Precise forecasting of vessel movements is crucial for efective maritime trafic monitoring and management. Automatic Identification System (AIS) data ofer rich information for trajectory prediction but sufer from irregular sampling, missing values, noise, and transmission errors that complicate modeling. To address these challenges, we propose a two-stage forecasting framework: first, a comprehensive preprocessing pipeline performs data cleaning, feature extraction, anomaly correction, and interpolation to produce consistent trajectories; second, an enhanced GRU network augmented with a dual-head self-attention layer jointly predicts future vessel positions, speed, and course up to 7 hours ahead. We evaluate our method on real AIS data from the port of Brest, France, and demonstrate that it outperforms LSTM, standard GRU, and single-head attention baselines in both loss and error metrics. These results highlight the efectiveness of combining rigorous data denoising with a tailored deep-learning architecture for accurate multi-step vessel trajectory forecasting.
Accurate forecasting of vessel trajectories is fundamental to safe and eficient maritime trafic management. With global shipping carrying over 80% of world trade by volume, port authorities and coastal surveillance systems depend on reliable predictions of vessel movements to prevent collisions, optimize trafic flow, and ensure environmental compliance.
The AIS provides the primary data source for these forecasts. The International Maritime Organization
(IMO) mandates AIS, which uses VHF transmissions to relay dynamic data (e.g., position, speed, course)
and static data (e.g., MMSI, vessel type, voyage info) [
Future trajectory forecasting is an active research domain, with a variety of techniques explored
for vessel trajectory prediction [
The key challenge is to bridge the gap between the complexities of AIS data preprocessing and the need for accurate future trajectory forecasting. To address this, we propose a rigorous data analysis pipeline alongside a prediction model that estimates both vessel position and kinematic variables speed and course - using a GRU architecture enhanced with a dual-head self-attention layer. The main contributions of this paper are summarized as follows: • A comprehensive preprocessing pipeline for AIS trajectories, incorporating noise filtering, interpolation of missing values, and normalization ensuring high-quality, analysis-ready sequences. • A robust sequence forecasting model, combining a single-layer GRU with a dual-head selfattention mechanism that enhances prediction accuracy. • A multi-task output design to jointly predict future vessel position, Speed Over Ground (SOG), and Course Over Ground (COG) up to 7 hours ahead, significantly outperforming LSTM and standard GRU baselines.
The remainder of this paper is organized as follows. Section 2 discusses the related work. In section 3 the GRU+self-attention forecasting architecture is described. Experimental setup, evaluation metrics, and results are presented in Section 4. Finally, Section 5 concludes the study and discusses directions for future research.
Several works exist in AIS data preprocessing addressing the aforementioned errors. In [
Building on the identification and categorization of AIS data errors, Zhao et al. [
Concerning that our goal is to prepare the AIS dataset for tasks such as trajectory prediction or
anomaly detection, we reviewed several studies that address both tasks. These approaches typically
follow a pipeline that begins with AIS data preprocessing to remove outliers and prepare clean inputs,
followed by trajectory prediction of the vessel’s next expected position, speed and course, and finally
anomaly detection based on deviations from the predicted trajectory. Studies consistently emphasize
sanitizing raw inputs by removing invalid records like positions on land, impossible speeds (e.g., <0
knots or >30 knots), incorrect MMSI formats, and null values [
In recent years, several advancements have been made in the trajectory forecasting problem using
NNbased prediction techniques. The authors in [
Unlike threshold-based filtering and simple moving average (MA) correction, [
This study follows a step-by-step methodology to create a solid dataset, clean of outliers and irregularly sampled vessel trajectories and perform eficient next-point trajectory prediction. Our forecasting model is a GRU encoder augmented with a dual-head self-attention layer, trained to predict vessel’s next geographic position (latitude and longitude), SOG and COG. This section details both the preprocessing steps applied to the raw AIS data and the architecture of the prediction framework.
Data preprocessing addresses AIS flaws, mentioned in 2, in terms of physical errors, spatial inconsistencies, and temporal inaccuracies.
