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1.INTRODUCTIONMaritime shipping, constituting the backbone of global commerce, transports over 90% of the world’s trade volume [1]. The recent impacts of climate change have compromised maritime infrastructure and disrupted trade, resulting in significant economic losses [2]. Moreover, increasing emissions from maritime shipping exacerbate climate change and detrimentally affect marine ecosystems [3]. Adverse weather, congested sea lanes, and navigational errors led to longer sailing times. Accurate long-term prediction of ship trajectories can alleviate these risks by enabling early detection of potential hazards, enhancing navigation efficiency, and reducing fuel consumption and travel time [4]. Thus, improving trajectory prediction is imperative for the shipping industry, climate change mitigation, and ecological conservation. Ship behavior is influenced by dynamic factors such as meteorological conditions [5], ocean currents [6], and vessel-specific operations, all of which vary significantly over time. These complexities render long-term prediction a challenge, requiring models capable of adapting to dynamic changes and accurately predicting trajectories. The current dominant approach in ship trajectory prediction is data-driven, particularly focusing on neural network methods. These methods scrutinize historical data to identify complex motion patterns, mainly learning from previous trajectories [7] [8]. While commonly used data features such as position, speed, and heading provide foundational information, they fall short of encompassing the full spectrum of factors that influence ship behavior [9]-[11]. Incorporating comprehensive data, including ship type, draft, vessel dimensions [12], and meteorological ocean data like wind speed, direction, and wave height, is critical as these elements substantially influence ship performance and maneuverability. Nevertheless, prior studies frequently neglected these complex influences, thereby constraining the accuracy and broader applicability of predictive models. Adopting a more holistic approach that integrates detailed ship trajectory data with performance and environmental data is crucial for developing robust models. However, this integration poses challenges due to the varying time resolutions of data sources and the increased dimensionality of feature spaces, potentially leading to overfitting and diminishing model performance. Our research addresses these issues by introducing a long-term ship trajectory prediction method that leverages multisource data. Key contributions of our study include:
The remaining sections of this paper are organized as follows: Section 2 reviews related work, Section 3 details the framework of the Feature-Aware Transformer, experimental results are presented in Section 4, and Section 5 concludes the paper, outlining potential future explorations. 2.RELATED WORKThe shipping industry has experienced substantial growth and significant advancements in technology, particularly with AIS. As a result, ship trajectory prediction has emerged as a crucial global research domain. Traditional models primarily utilize ship motion and behavioral data to predict trajectories [13] and often include environmental data to enhance accuracy. However, these models generally excel in short-term prediction but falter over extended periods. For instance, Millefiori et al. [14] presented a method employing mean regression stochastic processes for long-term prediction but observed a decline in accuracy when vessels changed speed or direction. Similarly, Uney et al. [15] developed a model based on the Ornstein-Uhlenbeck process, designed for non-maneuvering motion, which might not adequately account for environmental influences on ship trajectories. Recent advancements have shown that deep learning methods can significantly improve trajectory prediction. Mehri et al. [16] implemented an LSTM model tailored to various vessel types within Tianjin Port, achieving enhanced accuracy and performance. Zhang et al. [17] introduced a novel deep learning framework that integrates extracted features with vessel geographic information, using these as inputs for an attention-based Bi-LSTM regression model. Gan et al. [18] constructed an Artificial Neural Network model using clustering outcomes and vessel attributes such as speed, load capacity, weight, maximum power, and water level. Although effective for short to mid-term predictions, long-term accuracy and reliability diminish under unpredictable conditions. Huang et al. [19] developed the TripConvTransformer, which incorporates meteorological data through a complex convolutional structure, yet the interplay among various factors and their collective impact on trajectory prediction warrants further investigation. Over-simplification by feature discretization can lead to significant information loss, particularly with continuous variables such as weather data. Kim et al. [20] proposed a hybrid deep learning framework that combines CNN and Fully-Connected Neural Networks to extract both immediate motion-related features and higher-level attributes such as estimated time of arrival and ship type, illustrating the benefits of integrating diverse data sources to improve prediction accuracy. Despite these advancements, the integration of crucial external factors like sea currents and wind direction is often lacking in many current models. This limitation typically reduces accuracy in long-term predictions, affecting reliability and precision. Our research seeks to bridge these gaps by developing a robust model that thoroughly considers various influencing factors for precise long-term ship trajectory prediction. This approach focuses not only on capturing current states and environmental conditions but also on predicting ship behavior over prolonged periods. 