Air target trajectory prediction method and system based on space-time diagram convolutional network
By using a spatiotemporal graph convolutional network-based approach, we have solved the problems of spatiotemporal interaction modeling difficulties, insufficient nonlinear motion capture, and poor environmental adaptability in traditional methods for aerial target trajectory prediction. This approach achieves efficient and accurate trajectory prediction and is suitable for large-scale deployment.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- THE 724TH RESEARCH INSTITUTE OF CHINA STATE SHIPBUILDING CORP LTD
- Filing Date
- 2025-12-18
- Publication Date
- 2026-04-17
AI Technical Summary
Traditional methods are difficult to effectively model the complex spatiotemporal interaction relationships between multiple targets, cannot capture the nonlinear motion patterns of aerial targets, have poor environmental adaptability, and are difficult to meet the real-time requirements of aerial target trajectory prediction.
We employ a spatiotemporal graph convolutional network approach, which extracts temporal features through diffuse causal convolution to construct a temporally enhanced social force graph. We then use graph convolution to extract spatial features and perform trajectory prediction through temporal pooling, thus achieving end-to-end mapping.
It improves the accuracy and computational efficiency of aerial target trajectory prediction, is suitable for large-scale deployment, can process the spatiotemporal interaction relationships of multiple targets in parallel, and is adaptable to diverse scenarios.
Smart Images
Figure CN121880773A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of target trajectory prediction technology, and in particular to a method and system for predicting the trajectory of aerial targets based on spatiotemporal graph convolutional networks. Background Technology
[0002] In recent years, the widespread application of aerial resources such as drones and civil aviation has played a crucial role in the development of the aviation field, but it has also brought enormous challenges to aerial resources and traffic management. Especially when the number of flying targets surges, traditional prediction methods, such as Kalman filtering, struggle to cope with challenges like multi-target interaction and nonlinear motion patterns due to the complex flight trajectory characteristics of various targets. There is an urgent need to use new technologies such as spatiotemporal graph convolutional networks to achieve high-precision modeling and prediction of target trajectories in dynamic airspace, in order to meet the real-time and reliability requirements of scenarios such as urban airspace management and security monitoring.
[0003] The paper "A Trajectory Prediction Method Based on Fusion of Graph Interaction and Scene Awareness" proposes a real-time end-to-end trajectory prediction framework based on bird's-eye view, consisting of two modules: a graph interaction network and a pyramid perception network. Both modules simultaneously learn interaction and scene information. The graph interaction network encodes the interaction patterns between traffic participants through a spatiotemporal graph convolutional network, while the pyramid perception network models the surrounding information to obtain scene features. Then, the interaction features and scene features are fused at a single scale for classification and trajectory prediction. The paper "A Scene-Constrained Spatiotemporal Graph Convolutional Network for Pedestrian Trajectory Prediction" proposes a scene-constrained spatiotemporal graph convolutional neural network. This network embeds scene information into a mask matrix through a scene-based fine-tuning module, reducing prediction error by minimizing the negative log-likelihood of the true trajectory under kernel density estimation. In addition, invention patent CN 113888638 A discloses a graph neural network-based pedestrian trajectory prediction method based on attention mechanism. It uses pedestrian trajectory information to extract trajectory motion features, constructs the original node graph of pedestrian trajectory, generates the final node graph of pedestrian trajectory, extracts the spatiotemporal features of the final node graph of pedestrian trajectory through spatiotemporal graph convolutional neural network, constructs the original spatiotemporal feature graph of pedestrian trajectory based on the spatiotemporal features, and outputs the predicted pedestrian trajectory after filtering using graph channel attention mechanism.
[0004] The following problems exist in the trajectory prediction of aerial targets:
[0005] (1) Difficulty in modeling complex spatiotemporal interactions: Traditional methods such as Kalman filtering and extended Kalman filtering, which are based on physical models, are difficult to effectively model the complex spatiotemporal interactions between multiple targets. When multiple aerial targets move in a limited airspace, there are significant mutual influences between them. This collective intelligent behavior cannot be accurately described by a simple linear model.
[0006] (2) Insufficient capture of nonlinear motion patterns: The motion of aerial targets is affected by a variety of complex factors, including atmospheric turbulence, wind shear, airspace control rules, and flight mission requirements, resulting in strong nonlinear characteristics in their trajectories. Traditional sequence models such as LSTM have limited performance in capturing such high-order nonlinear dynamics.
[0007] (3) Poor environmental adaptability: Existing learning models lack generalization ability in diverse scenarios such as different airspace structures, different meteorological conditions, and different target types. Models trained in specific environments often cannot adapt to dynamic and changing real-world application scenarios.
