Ship trajectory prediction method based on irregular multivariate real trajectory time series

Abstract

The present application relates to a kind of trajectory prediction method, the ship trajectory prediction method based on irregular multivariate real trajectory time series of the present application, comprising the following steps: real ship trajectory data in region is as the input data of model, and interval information between trajectory point is calculated according to date information;Ship trajectory data is normalized by encoding layer to original data, and is processed from two dimensions of channel aggregation and channel independent respectively, and as the input of model;From the perspective of channel aggregation, the space-time characteristics of ship trajectory are extracted, and the state transition equation of ship trajectory movement is constructed in combination with the encoded trajectory data and time interval;Feature fusion module is constructed, and the space-time characteristics of ship trajectory and attribute characteristics are effectively fused to realize the prediction of ship trajectory.The method directly analyzes real ship trajectory, does not need to reconstruct trajectory data through space-time calibration preprocessing, and overcomes the limitations of traditional method when processing irregular trajectory points of different time intervals.

Description

TECHNICAL FIELD

[0001] The present application relates to a trajectory prediction method, in particular to a ship trajectory prediction method. BACKGROUND

[0002] Intelligent marine transportation plays a vital role in improving the efficiency of marine transportation and promoting global trade development. Accurate ship trajectory prediction not only helps to reduce the risk of ship collision, but also is the basis of route planning. In the actual scenario of ship navigation, ship motion prediction has high requirements for accuracy and real-time performance. Traditional models can only predict ship trajectory points based on time interval data, and require equal time intervals. However, real ship trajectory data is often irregular. The above method needs to calibrate the data first, and then realize the analysis and prediction of the motion of a single ship through improved algorithm. It cannot directly analyze the original data, and has problems such as calibration data error and data processing delay. Moreover, it is difficult to realize the simultaneous analysis and prediction of the motion of multiple ships. Moreover, the ship trajectory sequence from the automatic identification system is an irregular multivariate time series with variable time intervals. Existing deep learning methods are usually difficult to directly analyze real trajectory data, and need to be pre-processed by time and space calibration to reconstruct trajectory points at fixed time intervals. SUMMARY

[0003] The technical effect of the present application can overcome the above-mentioned defects, and provide a ship trajectory prediction method based on irregular multivariate real trajectory time series, which greatly improves the prediction effectiveness and accuracy of ship trajectory.

[0004] To achieve the above-mentioned purpose, the present application adopts the following technical scheme: comprising the following steps:

[0005] S1. The real ship trajectory data in the region is taken as the input data of the model, and the interval information between the trajectory points is calculated according to the date information;

[0006] S2. The original data is normalized by the encoding layer, and is processed from two dimensions of channel aggregation and channel independence respectively, and is taken as the input of the model;

[0007] S3. The spatiotemporal features of the ship trajectory are extracted from the channel aggregation perspective, the encoded trajectory data and the time interval are combined to construct the state transition equation of the ship trajectory motion, and the local and global spatiotemporal features of the ship trajectory are captured;

[0008] S4. The attribute features of the ship trajectory are extracted from the channel independent perspective, the encoded trajectory data is mapped to high-dimensional features from the attribute dimension, and the ship attribute features are extracted from the attribute data trend;

[0009] S5. Construct a feature fusion module to effectively fuse the spatio-temporal features and attribute features of the ship trajectory, and realize ship trajectory prediction.

[0010] A new dual-view Mamba model is used for ship trajectory prediction. Real ship trajectory data is used to construct selective state spaces for ship motion in channel integration and channel independence, respectively, and spatio-temporal features and attribute features of trajectory points are extracted. Then a feature fusion strategy is developed to integrate these features, promoting effective capture of contextual information to achieve accurate ship trajectory prediction. Experimental results show that DP-Mamba (Distillation Prompt Mamba, a Mamba architecture variant designed for multi-modal remote sensing image classification tasks) achieves excellent performance on multiple real AIS (Automatic Identification System) datasets, verifying the effectiveness of the method for trajectory prediction.