3.FEATURE-AWARE TRANSFORMER3.1Overall ArchitectureThis section describes the architecture of our proposed Feature-Aware Transformer (FAT) model for ship trajectory prediction, illustrated in Figure 1. The model consists of two primary modules: Multi-Source Data Fusion and Feature-Aware Prediction. The Multi-Source Data Fusion module preprocesses and integrates ship trajectory data with ship performance and meteorological ocean data, ensuring a comprehensive dataset for detailed analysis and precise prediction. The Feature-Aware Prediction module employs a transformer network architecture to map high-dimensional feature vectors into a lower-dimensional space, focusing on high-order interactions among features. This approach significantly enhances trajectory prediction accuracy by effectively capturing complex feature dependencies and patterns. 3.2Multi-Source Data Fusion3.2.1Preprocessing of Ship Trajectory DataTo mitigate potential inaccuracies in AIS data resulting from equipment malfunctions, transmission errors, or operational mistakes, we implemented several effective data cleaning procedures. These include excluding data points outside the study area to ensure geographic relevance; removing duplicate entries to eliminate redundancy; discarding records with unrealistic speeds or significant deviations in speed, heading, and position; omitting records of vessels in mooring or anchorage to focus on those in transit; discarding records of voyages under four hours to prioritize longer trips; segmenting non-continuous voyage records to maintain data continuity; filling in missing dynamic data or removing records with extensive gaps, supplementing with static data from similar records as necessary; and standardizing data point intervals at ten minutes to ensure consistent analysis. Collectively, these steps significantly enhance the dataset’s accuracy and relevance for analyzing ship trajectories. 3.2.2Data FusionTime alignment is critical during data fusion to ensure consistency across all datasets along the time dimension. Each AIS data point must correspond precisely to its timestamp to maintain temporal consistency. To achieve seamless integration and uniform time resolution across different data sources, interpolation may be necessary. Fusing ship trajectory data with ship performance data involves linking unique identification codes of ships to associate specific performance parameters with individual ship instances. Similarly, integrating ship trajectory data with meteorological ocean data requires matching both spatial and temporal dimensions. This involves calculating distances between ship positions and meteorological observation points using the Haversine formula and correlating each ship position with the nearest meteorological observation point based on timestamps. Given the significant time resolution differences between AIS data and meteorological ocean data, it is crucial to address continuity and consistency challenges in data fusion. To overcome these, we will explore various time interpolation methods, including Space-Time Kriging algorithms, Thin Plate Smoothing Spline interpolation, autoregressive moving average models, and least squares interpolation. Space-Time Kriging (STK): This algorithm combines the spatial analysis benefits of traditional Kriging interpolation with the time series modeling capabilities, specifically designed for predicting unknown locations or times within the spatiotemporal domain. Thin Plate Smoothing Spline (TPSS): This algorithm enhances interpolation accuracy by optimizing the balance between smoothness and precision in spline fitting. It employs a statistical model to link observed values at spatial points with spatial variables and covariates, efficiently capturing subtle spatial variations. Autoregressive Moving Average (ARMA): A classic time-series analysis model, ARMA integrates autoregressive and moving average components to describe the relationship between sequential values and stochastic disturbances. Least Squares Interpolation: This method minimizes the sum of squared discrepancies to establish the parameters of the fitting function, effectively characterizing trends in data changes. It constructs a function that minimizes the differences between its values at known data points and the actual observations, thereby accurately fitting time-series data. The efficacy of these methods will be assessed by comparing their interpolation results using Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). 3.3Feature-Aware PredictionThe architecture of the Feature-Aware Prediction module is thoughtfully structured into two principal components: the Feature-Aware module and the Transformer Prediction module. The Feature-Aware module comprises a feature embedding layer and a feature interaction layer. The Transformer Prediction module includes the transformer output layer, as illustrated in Figure 1. The feature embedding layer first processes a sparse high-dimensional feature vector, including ship trajectory, ship performance, and meteorological ocean features, and projects these features into a unified low-dimensional space. The feature interaction layer then refines these embedded features, dividing them into distinct ship interaction and ocean interaction layers. Each interaction layer functions as a multi-head self-attention neural network, utilizing attention mechanisms to effectively model and capture complex interactions among higher-order features. The transformer output layer subsequently receives the integrated feature data from the interaction layers and feeds it into a conventional Transformer network, which then generates the final trajectory prediction. 