incorporates vessel static attributes and navigational intent as semantic priors for long-term trajectory modeling. Specifically, a unified multimodal representation space is constructed, in which static semantic information is encoded by a pre-trained LLM and aligned with dynamic trajectory features through self-attention. To jointly capture global route planning and local motion variations, a dual-granularity Mixture-of-Experts (MoE) architecture is introduced, where sequence-level experts model global navigation trends and token-level experts refine fine-grained maneuvering behaviors. In addition, a Steering-Weighted Cross-Entropy loss is designed to alleviate the long-tail distribution of sparse turning samples and improve prediction accuracy in critical maneuvering scenarios. Experiments on a real-world Danish AIS dataset demonstrate that M\textsuperscript{3}-Former consistently outperforms state-of-the-art baselines across prediction horizons from 1 to 4 hours. In the 4-hour prediction task, the proposed method reduces Average Displacement Error (ADE) and Final Displacement Error (FDE) by 4.4% and 5.1%, respectively, compared with the strongest baseline. Qualitative and ablation analyses further verify that semantic fusion effectively reduces long-term trajectory drift, while the dual-granularity MoE improves robustness in complex waterways and route-branching scenarios. The proposed framework establishes a semantic-guided hierarchical prediction paradigm, in which high-level navigational intent and local motion dynamics are jointly modeled for robust long-term vessel trajectory forecasting.

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.

Vessel trajectory prediction is critical for maritime safety and accident prevention. While most existing trajectory prediction models rely on Automatic Identification System (AIS) data due to its precision and availability, small vessels mostly operate without AIS, resulting in a significant monitoring gap. To address this, we propose Mix&Fix-Net, a dual-stage mixer-based trajectory prediction model designed to handle vessel trajectory time-series data derived from both AIS and (non-AIS) vision data. Our architecture integrates a Primary Trajectory Predictor with a Residual Trajectory Adjuster, enabling more refined trajectory prediction. Additionally, we introduce a new video-based dataset derived from webcam streams, from which vessel trajectories are extracted to represent non-AIS data. Extensive evaluations on both AIS and non-AIS datasets across six metrics (mean squared error, mean absolute error, symmetric mean absolute percentage error, final displacement error, Frechet distance, and average Euclidean distance) demonstrate that Mix&Fix-Net consistently outperforms existing baselines across most metrics and datasets.

We present a training-free method for multi-modal trajectory prediction that achieves comparable accuracy to a 57M-parameter transformer while requiring no GPU and zero learned parameters. The method builds a transition table of historical state-to-next position pairs and retrieves neighbors using a product kernel over spatial proximity, bearing, speed, and temporal context. Two inference modes operate over this shared representation: diversity-penalized sampling produces trajectories covering distinct plausible routes, while beam search finds the highest-likelihood path. On the TrAISformer benchmark (Danish Maritime AIS), our method achieves competitive accuracy at full data availability and dramatically outperforms the transformer in data-scarce regimes---remaining stable down to 10% of training data where TrAISformer degrades catastrophically. This enables deployment in new geographic regions from an order of magnitude less historical data.

Accurate vessel trajectory prediction is critical for maritime safety and anomaly detection, yet existing models often struggle with geographic bias and navigational realism. We propose the Continuous Regression Hybrid Transformer (CRHT), a deep learning framework designed to forecast vessel motion using Automatic Identification System (AIS) data. To mitigate spatial data imbalance, we introduce an online K-means cluster sampling strategy that ensures diverse exposure to rare maneuvers during training. Our hybrid architecture integrates 1D convolutional layers for local kinematic feature extraction with a multi-head attention mechanism for global temporal context. CRHT demonstrates superior performance in short-term forecasting, achieving the lowest errors at the 1-hour horizon. The results demonstrate that while discrete models provide high navigational stability over long horizons, CRHT offers an optimal balance of precision and maneuver tracking for real-time maritime surveillance.

Long-term ship trajectory prediction is a fundamental capability for maritime safety and autonomous navigation. While recent Transformer-based architectures have improved forecasting horizons, they predominantly rely on historical kinematic states, treating vessel motion as an isolated system. In reality, maritime navigation is profoundly modulated by extrinsic factors like weather and constrained by static vessel characteristics. Existing multimodal approaches fundamentally model the joint distribution over states and contexts, treating environmental variables as peer features rather than encoding the directional physical dependence of vessel dynamics on environmental conditions. In this work, we propose the Conditional Informer, a novel encoder-decoder architecture that formulates trajectory prediction as a conditional generation task. We employ a dedicated Conditional Attention mechanism where the vessel state explicitly queries environmental contexts through cross-attention, encoding the physical prior that weather modulates - but is not generated by - vessel dynamics. Furthermore, to address the intermittency of real-world data, we introduce a Modality Masking training strategy to prevent catastrophic degradation during sensor fallback. Extensive experiments on AIS and ERA5 data demonstrate that our approach outperforms kinematic and concatenation-based baselines by 15.4% in prediction accuracy when context is available. Crucially, Modality Masking prevents shortcut learning, reducing fallback error by nearly an order of magnitude compared to unconstrained models.