[0008] (4) Real-time requirements are difficult to meet: With the rapid increase in the number of aerial targets, emerging application scenarios such as UAV swarm monitoring, air traffic management, and military early warning systems have put forward higher requirements for the real-time performance of trajectory prediction, which traditional complex models cannot handle efficiently. Summary of the Invention
[0009] The purpose of this invention is to provide a method and system for predicting the trajectory of aerial targets based on spatiotemporal graph convolutional networks, which has high accuracy, low computational complexity, strong parallel processing capability, and is suitable for large-scale deployment.
[0010] The technical solution to achieve the purpose of this invention is: a method for predicting the trajectory of aerial targets based on spatiotemporal graph convolutional networks, comprising the following steps:
[0011] Step 1: Collect historical trajectory data of the target and perform data preprocessing;
[0012] Step 2: Construct a spatiotemporal graph by using the spatial location of each aerial target at a specific time as a node in the spatiotemporal graph network;
[0013] Step 3: Expand the original trajectory data according to the target dimension to construct a time series, and extract the time dimension features through diffusing causal convolution;
[0014] Step 4: Construct a temporally enhanced social force graph, using the features output by temporal convolution as new features for graph vertices, and employing a symmetric normalization method to process the graph structure. Based on the temporal features, graph convolution extracts spatial dimension features.
[0015] Step 5: Capture key motion state change points through time-dimensional pooling to complete spatiotemporal feature fusion. Transform the complex spatiotemporal feature extraction results into specific trajectory prediction parameters through linear transformation and bias, complete the fully connected layer prediction, and analyze the trajectory distribution parameters.
[0016] Furthermore, the historical trajectory data of the target collected in step 1 is preprocessed as follows:
[0017] Step 1.1: Collect historical trajectory information data of flying targets in a certain airspace, including three-dimensional position information and the corresponding data collection time points. The input data is a continuous time series of aerial target trajectory data taken at fixed time intervals; the historical trajectory sequence is represented as:
[0018]
[0019] Each trajectory point It contains complete location information of the target in three-dimensional space, among which, The target longitude coordinates are normalized values. These are latitude coordinates, and the values have been normalized. These are height coordinates, and the values have been normalized. For historical time steps;
[0020] Step 1.2: To eliminate the impact of differences in coordinate dimensions on model training, the historical trajectory data of the target is normalized. The calculation method is as follows:
[0021]
[0022] Among them, parameters , , , , , Calculated from the training dataset.
[0023] Furthermore, step 2 involves using the spatial location of each aerial target at a specific moment as a node in the spatiotemporal graph network to construct the spatiotemporal graph, as detailed below:
[0024] The spatial location of each aerial target at a specific moment is taken as a node in the spatiotemporal graph network, and each node... In time The vertices are:
[0025]
[0026] The entire airspace scene in time The set of vertices is:
[0027]
[0028] in, This indicates the total number of targets in the current airspace, which changes dynamically over time.
[0029] Furthermore, step 3 involves expanding the original trajectory data according to the target dimension to construct a time series, and extracting time dimension features through diffusing causal convolution, as detailed below:
[0030] Step 3.1: Reorganize the input data by expanding the original trajectory data according to the target dimension to construct a time series:
[0031]
[0032] The time series for each target is as follows:
[0033]
[0034] Step 3.2, for the first The layer employs diffusion-causal convolution, a technique used in time-dimensional processing, to obtain the th... Layer time dimension features:
[0035]
[0036] in For the first Layer Each convolutional kernel weight; , indicating the first Layer expansion factor; The kernel size;
[0037] Step 3.2, after After the temporal convolution, the output temporal enhancement features are as follows:
[0038]
[0039] in Features are time-dimensional.
[0040] Furthermore, in step 4, the construction of a temporally enhanced social force graph uses the features output by the temporal convolution as new features for the graph vertices. A symmetric normalization method is used to process the graph structure, and spatial dimension features are extracted based on the temporal features of the graph convolution, as detailed below:
[0041] Step 4.1: Extract the features from the temporal convolution. As a new feature of the graph vertices The goal In time Based on the temporal enhancement features, a temporally enhanced social force graph is constructed. The interaction strength between targets is inversely proportional to their relative distance, and the adjacency matrix is calculated.
[0042]
[0043] in, Indicates the Euclidean distance between targets; This represents the maximum interaction distance threshold, which is set according to specific airspace rules and security standards. This is a numerical stability constant to prevent division by zero errors when the distance is zero.