Specifically, for each vessel, this work leverages some standard data cleansing operations including:
removing duplicate records (i.e., entries with identical timestamps or timestamps less than one second
apart), elimination of rows with column data for SOG with a value of 0. Additionally, all points with
SOG greater than 30 (outside of normal speed values) and COG outside 0-360 were removed. Also, in
order to exploit the static information of the dataset, vessels with ship type out of the oficial boundaries
(20-90), according to [
Trajectory extraction groups AIS data by MMSI to form vessel-specific trajectories [
To ensure the quality of the extracted trajectories, we implement two anomaly correction methods:
Speed outlier correction method prevents unrealistic jumps in SOG. Physically implausible accelerations or decelerations in vessel speed were detected and corrected. Given a maximum allowed acceleration (max) and deceleration (max), we enforce the following constraints in each trajectory: ∆ SOG = |SOG − SOG− 1| ∆ SOG ≤ {︃max · ∆ if accelerating
max · ∆ if decelerating where (max) and (max) were fixed in 0.15 knots/s (this value is approximately the average of acceleration for all ships) and ∆ = − − 1 is the time diference in seconds. So, if a violation is detected, the erroneous SOG value is replaced by time-weighted average of its neighbors: SOGcorrected = ∆ · SOG− 1 + ∆ − 1 · SOG+1
∆ − 1 + ∆
Position outlier correction detects unrealistic displacements using kinematic constraints (maximum allowed movement per timestep). The maximum allowed displacement ∆ from point i-1 to i is derived from: where − 1 = SOG− 1 · 0.514 (knots → m/s), and max = 0.15 knots/s · 0.514 (→ m/s²). The actual displacement ∆ is computed in UTM coordinates (meters):
∆ = √︀( − − 1)2 + ( − − 1)2 If ∆ > ∆ , we further check the next segment → + 1 to avoid overcorrection. If both segments violate constraints, the point is flagged for correction. Once an outlier is identified, an interpolation-based method is applied to perform the correction.
corrected = − 1 + ︂( − − 1 )︂ +1 − − 1 (+1 − − 1) (1) (2) (3) (4) (5) corrected = − 1 + ︂( − − 1 )︂
(+1 − − 1) +1 − − 1
The algorithm operates iteratively to progressively refine data corrections, as single-pass approaches often introduce new anomalies while resolving existing ones. Based on empirical evaluation on the selected dataset, we determined that three iterations provide a balanced trade-of between correction accuracy and computational eficiency. (6)
The final preprocessing step involves resampling trajectory points to uniform 1-minute intervals. This converts irregularly sampled data into temporally consistent sequences, helping models learn clearer time-based patterns and reducing noise from variable sampling rates. After segmentation (Section 3.1.2), which limits gaps between points to under 10 minutes, we chose a 1-minute interval, close to the mean sampling rate, to balance data smoothing with movement fidelity. Missing SOG values are recalculated using distance over time between interpolated positions. For COG, angular unwrapping is used to handle 0°/360° discontinuities, allowing smooth linear interpolation before rewrapping to the [0°, 360°) range.
This work employs a GRU-based neural network with multi-head attention to predict subsequent trajectory points. The architecture features an input layer, a recurrent layer (GRU) and a dual-head attention block. During training, the model processes normalized sliding windows of vessel trajectories, with inputs containing five temporal features (normalized position, SOG, and COG represented as sine-cosine components) and outputs predicting the subsequent position, speed, and course. The model structure is illustrated in Figure 1.
The input layer ingests fixed-length sequences of normalized trajectory points. Each raw trajectory point = (, , , ) where , are longitude/latitude, is SOG, and is COG, is transformed into a feature vector ′ = (︀ , , , cos , sin ︀) , where position coordinates (, ) are converted to UTM (meters), and along with speed are z-score normalized. Course is converted to radians = 180 and then mapped to sine-cosine components to avoid discontinuities at 0∘ /360∘ .
Sequential patterns are extracted via overlapping sliding windows of length = 5 over each vessel’s trajectory:
= {˜, ˜+1, ˜+2, ˜+3, ˜+4}, = ˜+5, with = 0, . . . , − 6, where M is the length of the trajectory. Each window shares four points with the previous one, ensuring smooth transitions and maximal use of the trajectory data for predicting the immediate next point.