[0011] In the AIS system, each ship device will send AIS messages at certain time intervals, which contain basic information, navigation state and ship position, etc. of the ship, forming a time series of ship motion trajectory data. Ship trajectory data usually shows potential temporal relationship and dynamic change, which can be modeled in the state space representation of the navigation state. In terms of time, these data show multi-scale temporal dependence, while from the perspective of variables, they show complex spatial dependence between variables. For ship motion tasks, the time interval between two consecutive AIS message information is an important factor affecting the prediction result, so the present invention proposes a DP-Mamba neural network structure, which introduces time interval data as an input variable of the state transition equation of Mamba, and combines a time perception module to solve the problem of trajectory prediction of irregular time sequence ship data.

[0012] According to the characteristics of real AIS data, the present invention proposes a new DP-Mamba model for ship trajectory prediction. This method directly analyzes real ship trajectories without reconstructing trajectory data through spatio-temporal calibration preprocessing, overcoming the limitations of traditional methods in handling irregular trajectory points with different time interval.

[0013] Compared with the traditional Mamba module, the present invention introduces a new variable-time weight into the state space structure of the spatio-temporal feature extraction module (TMamba), replacing the previous projection type time information representation, thereby integrating the real time interval information.

[0014] In addition, a multi-scale window is designed to divide the ship trajectory into segments of different time steps, capturing both global and local information and enhancing the extraction ability of trajectory features. To achieve channel independence, the VMamba module is used to extract attribute features, effectively reducing the mutual interference between variables and highlighting the overall trend of attribute dimensions.

[0015] Furthermore, a selective state space transfer method DP-Mamba is used to construct the ship movement process, which not only improves the explainability of trajectory prediction but also ensures high computational efficiency. The model requires only 14.68 MB of GPU memory and 3.2 milliseconds (ms) of batch processing time for each inference, fully meeting the real-time ship trajectory prediction requirements. Experimental results show that the DP-Mamba model performs best on real AIS data, with a maximum accuracy of 94.2%.

[0016] Compared with the traditional Mamba2 model, DP-Mamba improves the prediction accuracy by 11.2%, significantly improving the accuracy of ship trajectory prediction. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a network structure diagram of the present application;

[0018] Figure 2 is a multi-scale TMamba structure schematic diagram;

[0019] Figure 3 is a ship trajectory point data display schematic diagram;

[0020] Figure 4 is a prediction trajectory visualization schematic diagram based on the EMO dataset;

[0021] Figure 5 is a prediction trajectory visualization schematic diagram based on the dataset;

[0022] Figure 6 is a comparison schematic diagram of the computational complexity of different models;

[0023] Figure 7 is a schematic diagram of the hyperparameter sensitivity of the DP-Mamba model;

[0024] Figure 8 is a ship prediction trajectory effect schematic diagram: (a) turning; (b) zigzag navigation; (c) straight-line navigation; (d) continuous turning. DETAILED DESCRIPTION

[0025] The present application will be further described below in conjunction with the drawings and examples.

[0026] In the AIS system, each ship device will send AIS messages at certain time intervals, which contain basic information, navigation state and ship position, etc. of the ship, forming a time series of ship trajectory data. Ship trajectory data usually shows potential temporal relationship and dynamic change, which can be modeled in the state space representation of the navigation state. In time, these data show multi-scale time dependence, while from the perspective of variables, they show complex spatial dependence between variables. For ship movement tasks, the time interval between two consecutive AIS message information is an important factor affecting the prediction result, so the present application proposes a DP-Mamba neural network structure, which introduces time interval data as an input variable of the state transition equation of Mamba, and combines a time perception module to solve the trajectory prediction problem of non-fixed timing ship data, and the network architecture is as shown in Figure 1 .

[0027] S1, first, the real ship trajectory data in the region is taken as the input data of the DP-Mamba model, and the interval information between the trajectory points is calculated according to the date information.

[0028] S2, secondly, the ship trajectory data will be normalized by the encoding layer, and processed from two dimensions of channel aggregation and channel independence respectively, and taken as the input of the DP-Mamba model.