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.

This paper presents a trajectory prediction method for marine vessels based on optimal planning. Crude initial trajectories respecting static obstacles are first generated using A*-search to provide a feasible warm start. In the second step, a numerical optimizer is used to ensure COLREG compliance. The prediction problem is posed as sequential trajectory planning from the perspective of each surrounding vessel, requiring only their current positions, velocities, and intended destinations as input. As the latter is included in AIS messages, this enables faster predictions than learning-based methods that typically require longer data histories. The proposed method is validated using real-world scenarios constructed from AIS data.

Vessel trajectory prediction is important for intelligent shipping, maritime surveillance, and navigation safety. However, existing public maritime AIS resources are often limited by inconsistent forecasting protocols, uneven data quality, and the lack of benchmark-ready contextual annotations, which hinder fair comparison and context-aware modeling. To address this gap, we present EnvShip-Bench, a unified benchmark for short-term vessel trajectory prediction built from large-scale raw AIS data from the Danish Maritime Authority (DMA) and NOAA through a common processing pipeline. EnvShip-Bench adopts a standardized forecasting protocol with 10 minutes of observation, 10 minutes of prediction, and 20-second sampling in vessel-centric local metric coordinates. Beyond the large-scale core benchmark, it provides a quality-first compact subset for efficient and reproducible experimentation, together with synchronized environmental and nearby-vessel context extensions. As a result, EnvShip-Bench supports trajectory-only, environment-aware, and interaction-aware forecasting under a unified evaluation framework. Extensive benchmark statistics and analysis demonstrate that EnvShip-Bench offers a standardized, extensible, and context-aware foundation for maritime trajectory forecasting research.

Maritime situational awareness often relies on Automatic Identification System (AIS) transmissions to track vessel movements. However, in operational or conflict scenarios, these data may be unavailable due to signal loss, deliberate deactivation, or intentional spoofing. In such conditions, synthetic aperture radar (SAR) imagery becomes a critical sensing alternative for wide-area maritime monitoring, despite providing only static scene snapshots. This work introduces HARBOR (Heading Analysis and Reconstruction from Behavioral Observation and Radar), a complete pipeline for transforming a single SAR image into predictive motion information without requiring any auxiliary data source at inference time. The method begins with SAR image preprocessing to enhance and segment vessel candidates, followed by automatic detection, size-based classification, and heading estimation using skeleton geometry and local intensity patterns. AIS data are used exclusively during an offline calibration phase to derive vessel-type-dependent motion parameters, which are then applied to generate probabilistic heatmaps of candidate future vessel positions. A case study using real COSMO-SkyMed SAR imagery demonstrates the pipeline on a maritime scene in southern Brazil, showing its ability to extract motion tendencies and generate probabilistic projections of vessel positions in data-denied environments.

Long-horizon maritime trajectory prediction is important for shipping management, logistics planning, and maritime risk analysis, yet month-level forecasting remains insufficiently studied. Existing deep learning methods mainly focus on short- and mid-term coordinate extrapolation and often struggle to preserve route feasibility and destination correctness over extended horizons. This paper investigates joint long-horizon vessel trajectory and destination forecasting with reasoning-capable large language models, and develops a Maritime LLM post-training framework based on Reinforcement Learning with Verifiable Reward (RLVR). An AIS-based benchmark is constructed with 60-day historical trajectories and 30-day forecasting horizons, where trajectories are converted into semantic textual representations for RL prompt construction. RLVR aligns LLMs with maritime forecasting objectives by enforcing physical validity, providing early-weighted trajectory supervision, and evaluating destination correctness through hierarchical matching and curriculum learning. Experimental results show that RLVR-trained LLMs substantially improve over zero-shot LLMs and representative deep learning baselines, especially on destination-related metrics. Among the evaluated RLVR-trained variants, 4B LLMs achieve the best overall performance, suggesting that reward-compatible optimization and task-specific capacity matching are more important than simply using larger 8B or 14B LLMs. The results also show that LSTM remains a strong deep learning baseline under limited fine-tuning data, while Transformer-style spatio-temporal models typically require larger datasets and richer structured inputs. Overall, this work advances semantic, verifier-aligned maritime forecasting for operational decision support.