[0044] Step 4.2: Process the graph structure using the symmetric normalization method;
[0045] Step 4.3: Using the self-loop enhancement mechanism, add a self-connection matrix to the original adjacency matrix. The calculation formula is as follows:
[0046]
[0047] in, for The identity matrix;
[0048] Step 4.4, obtain Construct the angle matrix using the degree matrix calculation:
[0049]
[0050] diagonal elements Represents a node The degree is the sum of the weights of all edges connected to a node, which represents the node's importance and influence range in the graph.
[0051] Step 4.5, obtain Normalization is performed by scaling the adjacency matrix with the inverse square root of the degree matrix to balance the weights of nodes of different degrees during feature propagation. The calculation formula is as follows:
[0052]
[0053] Step 4.6, for the first Layer application graph convolution operation:
[0054]
[0055] in This indicates that the input to the graph convolution is the feature output in the time dimension; Represents the graph convolution weight matrix; Represents the graph convolution bias vector;
[0056] Step 4.7, after Layered graph convolution is used to obtain the temporal motion pattern of each target based on its historical trajectory, and spatial features of the dynamic spatial interaction influence of surrounding targets are fused:
[0057]
[0058] in, It is a spatial dimension feature.
[0059] Furthermore, step 5 involves capturing key motion state change points through time-dimensional pooling to achieve spatiotemporal feature fusion. Through linear transformation and bias, the complex spatiotemporal feature extraction results are transformed into specific trajectory prediction parameters, completing the fully connected layer prediction and analyzing the trajectory distribution parameters, as detailed below:
[0060] Step 5.1: The spatiotemporal features are fused using time-dimensional pooling to capture key motion state change points from the target's historical temporal features. The resulting spatiotemporal fusion is as follows:
[0061]
[0062] Maxpool is a downsampling operation used in deep learning;
[0063] Step 5.2: Take the maximum value of a local region of the input data as the output to obtain the fused feature matrix of all targets:
[0064]
[0065] Step 5.3: By applying a linear transformation and bias, the complex spatiotemporal feature extraction results are transformed into specific trajectory prediction parameters, achieving an end-to-end mapping from the feature space to the output space.
[0066]
[0067] in This represents the output layer weight matrix; This represents the output layer bias vector; These are the original output parameters;
[0068] Step 5.4, The output is rearranged to include the trajectory distribution parameters for each target. The resulting probabilistic output provides the most likely trajectory of the target and gives the prediction confidence level. The trajectory prediction parameters are as follows:
[0069]
[0070] in The mean vector represents the expected location of the target in three-dimensional space. This is the standard deviation vector, representing the degree of uncertainty in quantifying the predicted location; The correlation coefficient vector represents the coupling relationship between different motion directions.
[0071] An aerial target trajectory prediction system based on a spatiotemporal graph convolutional network is disclosed. This system implements the aforementioned aerial target trajectory prediction method based on a spatiotemporal graph convolutional network. The system includes an acquisition module, a spatiotemporal graph construction module, a time series construction module, a spatial dimension feature extraction module, and a prediction module.
[0072] The data acquisition module collects historical trajectory data of the target and performs data preprocessing.
[0073] The spatiotemporal graph construction module uses the spatial location of each aerial target at a specific moment as a node in the spatiotemporal graph network to construct the spatiotemporal graph.
[0074] The time series construction module expands the original trajectory data according to the target dimension to construct a time series, and extracts time dimension features through diffusing causal convolution.
[0075] The spatial dimension feature extraction module constructs a temporally enhanced social force graph, uses the features output by temporal convolution as new features for graph vertices, processes the graph structure using a symmetric normalization method, and extracts spatial dimension features based on graph convolution with temporal features.
[0076] The prediction module captures key motion state change points through time-dimensional pooling to achieve spatiotemporal feature fusion. Through linear transformation and bias, it transforms the complex spatiotemporal feature extraction results into specific trajectory prediction parameters, completes the prediction of the fully connected layer, and analyzes the trajectory distribution parameters.
[0077] An electronic device includes a memory and a processor, the memory and the processor being communicatively connected to each other, the memory storing computer instructions, and the processor executing the computer instructions to perform the aerial target trajectory prediction method based on spatiotemporal graph convolutional networks.
[0078] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the aerial target trajectory prediction method based on spatiotemporal graph convolutional networks.
[0079] A computer program product includes computer instructions for causing a computer to execute the aerial target trajectory prediction method based on a spatiotemporal graph convolutional network.