[0029] S3, then, the spatiotemporal feature of the ship trajectory is extracted from the channel aggregation perspective, and the state transition equation of the ship trajectory movement is constructed combining the encoded trajectory data and the time interval, from which the local and global spatiotemporal features of the ship trajectory are captured.

[0030] S4, subsequently, the attribute feature of the ship trajectory is extracted from the channel independent perspective, and the encoded trajectory data is mapped to high-dimensional features from the attribute dimension, and the ship attribute feature is extracted from the attribute data trend.

[0031] S5, finally, a feature fusion module is constructed to effectively fuse the spatiotemporal feature and the attribute feature of the ship trajectory, so as to improve the overall effect of trajectory data prediction.

[0032] In order to reduce the deviation that may be caused by data fluctuation in the model training process, the Z-score standardization method is used to process the original AIS data, and the calculation formula is as follows:

[0033] ,

[0034] Normalized() denotes the standard deviation-based normalization operation, denotes the input data, mean() denotes the mean function, is the standard deviation. Assume that the ship trajectory data is , where , two types of tokens are normalized in the channel fusion and channel-independent feature space, respectively, and mapped to high-dimensional vector representation, the calculation formula is as follows:

[0035] ,

[0036] ,

[0037] wherein, and denote the embedding representation of channel fusion and channel-independent input respectively, denotes the encoding operation.

[0038] Although the Mamba model has shown great potential in capturing the spatial patterns of multivariate time series prediction, it still has limitations in relating spatial dependent features of different time steps. The goal is to capture the multi-scale spatio-temporal dependent relationship in the ship trajectory data with irregular time intervals, thereby improving the model's ability to extract local and global trajectory features to better model short-term dependencies, as shown in Figure 1 In channel fusion, time information is integrated into the selective structured state space model to capture spatio-temporal features from windows of different scales. Real-time time interval data is mapped to time weights through a time-aware module to reduce the impact of factors such as excessively long time intervals. Assume that the time interval data is , the calculation formula of the time weight is as follows:

[0039] ,

[0040] wherein, is the minimum value, is the maximum value, denotes the threshold limiting function, is a learnable decay parameter. TMamba reconstructs the S6 model by introducing these time weights between adjacent state spaces, which is implemented as follows:

[0041] ,

[0042] ,

[0043] wherein, denotes the state at time , representing the state at time , , and are the information projected from the input data . Different sizes of state space are designed to capture global and local information from different scale windows, as shown in Figure 2 :

[0044] To extract global spatio-temporal features, all trajectory points are defined as the basic states to construct the selective structured state space, and the corresponding state transition equation is represented as follows:

[0045] ,

[0046] ,

[0047] To extract local spatio-temporal features, the state space matrix is divided into sub-matrix blocks with a size of , where the block size is . Assuming = 10 and = 5, the state space M5 can be represented as formula III-C:

[0048] ,

[0049] The ship trajectory features extracted by the TMamba model under different state space matrices can be represented as:

[0050] ,

[0051] represent the trajectory features extracted from different scale windows. These spatio-temporal features are fused through an information aggregation module to enhance the extraction effect of ship trajectory features, and the formula is as follows:

[0052] ,

[0053] represent the spatio-temporal trajectory features, denotes an information aggregation operation. Traditional neural network methods mainly focus on extracting local or global features from ship trajectory data. TMamba can capture both local and global trajectory information by constructing state space transition matrices of different scale window sizes. By introducing time weight generated by the time interval information and time perception module into the state space transition matrix, this model can effectively handle irregular measurement time series (IMST) data while more accurately capturing spatio-temporal features. Spatio-temporal features of different state spaces are fused through an information aggregation module, significantly improving the extraction of ship trajectory features.

[0054] Each attribute type of the ship trajectory usually exhibits inherent time dependence and dynamic changes. In order to reduce the mutual interference between different variables, the attributes of the trajectory points are processed as high-dimensional representations respectively, so as to extract attribute features independently in channel-independent feature spaces.

[0055] The specific implementation is as follows:

[0056] ,

[0057] denotes high-dimensional information, denotes a normalization operation for high-dimensional data. Each attribute representation is divided into multiple time blocks to facilitate the extraction of relationship features between attribute dimensions.