3.3.1Feature EmbeddingIn our study, we initially represent ship trajectory features, ship performance features, and meteorological ocean features as sparse vectors. These vectors are then combined into a unified feature vector f, formatted as f = [fT; fP; fM], where fT, fP, and fM specifically denote the feature domains of ship trajectory, ship performance, and meteorological ocean features, respectively. Due to the high sparsity and dimensionality characteristic of these categorical feature domains, we apply a method to map them into a lower-dimensional space. Each categorical feature within a domain is represented by a low-dimensional vector di = Eifi,Where, Ei is the embedding matrix for the i-th feature domain, and fi is a multi-hot vector. Recognizing that categorical features often exhibit multi-valued attributes, we adjust our model to accommodate these multi-valued features by averaging their respective feature embedding vectors 3.3.2Feature InteractionAfter mapping the domains of ship trajectory, ship performance, and meteorological ocean features to a shared low-dimensional space, we advance to modeling feature interactions within this space. Our approach employs a multi-head self-attention mechanism in the feature interaction layer to effectively capture domain interactions and dependencies. This mechanism is pivotal in elucidating complex interactions and connections within the data. The configuration of the feature interaction layer is depicted in Figure 2. The attention weight Here, Here, Here, H is the total number of heads, and ⨁ symbolizes the concatenation operation, which merges the feature representations generated by all heads in sequence into a single long vector. 3.3.3Transformer OutputThe transformer output layer within the prediction layer incorporates several key components of an encoder-decoder structure, including the attention module, feedforward network module, residual connections, and dropout module. This network adeptly handles dependencies in time-series data and non-linear characteristics in spatial data through its sophisticated attention mechanisms, comprising both self-attention and multi-head attention. The self-attention mechanism takes as input the query matrix Q, key matrix K, value matrix V, and the dimensionality dk of queries and keys. It calculates the dot product of Q and K, which is then scaled by the factor Utilizing multiple mappings of queries, keys, and values facilitates the acquisition of varied contextual information compared to a singular attention function. The self-attention function operates concurrently across each projected version of queries, keys, and values; the results are then concatenated and re-projected to produce the final output. Consequently, through the multi-head attention mechanism, the Transformer simultaneously extracts comprehensive features of trajectory data from different representational subspaces. The feedforward network consists of two linear transformations with a ReLU activation function applied after each. To enhance training efficiency and mitigate overfitting, residual connections and a dropout module are integrated. 4.EXPERIMENTAL AND RESULT4.1Experimental Setup4.1.1Experiment SettingsIn this study, we utilized an encoder-decoder Transformer architecture equipped with eight attention heads, trained with a learning rate of 0.01 and a dropout rate of 0.1. The network comprises multi-head self-attention layers, each with 32 hidden units, two attention heads per layer, and a dropout rate of 0.1. We conducted training and inference on PyTorch, optimizing the process with the Adam optimizer. 4.1.2DatasetOur study employed three datasets for ship trajectory prediction: ship trajectory data, ship performance data, and meteorological ocean data. Details of these datasets are provided below: Ship Trajectory Dataset: Sourced from the Danish Maritime Authority (DMA), this dataset comprises publicly available AIS data from January 2nd to February 24th, 2024. It documents real-time ship positions and navigation conditions across a geographic range from 10.30W to 13.00W longitude and 55.50N to 58.00N latitude. The dataset is comprehensive, containing records of timestamp (precision of 1 second), latitude, longitude, speed over ground (SOG), and course over ground (COG), totaling 98,304,795 records. Ship Performance Dataset: Also derived from the DMA’s AIS data, this dataset focuses on ship performance, cataloging different vessel types such as oil tankers, passenger ships, and fishing boats, totaling 3648 records. It includes specific attributes like type, length, width, and draft. Meteorological Ocean Dataset: Sourced from the European Centre for Medium-Range Weather Forecasts (ECMWF) and accessed via the World Weather Online API, this dataset aligns with the temporal and spatial parameters of the ship trajectory data. It details weather conditions including timestamp (precision of 3 hours), latitude, longitude, temperature, wind direction, wind speed, and wave height, encompassing a total of 1,153,654 records. 4.1.3Evaluation MetricWe use the Haverson distance to calculate the prediction error between the true position and the predicted position: Where R is the radius of the Earth, typically around 6371 kilometers. ϕ1 and ϕ2 are the latitudes of the true position and the predicted position, respectively, and λ1 and λ2 are their longitudes. 4.2Experimental Results4.2.1Data fusionIn this study, we conducted time interpolation on temperature, wind speed, wind direction, and wave height attributes from meteorological ocean datasets using four algorithms: Least Squares Interpolation, TPSS, ARMA, and STK, with the results displayed in Table 1. Table 1.Results of the effects of four interpolation algorithms