[0080] Compared with the prior art, the present invention has the following significant advantages: (1) Temporal priority serial architecture: The processing method of "temporal feature extraction → spatial interaction modeling" is adopted. First, the motion law of each target is independently learned through diffusion temporal convolution, and then the spatial interaction between targets is modeled by graph convolution, which avoids the coupling and confusion of spatiotemporal features; (2) Diffusion temporal convolution network: Long temporal dependencies are captured by multi-scale diffusing convolution. The motion features of each target are fully enhanced before entering the spatial interaction module, which improves the accuracy of spatial relationship modeling; (3) Temporally enhanced graph structure: The vertex features of graph convolution are no longer the original coordinates, but the depth features enhanced by temporal convolution, which makes spatial interaction modeling based on a richer temporal context; (4) Optimized computational efficiency: The serial architecture reduces the computational complexity of processing spatiotemporal dimensions at the same time. Temporal convolution can process all targets in parallel, and graph convolution can process all time steps in parallel, which is suitable for large-scale deployment. Attached Figure Description
[0081] Figure 1 This is a flowchart illustrating an aerial target trajectory prediction method based on a spatiotemporal graph convolutional network according to the present invention. Detailed Implementation
[0082] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.
[0083] like Figure 1 As shown, the present invention provides a method for predicting the trajectory of aerial targets based on spatiotemporal graph convolutional networks, comprising the following steps:
[0084] Step 1: Collect historical trajectory data of the target and perform data preprocessing, as follows:
[0085] Step 1.1: Collect historical trajectory information data of flying targets in a certain airspace, including three-dimensional position information and the corresponding data collection time points. The input data is a continuous time series of aerial target trajectory data taken at fixed time intervals; the historical trajectory sequence is represented as:
[0086]
[0087] Each trajectory point It contains complete location information of the target in three-dimensional space, among which, The target longitude coordinates are normalized values. These are latitude coordinates, and the values have been normalized. These are height coordinates, and the values have been normalized. For historical time steps;
[0088] Step 1.2: To eliminate the impact of differences in coordinate dimensions on model training and improve numerical stability, the historical trajectory data of the target is normalized. The calculation method is as follows:
[0089]
[0090] Among them, parameters , , , , , Calculated from the training dataset.
[0091] Step 2: Using the spatial location of each aerial target at a specific time as a node in the spatiotemporal graph network, construct the spatiotemporal graph as follows:
[0092] The spatial location of each aerial target at a specific moment is taken as a node in the spatiotemporal graph network, and each node... In time The vertices are:
[0093]
[0094] The entire airspace scene in time The set of vertices is:
[0095]
[0096] in, This represents the total number of targets in the current airspace, and this number changes dynamically over time.
[0097] Step 3: Expand the original trajectory data according to the target dimension to construct a time series, and extract the time dimension features through diffusing causal convolution, as detailed below:
[0098] Step 3.1: Reorganize the input data by expanding the original trajectory data according to the target dimension to construct a time series:
[0099]
[0100] The time series for each target is as follows:
[0101]
[0102] Step 3.2, for the first The layer employs diffusion-causal convolution, a technique used in time-dimensional processing, to obtain the th... Layer time dimension features:
[0103]
[0104] in For the first Layer Each convolutional kernel weight; , indicating the first Layer expansion factor; The kernel size;
[0105] Step 3.2, after After the temporal convolution, the output temporal enhancement features are as follows:
[0106]
[0107] in Features are time-dimensional.
[0108] Step 4: Construct a temporally enhanced social force graph. Use the features output by the temporal convolution as new features for the graph vertices. Apply symmetric normalization to process the graph structure. Extract spatial dimension features based on the temporal features of the graph convolution, as detailed below:
[0109] Step 4.1: Extract the features from the temporal convolution. As a new feature of the graph vertices The goal In time Based on the temporal enhancement features, a temporally enhanced social force graph is constructed. The interaction strength between targets is inversely proportional to their relative distance, and the adjacency matrix is calculated.
[0110]
[0111] in, Indicates the Euclidean distance between targets; This represents the maximum interaction distance threshold, which is set according to specific airspace rules and security standards. This is a numerical stability constant to prevent division by zero errors when the distance is zero.
[0112] Step 4.2: To enhance the numerical stability of graph convolution and avoid gradient vanishing or exploding problems, a symmetric normalization method is used to process the graph structure to ensure effective training of deep graph neural networks.
[0113] Step 4.3: Using the self-loop enhancement mechanism, add a self-connection matrix to the original adjacency matrix. The calculation formula is as follows:
[0114]
[0115] in, for The identity matrix;
[0116] Step 4.4, obtain Construct the angle matrix using the degree matrix calculation:
[0117]
[0118] diagonal elements Represents a node The degree is the sum of the weights of all edges connected to the node, which represents the node's connectivity importance and influence range in the graph.