[0058] ,

[0059] denotes the attribute features extracted after segmentation, is the number of blocks, denotes a segmentation operation.

[0060] The VMamba module is used to capture attribute features, and the specific implementation is as follows:

[0061] ,

[0062] wherein, denotes the extracted attribute features, is the number of variables. The VMamba model aims to capture the state space transition process of the trajectory variables, especially focusing on the overall trend of attribute dimension changes. This model can generate time weight based on input variable information for state space transition, thereby reducing the impact of attribute data changes at different time intervals. In addition, a channel-independent strategy is adopted to extract each attribute feature of the ship trajectory separately, avoiding mutual interference between different variables and improving the performance of attribute feature extraction.

[0063] In view of the relative independence of the dual-view feature space, fusing these features is crucial to realize the complementary fusion of trajectory-dependent features and attribute-dependent features. Therefore, the cross-attention (CA) mechanism is adopted as the feature fusion module, and its calculation formula is as follows:

[0064] ,

[0065] wherein, denotes a query vector, denotes a key vector, denotes a value vector, denotes a feature dimension.

[0066] Multi-head cross-attention (MCA) can be expressed as:

[0067] ,

[0068] ,

[0069] wherein, denotes the fused attribute feature, denotes a concatenation operation.

[0070] In order to enhance the fusion effect of dual-view features, the trajectory features extracted by the TMamba module are segmented according to their corresponding attributes.

[0071] ,

[0072] wherein, denotes the corresponding attribute feature, denotes a segmentation operation. The trajectory feature is taken as the main feature to calculate the query vector (query), and multiple attribute features are used to calculate the key vector (key) and the value vector (value) respectively.

[0073] The process of feature fusion is as follows:

[0074] ,

[0075] ,

[0076] ,

[0077] ,

[0078] wherein, denotes the final fused trajectory feature, , and Respectively, the value of the query (query), key (key) and value (value) vector. The feature fusion module adopts a multi-head cross attention mechanism to integrate the attribute features corresponding to each dimension of the trajectory feature. The fused trajectory feature contains multi-scale spatio-temporal features and attribute change features, thereby improving the accuracy of ship trajectory prediction.

[0079] Since the predicted trajectory is not completely consistent with the true value, Soft-DTW is used as a loss function to quantify the similarity between the predicted trajectory and the true trajectory.

[0080] The loss function is defined as follows:

[0081] ,

[0082] ,

[0083] ,

[0084] ,

[0085] Wherein, Indicates the batch size (batch size), Indicates the sequence length, Indicates the number of feature dimensions, Is the batch index, Is the time index, Is the feature dimension index, Indicates the predicted value, Indicates the true value, Indicates the predicted direction, Indicates the true direction, Indicates the point-by-point error, Indicates the trend error, Indicates the direction error, Indicates the comprehensive loss error.

[0086] The present application uses AIS data of a certain region to construct a ship trajectory data set. According to the regional division, the ship trajectories of Jiaozhou Bay and Laizhou Bay are selected for experimental test, and the distribution of part of the ship trajectories is as shown in Figure 3 The data set contains 5,000 ship trajectory sequences, and each sequence contains 40 real trajectory points with different time interval.

[0087] To evaluate the effectiveness of the DP-Mamba method, the present application selected three published AIS datasets for comparative experiments, respectively from the European Marine Observation (EMO), the Danish Maritime Authority (DMA), and the U.S. Coast Guard (USCG). The EMO and DMA datasets are regular and complete trajectory observations reconstructed by spatiotemporal calibration, while the USCG dataset is a real ship trajectory generated from original AIS data without spatiotemporal calibration. These sea areas are different in actual scenarios and functional purposes, resulting in significant differences in the number of ships and traffic flow. For all areas, each dataset is divided into three subsets: 60% for training, 20% for testing, and 20% for validation. The detailed information of these datasets is shown in Table 1.