Vessel trajectory prediction from Automatic Identification System (AIS) data is essential for maritime situational awareness, yet it remains challenging due to irregular sampling, missing reports, and complex dynamics. Beyond accurate point forecasts, maritime applications also demand well-calibrated uncertainty estimates for reliable decision-making. Bayesian Neural Ordinary Differential Equations (ODEs) offer a principled framework for continuous-time trajectory modeling with uncertainty quantification by placing a prior over the neural vector field parameters. However, the commonly used isotropic Gaussian weight prior fails to encode informative structural properties of vessel dynamics, such as smoothness and locality. Existing function-space Bayesian neural network methods address this limitation for static mappings, but do not transfer directly to Neural ODEs, where the primary quantity of interest is the trajectory rather than the vector field itself. In principle, one could place a Gaussian process (GP) prior directly over ODE solutions, but this requires propagating distributions through a nonlinear ODE solver, which is analytically intractable. To address this challenge, we adopt a practical approach that imposes a GP-kernel-based prior directly on the vector field evaluated at a finite set of measurement points. Specifically, we augment the standard weight-space variational objective with a kernel-based regularizer that penalizes deviations of the vector field from the structure implied by a GP prior. To handle long and irregular AIS trajectories, we further combine this function-space regularization with probabilistic multiple shooting, which decouples inference across temporal segments while maintaining global consistency.

Accurate vessel trajectory prediction is essential for safe and efficient maritime operations, enabling collision avoidance and supporting route optimization. Although memory-augmented neural networks have recently shown strong performance in pedestrian and road-vehicle trajectory prediction by selectively retrieving relevant information from an external memory, their potential for vessel trajectory prediction remains underexplored. This paper presents an empirical investigation of memory-based trajectory prediction using Automatic Identification System (AIS) data. Experiments on data from the Gulf of Mexico and the New York Bight demonstrate consistent and substantial performance gains over a range of deep learning baselines that do not incorporate an external memory.

Maritime intelligent transportation systems (MITS) are essential for ensuring navigation safety and efficiency in busy waterways. However, accurate vessel trajectory prediction remains challenging due to the limitations of single-source data. Automatic identification system (AIS) data is often sparse or unavailable for small vessels, while closed-circuit television (CCTV) data alone cannot fully capture dynamic vessel behavior. To mitigate these challenges, we propose a cross-modal interaction-based vessel trajectory prediction (named CmIVTP) framework to model the intricate interactions between vessel dynamics and environmental constraints. Specifically, we introduce a target-aware scene encoder to extract scene semantic features, effectively capturing vessel-environment interactions and enhancing trajectory prediction accuracy. In addition, we propose a cross-modal interaction transformer, which integrates AIS-derived motion features, CCTV-based environmental features, and scene representations. It leverages cross-modal attention mechanisms to simultaneously capture intra-modal semantics and inter-modal interactions, ensuring dynamically consistent and environmentally feasible predictions. Furthermore, we construct a vessel group trajectory bank by clustering historical AIS trajectories into representative motion patterns, providing an efficient and scalable approach for candidate trajectory generation. Additionally, we introduce the maritime multimodal dataset plus (named Maritime-MmD$^+$), a large-scale dataset that synchronizes AIS data and CCTV video data, providing robust support for multimodal trajectory prediction research. Extensive experiments demonstrate that CmIVTP achieves better performance on multimodal-driven vessel trajectory prediction benchmarks. The code resources for this work can be available at https://github.com/LouisYxLu/CmIVTP.

Accurate multi-step port-of-call sequence prediction is vital for tactical resource orchestration and logistical efficiency. However, existing methods struggle with unreliable voyage schedules and the inability of AIS data to provide visibility beyond the immediate next port. To address this, this study proposes a Connectivity-Constrained and Retrieval-Enhanced (CCRE) deep learning framework. Inspired by Retrieval-Augmented Generation, CCRE introduces a retrieval-enhanced historical encoder that queries a global maritime database for contextually similar navigational precedents. Transforming these scenarios into candidate-level semantic representations compensates for data sparsity in long-tail routes and resolves routing ambiguities. Integrating this with a Transformer-based trajectory encoder, the architecture executes adaptive "middle fusion" via cross-attention. This dynamically shifts predictive reliance from real-time kinematics for short-term accuracy to historical context for long-term strategic stability. To ensure sequence-level coherence, forecasting is formulated as a joint sequence generation problem using an autoregressive Transformer decoder enriched with Scheduled Sampling and Gumbel-Softmax relaxation. This mitigates error accumulation, while topology masks strictly enforce maritime network reachability to eliminate operationally infeasible routes. Evaluated on a global dataset, CCRE achieves a 72.3% first-destination accuracy and a 61.4% average three-step accuracy, outperforming baselines like CatBoost and LSTM by average margins of 12.6% and 11.3%, respectively. Case studies further corroborate the model's scalability and ability to capture complex routing patterns across diverse international trade lanes.