[0119] Step 4.5, obtain Normalization is performed by scaling the adjacency matrix with the inverse square root of the degree matrix. This balances the weights of nodes with different degrees during feature propagation, avoiding excessive influence of high-weight nodes on feature propagation and improving the numerical stability of the training process. The calculation formula is as follows:
[0120]
[0121] Step 4.6, for the first Layer application graph convolution operation:
[0122]
[0123] in This indicates that the input to the graph convolution is the feature output in the time dimension; Represents the graph convolution weight matrix; Represents the graph convolution bias vector;
[0124] Step 4.7, after Layered graph convolution is used to obtain the temporal motion pattern of each target based on its historical trajectory, and spatial features of the dynamic spatial interaction influence of surrounding targets are fused:
[0125]
[0126] in, It is a spatial dimension feature.
[0127] Step 5: Capture key motion state change points through time-dimensional pooling to complete spatiotemporal feature fusion. Then, through linear transformation and bias, transform the complex spatiotemporal feature extraction results into specific trajectory prediction parameters, complete the fully connected layer prediction, and analyze the trajectory distribution parameters, as detailed below:
[0128] Step 5.1: The spatiotemporal features are fused using time-dimensional pooling to capture key points of motion state change from the target's historical temporal features, reducing the feature dimensionality. The resulting spatiotemporal fusion result is as follows:
[0129]
[0130] Maxpool is a downsampling operation used in deep learning;
[0131] Step 5.2: Take the maximum value of a local region of the input data as the output to obtain the fused feature matrix of all targets:
[0132]
[0133] Step 5.3: By applying a linear transformation and bias, the complex spatiotemporal feature extraction results are transformed into specific trajectory prediction parameters, achieving an end-to-end mapping from the feature space to the output space.
[0134]
[0135] in This represents the output layer weight matrix; This represents the output layer bias vector; These are the original output parameters;
[0136] Step 5.4, The output is rearranged to represent the trajectory distribution parameters for each target. The resulting probabilistic output provides the most likely trajectory of the target and gives the confidence level of the prediction. The trajectory prediction parameters are as follows:
[0137]
[0138] in The mean vector represents the expected location of the target in three-dimensional space. This is the standard deviation vector, representing the degree of uncertainty in quantifying the predicted location; The correlation coefficient vector represents the coupling relationship between different motion directions.
[0139] This invention also provides an aerial target trajectory prediction system based on a spatiotemporal graph convolutional network. This system is used to implement the aforementioned aerial target trajectory prediction method based on a spatiotemporal graph convolutional network. The system includes an acquisition module, a spatiotemporal graph construction module, a time series construction module, a spatial dimension feature extraction module, and a prediction module.
[0140] The data acquisition module collects historical trajectory data of the target and performs data preprocessing.
[0141] The spatiotemporal graph construction module uses the spatial location of each aerial target at a specific moment as a node in the spatiotemporal graph network to construct the spatiotemporal graph.
[0142] The time series construction module expands the original trajectory data according to the target dimension to construct a time series, and extracts time dimension features through diffusing causal convolution.
[0143] The spatial dimension feature extraction module constructs a temporally enhanced social force graph, uses the features output by temporal convolution as new features for graph vertices, processes the graph structure using a symmetric normalization method, and extracts spatial dimension features based on graph convolution with temporal features.
[0144] The prediction module captures key motion state change points through time-dimensional pooling to achieve spatiotemporal feature fusion. Through linear transformation and bias, it transforms the complex spatiotemporal feature extraction results into specific trajectory prediction parameters, completes the prediction of the fully connected layer, and analyzes the trajectory distribution parameters.
[0145] The present invention also provides an electronic device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the aerial target trajectory prediction method based on spatiotemporal graph convolutional network.
[0146] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the steps in the aerial target trajectory prediction method based on spatiotemporal graph convolutional networks.
[0147] The present invention also provides a computer program product, including computer instructions for causing a computer to execute the aerial target trajectory prediction method based on spatiotemporal graph convolutional networks.
[0148] Example
[0149] like Figure 1 As shown, this embodiment provides a method for predicting the trajectory of aerial targets based on spatiotemporal graph convolutional networks, including the following steps:
[0150] Step 1: Collect historical trajectory data of the target and perform data preprocessing, as follows:
[0151] Step 1.1: Collect target trajectory data from multiple sensors, including radar, ADS-B, and optical tracking equipment, for targets flying in a certain airspace. This includes three-dimensional position information and the corresponding data acquisition time points. The input data is a continuous time series of aerial target trajectory data taken at fixed time intervals. For each target to be predicted, extract its most recent... The historical trajectory of a continuous time step constitutes a sequence Each point contains longitude, latitude, and altitude information, i.e. ;
[0152] Step 1.2: To eliminate the impact of differences in coordinate dimensions on model training and improve numerical stability, the components of each set of coordinates are normalized using the difference between the maximum and minimum values, scaling all data to the specified values. Within the interval, to eliminate dimensional differences and accelerate model convergence. Normalization parameters (maximum and minimum values) are statistically obtained from the training set and used during prediction.