[0088] Table 1 Detailed information of datasets

[0089]

[0090] The present application selected a variety of advanced and representative time series prediction deep learning models, including Bi-LSTM, GRU, PatchTST

[29] , TimeNet, Informer

[31] , iTransformer, and S-Mamba, as benchmark models for ship trajectory prediction. All models are configured with approximately the same hyperparameters to ensure the consistency of the comparative experiments. The model training uses the Adam optimizer with an initial learning rate of 0.0001, which is halved every 15 training cycles to facilitate model convergence. To prevent overfitting, a dropout rate of 0.01 is used for each layer during the 50 training iterations.

[0091] The specific configurations of each model are shown in Table 2.

[0092] Table 2 Model hyperparameter settings

[0093]

[0094] The evaluation indicators of the model are mean square error (MSE), dynamic time warping (DTW), and final displacement error (FDE). Assuming that the real ship trajectory is and the predicted trajectory is where represents the real trajectory information (latitude, longitude, speed, and heading), represents the predicted trajectory information, and its calculation formula is as follows:

[0095] ​

[0096] ,

[0097] ,

[0098] MSE is used to evaluate the average deviation between the predicted trajectory information and the sample true value; DTW is used to measure the similarity between the predicted trajectory and the actual sample; FDE is used to calculate the final displacement error between the predicted trajectory and the true trajectory.

[0099] To comprehensively evaluate the performance of the proposed DP-Mamba method, comparative experiments are conducted on four ship trajectory datasets, and the corresponding results are shown in Table 3.

[0100] Table 3 Comparative experiments

[0101]

[0102] As can be seen from Table 3, all deep learning methods have achieved relatively satisfactory prediction results on the EMO and DMA datasets. This is mainly due to the relatively uniform time interval between the trajectory points in these two datasets, which enables the model to effectively process and capture the trajectory features. The trajectories of the DMA dataset are more complex than those of the EMO dataset, resulting in a slight decline in the performance of all models on this dataset. Compared with these methods, the proposed model has achieved improvements in performance and prediction accuracy. In contrast, in the USCG dataset and the self-built dataset of the present application, the time interval between the trajectory points is variable, and the experimental results show significant differences. Due to the limitations of the traditional recurrent neural network structure, GRU and Bi-LSTM are difficult to capture features under non-uniform time intervals, resulting in the worst trajectory prediction results. Informer and PatchTST extract trajectory features through hierarchical and fragment-based mechanisms, which can effectively capture local information and to some extent alleviate the impact of irregular time intervals on trajectory prediction. In contrast, iTransformer and S-Mamba map trajectory data to a high-dimensional feature space and generate time information by fusing data features, thereby reducing the impact of time interval changes and achieving relatively good experimental results.

[0103] The DP-Mamba model proposed by the present application introduces real time information into the state space transition process, which can analyze real trajectory sequences with variable time intervals, thereby effectively capturing spatio-temporal features and achieving the best prediction performance on all datasets. To further illustrate the advantages of the DP-Mamba model compared to other models, Figure 4 The visualization results of the predicted trajectories of each model are shown.

[0104] The visualization results show that the performance of ship trajectory prediction is consistent with the results of the comparative experiment, and improves with the increase of the precision of different models. Whether it is a traditional method or an advanced model, all models can accurately predict the ship trajectory on the EMO and DMA datasets with regular and complete observation trajectory sequences. However, as shown in Figure 5 , when applied to datasets with irregular ship trajectory data, the prediction performance of different models shows significant differences. The DP-Mamba model achieves the best performance, and its predicted trajectory is basically consistent with the actual trajectory. This further proves that the proposed method can effectively overcome the irregularity problem in modeling the internal dependence of time series, thereby improving the trajectory prediction accuracy based on real ship trajectory data.

[0105] In terms of complexity indicators, the computational complexity of the model is usually measured by FLOPs (floating point operations). Figure 6 The comparative results of the average FLOPs of different models on the four AIS datasets are shown. Compared with traditional RNN and Transformer models, the FLOPs of the DP-Mamba model is reduced by at least 42.97%. Compared with the S-Mamba model, the prediction accuracy of the proposed model is significantly improved at the cost of increasing the FLOPs by 1.08 times. Therefore, the FLOPs results show that the DP-Mamba model has superior computational efficiency.