The recurrent base consists of a single-layer GRU with hidden size ℎ = 256. At each time step , the GRU updates its hidden state ℎ by combining the current input ˜ with the previous state ℎ− 1: ℎ = GRU(︀ ˜, ℎ− 1)︀
It generates full sequences of hidden states = {ℎ1, ℎ2, ..., ℎ } ∈ × 256, where = window
length. The GRU [
Following the GRU encoder, a dual-head self-attention mechanism [
() with = 128 for the two heads. The √ head outputs are then concatenated [head(1); head(2)] ∈ R × 256 and projected with ∈ R256× 256. This output combines with the original GRU states through residual connection and layer normalization: out = LayerNorm (︁ + [head(1); head(2)]⊤ + , ︁) where ∈ R256 is a bias term, preserving temporal features while enhancing contextual awareness.
The two head outputs are concatenated to restore dimension ℎ = 256. The fused representation is fed into three specialized output heads predicting: (1) Position, two-dimensional coordinates in normalized space, (2) Speed (SOG) which is a scalar value, (3) Course (COG) a sine-cosine pair.
Input Layer
GRU Layer Multi-Head Self-Attention
Concatenate First Head
Second Head Position FFN
Speed FFN
Course FFN latitude, longitude speed
cos(course), sin(course) predictions of directional angles. The final loss is given by: ( − ˆ)2 + ( − ˆ)2 + ( − ˆ)2 + ︁( 1 − (cos cos ˆ + sin sin ˆ) ︁)]︁ (7)
For the evaluation of our method, we chose the Brest dataset [
In Section 3.1, we outlined our end-to-end preprocessing pipeline covering data cleaning, trajectory segmentation, and temporal resampling. As shown in Figure 2, spatial integrity issues, such as land crossings and illogical position jumps, have been efectively corrected. Table 1 summarizes the results of speed and position anomaly corrections aimed at reinforcing kinematic consistency, while Table 2 details the impact of each cleaning stage on dataset size, trajectory count, and vessel coverage. Trajectory extraction enhances the dataset by partitioning continuous AIS tracks into consistent sub-sequences, thereby increasing the diversity of vessel behavior patterns.
(a) Raw BREST dataset (b) Preprocessed dataset
The key insights from the table highlight two major stages where a significant number of points were removed. The first stage is during the speed filtering step, which eliminates vessels with either zero SOG or unrealistic values above 30 knots. Most of the removed points had SOG = 0, indicating many stationary vessels or erroneous readings that could have negatively impacted the prediction model. In the second stationary trajectory filtering applied after segmentation, the rest of route segments where vessels remain static were also removed. These steps ensure that the final dataset primarily contains meaningful kinematic information suitable for trajectory prediction. The second stage is at the temporal resampling which uniformly down-samples the data to fixed intervals, smoothing out irregular sampling and improving the stability of downstream prediction models. Another observation from the table is that the extraction procedure resulted in a significant reduction in the number of vessels, while the total number of trajectory points decreased far less proportionally. This suggests that the 10-minute time-gap threshold led to the creation of many short trajectories either single point or fewer than 24 points which were subsequently discarded. As a result, many vessels with dense but uneven sampling were removed from the dataset.
This work implements and trains the model using the PyTorch framework over 200 training epochs, with early stopping (patience=20 epochs) to prevent overfitting. The model optimization employs the Adam optimizer with a learning rate of 0.001 and a step decay scheduler (gamma=0.1 at every 10 epochs). This configuration promotes stable convergence during training while mitigating gradient-related issues such as explosion or vanishing gradients. We employed a batch size of 128 and the dataset was split into 70% for training, 10% for validation, and 20% for testing and finally, k-fold cross-validation was used to ensure the robustness and generalizability of the model across diferent subsets of the data.
To evaluate our model’s predictive performance, we apply it to the test set, which is preprocessed in the same way as the training data. For each trajectory, we slide a window of length over the sequence: at each step (where = + 1, . . . , ), the model observes the previous points and predicts the -th point. We then compare this prediction to the true value at time to obtain an instantaneous loss . By sliding the window across all points, we accumulate these losses and compute the average prediction error as follows: =
1 ∑︁ − =+1 where is the total number of points in the trajectory and is the window size.