[0153] Step 2: Using the spatial location of each aerial target at a specific time as a node in the spatiotemporal graph network, construct the spatiotemporal graph as follows:
[0154] For each aerial target's spatial location at a specific moment, treated as a node in the spatiotemporal graph network, each node... In time Vertex: The entire airspace scene in time The set of vertices is:
[0155]
[0156] in, This represents the total number of targets in the current airspace, which changes dynamically over time, thus constructing a spatiotemporal map.
[0157] Step 3: Expand the original trajectory data according to the target dimension to construct a time series, and extract the time dimension features through diffusing causal convolution, as detailed below:
[0158] Step 3.1: Reorganize the input data by expanding the original trajectory data according to the target dimension to construct a time series:
[0159]
[0160] The time series for each target is as follows:
[0161]
[0162] Step 3.2, for the first The layer employs diffusion-causal convolution, a technique used in time-dimensional processing, to obtain the th... Layer time dimension features:
[0163]
[0164] in For the first Layer Each convolutional kernel weight; , indicating the first Layer expansion factor; The kernel size;
[0165] Step 3.2, after After the temporal convolution, the output temporal enhancement features are as follows:
[0166]
[0167] in Features are time-dimensional.
[0168] Step 4: Construct a temporally enhanced social force graph. Use the features output by the temporal convolution as new features for the graph vertices. Apply symmetric normalization to process the graph structure. Extract spatial dimension features based on the temporal features of the graph convolution, as detailed below:
[0169] Step 4.1: Extract the features from the temporal convolution. As a new feature of the graph vertices The goal In time Based on the temporal enhancement features, a temporally enhanced social force graph is constructed. The interaction strength between targets is inversely proportional to their relative distance, and the adjacency matrix is calculated.
[0170]
[0171] in, Indicates the Euclidean distance between targets; This represents the maximum interaction distance threshold, which is set according to specific airspace rules and security standards. This is a numerical stability constant to prevent division by zero errors when the distance is zero.
[0172] Step 4.2: To enhance the numerical stability of graph convolution and avoid gradient vanishing or exploding problems, a symmetric normalization method is used to process the graph structure to ensure effective training of deep graph neural networks.
[0173] Step 4.3: Using the self-loop enhancement mechanism, add a self-connection matrix to the original adjacency matrix. The calculation formula is as follows:
[0174]
[0175] in, for The identity matrix;
[0176] Step 4.4, obtain Construct the angle matrix using the degree matrix calculation:
[0177]
[0178] diagonal elements Represents a node The degree is the sum of the weights of all edges connected to the node, which represents the node's connectivity importance and influence range in the graph.
[0179] Step 4.5, obtain Normalization is performed by scaling the adjacency matrix with the inverse square root of the degree matrix. This balances the weights of nodes with different degrees during feature propagation, avoiding excessive influence of high-weight nodes on feature propagation and improving the numerical stability of the training process. The calculation formula is as follows:
[0180]
[0181] Step 4.6, for the first Layer application graph convolution operation:
[0182]
[0183] in This indicates that the input to the graph convolution is the feature output in the time dimension; Represents the graph convolution weight matrix; Represents the graph convolution bias vector;
[0184] Step 4.7, after Layered graph convolution is used to obtain the temporal motion pattern of each target based on its historical trajectory, and spatial features of the dynamic spatial interaction influence of surrounding targets are fused:
[0185]
[0186] in, It is a spatial dimension feature.
[0187] Step 5: Capture key motion state change points through time-dimensional pooling to complete spatiotemporal feature fusion. Then, through linear transformation and bias, transform the complex spatiotemporal feature extraction results into specific trajectory prediction parameters, complete the fully connected layer prediction, and analyze the trajectory distribution parameters, as detailed below:
[0188] Step 5.1: The spatiotemporal features are fused using time-dimensional pooling to capture key points of motion state change from the target's historical temporal features, reducing the feature dimensionality. The resulting spatiotemporal fusion result is as follows:
[0189]
[0190] Maxpool is a downsampling operation used in deep learning;
[0191] Step 5.2: Take the maximum value of a local region of the input data as the output to obtain the fused feature matrix of all targets:
[0192]
[0193] Step 5.3: By applying a linear transformation and bias, the complex spatiotemporal feature extraction results are transformed into specific trajectory prediction parameters, achieving an end-to-end mapping from the feature space to the output space.