[0106] To evaluate the effectiveness of each component, a series of ablation experiments based on the DP-Mamba model were conducted, and the results are shown in Table 4. The experimental results show that the TMamba trajectory feature extraction module and the VMamba attribute feature extraction module both significantly improve the accuracy of ship trajectory prediction. Specifically, compared with the baseline Mamba2 model, the prediction accuracy of the two modules is improved by 3.23% and 1.23%, respectively. When the two feature extraction modules are used together, the accuracy of the model reaches 91.4%. To further improve the trajectory prediction effect, this paper proposes a feature fusion module based on multi-head cross attention (MCA). By fusing the above features, the accuracy of the model is further improved to 94.2%, and the overall performance is improved by nearly 11.2% compared with the baseline model.

[0107] Table 4 Ablation experiments of DP-Mamba model

[0108]

[0109] Different hyperparameter settings were used to evaluate the hyperparameter sensitivity of the DP-Mamba model to the following factors: learning rate (Lr), variable label hidden dimension (Hd), and the number of Mamba modules (Bl). The hyperparameter sensitivity experiment results are shown in Figure 7The hidden dimension is chosen carefully in DP-Mamba as the most common influencing factor, since the selection of hidden dimension has a significant impact on model performance as the complexity of trajectory features increases. Since the proposed method is based on a linear complexity Mamba model, an excessively large hidden dimension can lead to overfitting, thereby affecting its performance. The number of modules and learning rate also have some impact on model accuracy, and it is not necessarily better in DP-Mamba. According to the experimental results, the learning rate of the DP-Mamba model is set to 0.0001, the number of modules is set to 3, and the hidden layer size is set to 256.

[0110] To evaluate the generalization ability of the DP-Mamba model, the experiment uses one-fourth of the data set for training, and the remaining three data sets for testing. The results show that the DP-Mamba model maintains high prediction accuracy in different sea scenarios, demonstrating strong generalization ability. This excellent performance highlights the robustness and adaptability of the model, verifying its effectiveness in the ship trajectory prediction task.

[0111] The present application also selects representative ship trajectory data to evaluate the performance of the DP-Mamba model under various motion states, including straight sailing, zigzag sailing, turning, and continuous turning, as shown in Figure 8 The experimental results show that the DP-Mamba model performs well in all four motion conditions, with a significant prediction accuracy in straight sailing. Even in the case of rapid ship turning, the model can still maintain a certain prediction accuracy, effectively capturing the motion characteristics of the ship. The above results show that the DP-Mamba model has strong generalization ability and application potential, providing an effective solution for ship trajectory prediction.

Claims

1. A method for predicting ship trajectories based on irregular multivariate real trajectory time series, characterized in that, Includes the following steps: S1. Use real ship trajectory data within the region as input data for the model, and calculate the interval information between trajectory points based on date information; S2. Ship trajectory data is normalized through an encoding layer, and processed separately from two dimensions: channel aggregation and channel independence, and then used as input to the model; S3. Extract the spatiotemporal features of ship trajectories from the perspective of channel aggregation, and construct the state transition equation of ship trajectory motion by combining the encoded trajectory data and time intervals, thereby capturing the local and global spatiotemporal features of ship trajectories; In channel aggregation, temporal information is incorporated into a selectively structured state-space model to capture spatiotemporal features from windows of different scales; Real-time time interval data is mapped to time weights through a time-aware module to reduce the impact of excessively long time intervals; the time interval data is The formula for calculating time weight is as follows: , in, It is the minimum value. It is the maximum value. This represents the threshold constraint function. It is a learnable decay parameter; The selectively structured state-space model was reconstructed by introducing time weights between adjacent state spaces, as follows: ， ， in, Indicates time state, Indicates time state, , and It is composed of input data Information obtained from projection; S4. Extract the attribute features of ship trajectories from the channel-independent perspective, map the encoded trajectory data to high-dimensional features from the attribute dimension, and extract ship attribute features from the changing trends of the attribute data; S5. Construct a feature fusion module to effectively fuse the spatiotemporal features and attribute features of ship trajectories to achieve ship trajectory prediction.