To evaluate the selection of GRU with dual-head self-attention layer as the best model, we experimented with other methods that are usually used to solve such time-series forecasting tasks. The models tested are LSTM, GRU without attention layer and also GRU with a single-head attention layer to justify the usefulness of the second head.
In this section, we present the results of the prediction framework. Table 3 shows a detailed comparison of diferent models to identify the best-performing one, and on Table 4 the rest of the performance measurements of the best performing model are presented. While the enhanced MSE loss was used during training, it proved insuficient on its own for evaluating model performance. Therefore, we also report additional metrics, including the mean, median, and maximum distance errors across the entire dataset, to provide a more comprehensive evaluation.
LSTM GRU GRU+Single-head Attention Layer GRU+Dual-head Attention Layer
Self-attention layer allows the model to dynamically re-weight past time steps, enabling it to capture long range dependencies and abrupt maneuvering behaviors that purely recurrent layers may overlook. By computing pairwise afinities across the entire sequence, self-attention can emphasize critical context—such as an earlier course change or speed adjustment when predicting the next point. In our ablation (Table 3), adding a single attention head already yields a substantial drop in median error (from 86.3 m to 63.1 m) by focusing on the most informative time steps. Splitting into two parallel heads further boosts performance reducing interference between these distinct modalities. This dual-head design leads to the lowest overall loss and best error statistics (median 58.5 m, average 90.4 m), demonstrating that two parallel attention heads significantly improve trajectory prediction accuracy.
For further evaluation, we select two vessels with diferent total prediction errors as examples. Figure 3 shows the experimental results for one vessel with an average distance error of 25.9 m. Specifically, Figure 3a shows the ground truth represented by a blue line and the predicted points marked as red crosses, and the other two figures 3b, 3c illustrate the SOG and COG predictions, compared with the ground truth. Also, Figure 4 shows the comparison charts for another vessel with an average error of 26.2 m. This vessel is particularly interesting because, from the position and SOG plots, we observe that it remains stationary for 155 minutes; despite this, the prediction accuracy remains strong for up to 208 minutes, with the longest successful prediction extending to 7 hours. An analytical error distribution for the two vessels is shown in Figures 5 and 6, respectively.
(a) Latitude and longitude position prediction
(a) Latitude and longitude position prediction
In this study, we presented a vessel trajectory prediction framework that combines robust preprocessing of AIS data with a GRU-based model augmented by a dual-head self-attention layer. Using historical AIS records from the port of Brest, France, our experiments demonstrate that: • The proposed preprocessing pipeline successfully handles a heterogeneous dataset containing diverse vessel types. By filtering spurious points, interpolating gaps, and normalizing features, we reduce noise and produce smooth, analysis-ready trajectories. • The GRU + dual-head self-attention architecture reliably forecasts future positions up to more than 7 hours ahead. In addition to spatial coordinates, it jointly predicts SOG and COG with strong accuracy, as evidenced by consistently low median and average error metrics. • Incorporating two parallel attention heads, yields the best overall performance, reducing interference between modalities and improving both loss and error statistics relative to single-head and purely recurrent baselines.
In future work, our goal is to validate the generality of our approach on additional AIS datasets from diferent regions and trafic conditions to prove its robustness. Another goal is to compare our forecasting performance against state-of-the-art methods in trajectory prediction benchmarks, and specifically bidirectional RNNs and transformers, to quantify relative gains. Furthermore, we intend to use this model as a foundation to extend to anomaly detection: by comparing live AIS streams against our predicted trajectories, speeds, and headings, we aim to identify unusual vessel behavior in real time.
This work has received funding from the European Defence Fund programme under grant agreement No 101103386, FaRADAI project. The views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the granting authority can be held responsible for them.
Special thanks to the IIT group MagCIL and in particular research associates Christos Nikou and Christos Sgouropoulos for their scientific support and comments.
During the preparation of this work, the authors used ChatGPT, Grammarly in order to: Grammar and spelling check. After using these tools, the authors reviewed and edited the content as needed and take full responsibility for the publication’s content.