[0194]
[0195] in This represents the output layer weight matrix; This represents the output layer bias vector; These are the original output parameters;
[0196] Step 5.4, The output is rearranged to represent the trajectory distribution parameters for each target. The resulting probabilistic output provides the most likely trajectory of the target and gives the confidence level of the prediction. The trajectory prediction parameters are as follows:
[0197]
[0198] in The mean vector represents the expected location of the target in three-dimensional space. This is the standard deviation vector, representing the degree of uncertainty in quantifying the predicted location; The correlation coefficient vector represents the coupling relationship between different motion directions.
[0199] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for predicting the trajectory of aerial targets based on spatiotemporal graph convolutional networks, characterized in that, Includes the following steps: Step 1: Collect historical trajectory data of the target and perform data preprocessing; Step 2: Construct a spatiotemporal graph by using the spatial location of each aerial target at a specific time as a node in the spatiotemporal graph network; Step 3: Expand the original trajectory data according to the target dimension to construct a time series, and extract the time dimension features through diffusing causal convolution; Step 4: Construct a temporally enhanced social force graph, using the features output by temporal convolution as new features for graph vertices, and employing a symmetric normalization method to process the graph structure. Based on the temporal features, graph convolution extracts spatial dimension features. Step 5: Capture key motion state change points through time-dimensional pooling to complete spatiotemporal feature fusion. Transform the complex spatiotemporal feature extraction results into specific trajectory prediction parameters through linear transformation and bias, complete the fully connected layer prediction, and analyze the trajectory distribution parameters.
2. The aerial target trajectory prediction method based on spatiotemporal graph convolutional networks according to claim 1, characterized in that, Step 1 involves collecting historical trajectory data of the target and performing data preprocessing, as detailed below: Step 1.1: Collect historical trajectory information data of flying targets in a certain airspace, including three-dimensional position information and the corresponding data collection time points. The input data is a continuous time series of aerial target trajectory data taken at fixed time intervals; the historical trajectory sequence is represented as: ； Each trajectory point It contains complete location information of the target in three-dimensional space, among which, The target longitude coordinates are normalized values. These are latitude coordinates, and the values have been normalized. These are height coordinates, and the values have been normalized. For historical time steps; Step 1.2: To eliminate the impact of differences in coordinate dimensions on model training, the historical trajectory data of the target is normalized. The calculation method is as follows: ； Among them, parameters , , , , , Calculated from the training dataset.
3. The aerial target trajectory prediction method based on spatiotemporal graph convolutional networks according to claim 2, characterized in that, Step 2 involves using the spatial location of each aerial target at a specific moment as a node in the spatiotemporal graph network to construct the spatiotemporal graph, as detailed below: The spatial location of each aerial target at a specific moment is taken as a node in the spatiotemporal graph network, and each node... In time The vertices are: ； The entire airspace scene in time The set of vertices is: ； in, This indicates the total number of targets in the current airspace, which changes dynamically over time.
4. The aerial target trajectory prediction method based on spatiotemporal graph convolutional networks according to claim 3, characterized in that, Step 3 involves expanding the original trajectory data according to the target dimension to construct a time series, and extracting time dimension features through diffusing causal convolution, as detailed below: Step 3.1: Reorganize the input data by expanding the original trajectory data according to the target dimension to construct a time series: ； The time series for each target is as follows: ； Step 3.2, for the first The layer employs diffusion-causal convolution, a technique used in time-dimensional processing, to obtain the 1st... Layer time dimension features: ； in For the first Layer Each convolutional kernel weight; , indicating the first Layer expansion factor; The kernel size; Step 3.2, after After the temporal convolution, the output temporal enhancement features are as follows: ； in Features are time-dimensional.