Of these methods, TPSS Interpolation exhibited the highest accuracy for temperature, wind speed, and wave height, as indicated by the lowest RMSE and MAE values. Conversely, Least Squares Interpolation resulted in the highest RMSE and MAE, signifying lower accuracy. For wind direction, both STK and TPSS proved effective, whereas ARMA and Least Squares exhibited limitations, particularly in capturing wave height attributes accurately. Overall, TPSS was the most effective technique, especially in interpolating missing values in temperature, wave height, and wind speed, thus demonstrating its high suitability for addressing data gaps in oceanographic datasets. 4.2.2Trajectory PredictionIn this study, we explored various deep learning models for ship trajectory prediction and comprehensively compared their performance. Our results, displayed in Table 2, demonstrate that the Feature-Aware Transformer (FAT) model consistently outperformed other models in prediction accuracy across all time intervals. Table 2.Mean prediction performance (in kilometers) of the models
We assessed the prediction errors of these models over periods of 1 hour, 2 hours, 3 hours, and 6 hours. The performance of the Deep Long Short-Term Memory (DLSTM) model declined with longer time intervals. Both the DBSCAN_Attention_LSTM and the TrAISformer model exhibited more stable performance and slower error growth, yet they did not achieve the effectiveness of the FAT model. The AttentionSeq2Seq model, while showing improvements in short-term prediction, was less effective for long-term prediction. A quantitative evaluation further highlighted performance disparities among the models, as depicted in Figure 3. The FAT model demonstrated superior accuracy and minimal deviation from actual ship trajectories, emphasizing its robust feature learning and analytical capabilities. Notably, the FAT excelled in specific navigational tasks such as turn prediction, where it significantly surpassed competing models by adeptly capturing long-term dependencies. Its self-attention mechanism enabled precise detection of trajectory changes associated with turns, accurately predicting ship turning behavior. Additionally, in straight-line trajectory prediction, the FAT maintained high consistency and effectively recognized stable navigation states, showcasing its ability to suppress noise and accurately track real trajectories. 4.3Ablation studyIn this study, we conducted a series of ablation experiments to evaluate the impact of various feature integrations on the performance of ship trajectory prediction. These experiments were designed to determine the contributions of ship performance data, meteorological ocean data, and the Feature-Aware module in enhancing prediction accuracy. The results are presented in Table 3. Table 3.Mean prediction performance (in kilometers) of the models in the ablation study
When using the complete model, which integrates ship trajectory data, ship performance data, and meteorological data, our model recorded error values of 0.7015, 1.1554, 1.7242, and 3.8271 at prediction intervals of 1 hour, 2 hours, 3 hours, and 6 hours, respectively. Omitting meteorological ocean data led to a noticeable decrease in performance, especially over longer prediction intervals. The absence of ship performance data highlighted its critical role in trajectory prediction. Similarly, excluding both meteorological ocean data and ship performance data confirmed the essential contribution of these features to prediction accuracy. The removal of the Feature-Aware module resulted in increased error rates of 0.7692, 1.3766, 2.1405, and 4.5791, emphasizing the module’s vital role in synthesizing and optimizing feature data to enhance performance. In summary, the ablation study results emphasize the significant impact of ship performance data and meteorological data on improving trajectory prediction accuracy. While trajectory information alone provides some predictive value, incorporating ships’ dynamic performance and environmental factors substantially enhances the model’s efficacy. 5.CONCLUSION AND FUTURE PROSPECTSIn this study, we introduced a Feature-Aware Transformer model for ship trajectory prediction, integrating meteorological ocean data and ship performance data. This model demonstrated a 13% improvement in long-term prediction accuracy over existing transformer-based methods, achieving an average error of less than 4 kilometers over 6 hours. Leveraging meteorological, performance, and AIS trajectory data within a Transformer architecture, our model showed exceptional precision, as confirmed by ablation experiments that highlighted the critical importance of each data type and the Feature-Aware module. Despite these advancements, future enhancements could include exploring advanced feature fusion techniques and deep learning models to improve accuracy and efficiency further. Additionally, expanding research to assess the impacts of global climate change on maritime navigation and optimizing computational efficiency for real-time maritime decision support could enable the handling of large-scale data more swiftly and effectively. 6.6.REFERENCESG. Dobie,
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