Long-horizon vessel trajectory forecasting under real ocean conditions is critical for collision avoidance, traffic management, and route planning. However, achieving accurate predictions is challenging due to long-range temporal dependencies and dynamic environmental factors such as currents, wind, and waves. To address these issues, we propose a hierarchical two-stage framework that combines a coarse long-term predictor with a grid-aware short-term predictor through a hierarchical fusion mechanism. The short-term branch leverages a Spatio-Temporal Graph Transformer on discretized maritime cells to capture localized dynamics, while the long-term branch encodes overarching navigational intent. An integrated environmental module incorporates oceanographic parameters, including surface currents, wind vectors, and significant wave height, using cross-modal attention and feature-wise modulation for adaptive response to varying sea conditions. Additionally, a learnable Savitzky-Golay smoothing layer enhances temporal coherence in fused trajectories. We evaluate our approach on Australian Craft Tracking System (CTS) data from the North West region, aligned with Copernicus Marine Service products, using a 3-hour input and a 10-hour prediction horizon. Experimental results show that our framework outperforms the state-of-the-art by 25% in Average Displacement Error (ADE) and 17% in Final Displacement Error (FDE). Ablation studies further validate the contribution of each component.

Accurate predictions of ship trajectories in crowded environments are essential to ensure safety in inland waterways traffic. Recent advances in deep learning promise increased accuracy even for complex scenarios. While the challenge of ship-to-ship awareness is being addressed with growing success, the explainability of these models is often overlooked, potentially obscuring an inaccurate logic and undermining the confidence in their reliability. This study examines an LSTM-based vessel trajectory prediction model by incorporating trained ship domain parameters that provide insight into the attention-based fusion of the interacting vessels' hidden states. This approach has previously been explored in the field of maritime shipping, yet the variety and complexity of encounters in inland waterways allow for a more profound analysis of the model's interpretability. The prediction performance of the proposed model variants are evaluated using standard displacement error statistics. Additionally, the plausibility of the generated ship domain values is analyzed. With an final displacement error of around 40 meters in a 5-minute prediction horizon, the model performs comparably to similar studies. Though the ship-to-ship attention architecture enhances prediction accuracy, the weights assigned to vessels in encounters using the learnt ship domain values deviate from the expectation. The observed accuracy improvements are thus not entirely driven by a causal relationship between a predicted trajectory and the trajectories of nearby ships. This finding underscores the model's explanatory capabilities through its intrinsically interpretable design. Future work will focus on utilizing the architecture for counterfactual analysis and on the incorporation of more sophisticated attention mechanisms.

Recent advancements in reinforcement fine-tuning have significantly improved the reasoning ability of large language models (LLMs). In particular, methods such as group relative policy optimization (GRPO) have demonstrated strong capabilities across various fields. However, applying LLMs to ship trajectory prediction remains largely unexplored. In this paper, we propose ShipTraj-R1, a novel LLM-based framework that reformulates ship trajectory prediction as a text-to-text generation problem. (1) We design a dynamic prompt containing trajectory information about conflicting ships to guide the model to achieve adaptive chain-of-thought (CoT) reasoning. (2) We introduce a comprehensive rule-based reward mechanism to incentivize the reasoning format and prediction accuracy of the model. (3) Our ShipTraj-R1 is reinforced through the GRPO mechanism guided by domain-specific prompts and rewards, and utilizes the Qwen3 as the model backbone. Extensive experimental results on two complex and real-world maritime datasets show that the proposed ShipTraj-R1 achieves the least error compared with state-of-the-art deep learning and LLM-based baselines.

Autonomous landing of Uncrewed Aerial Vehicles (UAVs) on oscillating marine platforms is severely constrained by wave-induced multi-frequency oscillations, wind disturbances, and prediction phase lags in motion prediction. Existing methods either treat platform motion as a general random process or lack explicit modeling of wave spectral characteristics, leading to suboptimal performance under dynamic sea conditions. To address these limitations, we propose SpecFuse: a novel spectral-temporal fusion predictive control framework that integrates frequency-domain wave decomposition with time-domain recursive state estimation for high-precision 6-DoF motion forecasting of Uncrewed Surface Vehicles (USVs). The framework explicitly models dominant wave harmonics to mitigate phase lags, refining predictions in real time via IMU data without relying on complex calibration. Additionally, we design a hierarchical control architecture featuring a sampling-based HPO-RRT* algorithm for dynamic trajectory planning under non-convex constraints and a learning-augmented predictive controller that fuses data-driven disturbance compensation with optimization-based execution. Extensive validations (2,000 simulations + 8 lake experiments) show our approach achieves a 3.2 cm prediction error, 4.46 cm landing deviation, 98.7% / 87.5% success rates (simulation / real-world), and 82 ms latency on embedded hardware, outperforming state-of-the-art methods by 44%-48% in accuracy. Its robustness to wave-wind coupling disturbances supports critical maritime missions such as search and rescue and environmental monitoring. All code, experimental configurations, and datasets will be released as open-source to facilitate reproducibility.