5. The aerial target trajectory prediction method based on spatiotemporal graph convolutional networks according to claim 4, characterized in that, Step 4 describes the construction of a temporally enhanced social force graph. The features output by the temporal convolution are used as new features for the graph vertices. A symmetric normalization method is employed to process the graph structure, and spatial dimension features are extracted based on the temporal features through graph convolution. Specifically: Step 4.1: Extract the features from the temporal convolution. As a new feature of the graph vertices The goal In time Based on the temporal enhancement features, a temporally enhanced social force graph is constructed. The interaction strength between targets is inversely proportional to their relative distance, and the adjacency matrix is calculated. ； in, Indicates the Euclidean distance between targets; This represents the maximum interaction distance threshold, which is set according to specific airspace rules and security standards. This is a numerical stability constant to prevent division by zero errors when the distance is zero. Step 4.2: Process the graph structure using the symmetric normalization method; Step 4.3: Using the self-loop enhancement mechanism, add a self-connection matrix to the original adjacency matrix. The calculation formula is as follows: ； in, for The identity matrix; Step 4.4, obtain Construct the angle matrix using the degree matrix calculation: ； diagonal elements Represents a node The degree is the sum of the weights of all edges connected to a node, which represents the node's importance and influence range in the graph. Step 4.5, obtain Normalization is performed by scaling the adjacency matrix with the inverse square root of the degree matrix to balance the weights of nodes of different degrees during feature propagation. The calculation formula is as follows: ； Step 4.6, for the first Layer application graph convolution operation: ； in This indicates that the input to the graph convolution is the feature output in the time dimension; Represents the graph convolution weight matrix; Represents the graph convolution bias vector; Step 4.7, after Layered graph convolution is used to obtain the temporal motion pattern of each target based on its historical trajectory, and spatial features of the dynamic spatial interaction influence of surrounding targets are fused: ； in, It is a spatial dimension feature.
6. The aerial target trajectory prediction method based on spatiotemporal graph convolutional networks according to claim 5, characterized in that, Step 5 describes capturing key motion state change points through time-dimensional pooling to achieve spatiotemporal feature fusion. Through linear transformation and bias, the complex spatiotemporal feature extraction results are transformed into specific trajectory prediction parameters, completing the fully connected layer prediction and analyzing the trajectory distribution parameters, as detailed below: Step 5.1: The spatiotemporal features are fused using time-dimensional pooling to capture key motion state change points from the target's historical temporal features. The resulting spatiotemporal fusion is as follows: ； Maxpool is a downsampling operation used in deep learning; Step 5.2: Take the maximum value of a local region of the input data as the output to obtain the fused feature matrix of all targets: ； Step 5.3: By applying a linear transformation and bias, the complex spatiotemporal feature extraction results are transformed into specific trajectory prediction parameters, achieving an end-to-end mapping from the feature space to the output space. ； in This represents the output layer weight matrix; This represents the output layer bias vector; These are the original output parameters; Step 5.4, The output is rearranged to include the trajectory distribution parameters for each target. The resulting probabilistic output provides the most likely trajectory of the target and gives the prediction confidence level. The trajectory prediction parameters are as follows: ； in The mean vector represents the expected location of the target in three-dimensional space. This is the standard deviation vector, representing the degree of uncertainty in quantifying the predicted location; The correlation coefficient vector represents the coupling relationship between different motion directions.
7. An aerial target trajectory prediction system based on spatiotemporal graph convolutional networks, characterized in that, This system is used to implement the aerial target trajectory prediction method based on spatiotemporal graph convolutional networks as described in any one of claims 1 to 6. The system includes an acquisition module, a spatiotemporal graph construction module, a time series construction module, a spatial dimension feature extraction module, and a prediction module. The data acquisition module collects historical trajectory data of the target and performs data preprocessing. The spatiotemporal graph construction module uses the spatial location of each aerial target at a specific moment as a node in the spatiotemporal graph network to construct the spatiotemporal graph. The time series construction module expands the original trajectory data according to the target dimension to construct a time series, and extracts time dimension features through diffusing causal convolution. The spatial dimension feature extraction module constructs a temporally enhanced social force graph, uses the features output by temporal convolution as new features for graph vertices, processes the graph structure using a symmetric normalization method, and extracts spatial dimension features based on graph convolution with temporal features. The prediction module captures key motion state change points through time-dimensional pooling to achieve spatiotemporal feature fusion. Through linear transformation and bias, it transforms the complex spatiotemporal feature extraction results into specific trajectory prediction parameters, completes the prediction of the fully connected layer, and analyzes the trajectory distribution parameters.
8. An electronic device, characterized in that, include: The system includes a memory and a processor, which are interconnected. The memory stores computer instructions, and the processor executes the computer instructions to perform the aerial target trajectory prediction method based on spatiotemporal graph convolutional networks as described in any one of claims 1 to 6.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the aerial target trajectory prediction method based on spatiotemporal graph convolutional networks as described in any one of claims 1 to 6.
10. A computer program product, characterized in that, The method includes computer instructions for causing a computer to execute the aerial target trajectory prediction method based on spatiotemporal graph convolutional networks as described in any one of claims 1 to 6.
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Graph neural network pedestrian trajectory prediction method based on attention mechanism
CN113888638A