2. The ship trajectory prediction method based on irregular multivariate real trajectory time series according to claim 1, characterized in that, The model in step S1 is the dual-view Mamba model.

3. The ship trajectory prediction method based on irregular multivariate real trajectory time series according to claim 1, characterized in that, In step S2, the Z-score normalization method is used to process the original data, and the calculation formula is as follows: ； Normalized() represents a normalization operation based on the standard deviation. This represents the input data, and mean() represents the mean function. The standard deviation is given; the ship trajectory data is P = {P1, P2, ..., P}. n }, where P∈ℝⁿ×ᴺ, then the two types of labels are normalized in the feature spaces of channel fusion and channel independence, respectively, and mapped to high-dimensional vector representations, as calculated by the following formula: ， ， in, and These represent the embedding representations of channel fusion and channel-independent inputs, respectively. This indicates an encoding operation.

4. The ship trajectory prediction method based on irregular multivariate real trajectory time series according to claim 1, characterized in that, To extract global spatiotemporal features, all trajectory points are defined as the basic states for constructing a selectively structured state space, and the corresponding state transition equations are as follows: ， ； To extract local spatiotemporal features, the state space matrix is... Divided into sizes The submatrix blocks, where the block size is ; Using the dual-view Mamba model in different state space matrices The extracted ship trajectory features can be represented as: ， in, This represents trajectory features extracted from windows of different scales; These spatiotemporal features are fused using an information aggregation model to enhance the extraction of ship trajectory features. The formula is as follows: , in, Represents spatiotemporal trajectory characteristics, This represents an information aggregation operation.

5. The ship trajectory prediction method based on irregular multivariate real trajectory time series according to claim 3, characterized in that, In step S4, each attribute type of the ship trajectory exhibits inherent time dependence and dynamic changes. To reduce mutual interference between different variables, the attributes of the trajectory points are processed into high-dimensional representations, thereby independently extracting attribute features in channel-independent feature spaces. The specific implementation is as follows: ， in, Represents high-dimensional information. This represents a normalization operation for high-dimensional data. Each attribute representation is divided into multiple time blocks to facilitate the extraction of relational features between attribute dimensions: ， This represents the attribute features extracted after segmentation. It is the number of blocks. This indicates a segmented operation; The dual-view Mamba model is used to capture attribute features, and its specific implementation is as follows: ， in, This represents the extracted attribute features. It represents the number of variables.

6. The ship trajectory prediction method based on irregular multivariate real trajectory time series according to claim 1, characterized in that, In step S5, the cross-attention (CA) mechanism is used as the feature fusion module, and its calculation is as follows: ， in, Represents the query vector. Represents the key vector. Represents a value vector. Indicates the feature dimension; Multi-head cross-attention (MCA) can be represented as: ， ， This represents the attribute characteristics after fusion. This indicates a splicing operation.

7. The ship trajectory prediction method based on irregular multivariate real trajectory time series according to claim 6, characterized in that, To enhance the fusion effect of dual-view features, the trajectory features extracted by the dual-view Mamba model are segmented according to their corresponding attributes: , in, Indicates the corresponding attribute characteristics. Indicates a splitting operation; The query vector is calculated using trajectory features as the primary feature, while multiple attribute features are used to calculate the key vector and value vector, respectively. The feature fusion process is as follows: ， ， ， ， in, This represents the trajectory features after final fusion. , and These represent the values ​​for the query, key, and value vector, respectively.

8. The ship trajectory prediction method based on irregular multivariate real trajectory time series according to claim 7, characterized in that, Soft-DTW is used as the loss function to quantify the similarity between the predicted trajectory and the true trajectory.

9. The ship trajectory prediction method based on irregular multivariate real trajectory time series according to claim 8, characterized in that, The loss function is defined as follows: ， ， ， ， in, Indicates batch size. Indicates the sequence length. Indicates the number of feature dimensions. For batch indexing, For time indexing, Indexed by feature dimensions, Indicates the predicted value. Represents the actual value. Indicates the predicted direction. Indicates the true direction. Indicates point-by-point error. Indicates trend error. Indicates directional error. This represents the overall loss error.

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