Intention recognition method based on unmanned aerial vehicle cluster three-dimensional trajectory analysis

Abstract

The invention provides an intention recognition method based on unmanned aerial vehicle cluster three-dimensional trajectory analysis, and relates to the field of group behavior recognition of unmanned aerial vehicle clusters. Through preprocessing the three-dimensional trajectory, the consistency of the trajectory in time and space dimensions is ensured, the stability and quality of data are improved, the subsequent intention recognition process is more accurate and reliable, through the improved HDBSCAN algorithm, the direction information of the trajectory is effectively recognized, and the clustering structure is dynamically adjusted under different density levels, so that the accuracy of intention recognition is improved. And the intention identification of the unmanned aerial vehicle in different group scales and complex task scenes is more accurate. In combination with a deep learning network, the method can better capture the time dependency relationship of a three-dimensional track, improves the analysis capability of a complex behavior mode in an intention recognition process, improves the accuracy and reliability of a recognition result, and improves the recognition efficiency in complex scenes such as multi-unmanned aerial vehicle cooperative combat. More effective identification of the unmanned aerial vehicle cluster intention is realized, and the intention identification performance is greatly improved.

Description

Technical Field

[0001] The present invention relates to the field of group behavior recognition of drone clusters, and in particular to an intention recognition method based on three-dimensional trajectory analysis of drone clusters. Background Art

[0002] With the rapid development of UAV technology, especially in the military field, the tactical application of UAV swarms is increasing. UAVs can perform complex tasks collaboratively and provide higher operational flexibility. However, with the increasing complexity of the combat environment, the commander's real-time analysis and intention recognition of UAV swarm behavior is difficult to meet the requirements of timely and accurate decision-making, and it will also affect the rapid and accurate response of existing weapon systems. Therefore, there is an urgent need for an intention recognition method suitable for UAV swarm trajectory analysis.

[0003] In recent years, with the rapid expansion of drone applications, drone intention recognition methods have gradually become a research hotspot and have received widespread attention. The purpose of drone intention recognition is to infer the current or future tasks and actions of drones by analyzing their behaviors, trajectories, and other related information, thereby providing decision support for defense and control. In this process, it is crucial to accurately identify the intention of drones, which directly affects the response speed and accuracy of the defense system. Existing intent recognition methods include rule-based methods, statistical learning-based methods, and deep learning-based methods. However, the above intent recognition methods face many challenges, mainly manifested in the following aspects: (1) Rule-based methods rely on manually set parameters and rules, lack adaptive capabilities, and are difficult to cope with complex and dynamically changing environments; (2) Statistical learning-based methods, such as SVM and random forest, can learn from data, but feature engineering is complex and it is difficult to process multi-dimensional and highly complex data; (3) Most of these methods require the integration of multi-source information, such as radar data, electronic interference status, communication information, etc., to achieve more comprehensive intent recognition. However, in the process of multi-source information fusion, data processing and synchronization often bring large computational overhead, affecting real-time and system robustness; (4) With the increasing demand for drone group coordinated operations, the recognition of group intentions has become more complicated. The problem of multi-target coordination has not been fully solved. How to extract accurate group intentions from the trajectories of multi-drone interactions is a difficult problem that needs to be solved urgently. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides an intention recognition method based on three-dimensional trajectory analysis of drone clusters, which uses data preprocessing, cluster analysis, deep learning and other methods to solve the problem of quickly and efficiently identifying the intention of drone clusters in war.

[0005] An intention recognition method based on three-dimensional trajectory analysis of drone clusters includes the following steps:

[0006] S1: Obtain a three-dimensional trajectory data set of a drone cluster and preprocess the three-dimensional trajectories therein to obtain preprocessed three-dimensional trajectories; the three-dimensional trajectory data set of the drone cluster includes three-dimensional trajectories of multiple drones, and the three-dimensional trajectory of each drone includes a number of time steps and the three-dimensional spatial coordinates of the trajectory points at the time step;

[0007] S1.1: Obtain the three-dimensional trajectories of the drones in the drone cluster, obtain the three-dimensional trajectory dataset of the drone cluster, and filter the obtained three-dimensional trajectories to delete incomplete three-dimensional trajectories and abnormal three-dimensional trajectories;

[0008] The three-dimensional trajectory of UAV m is:

[0009] T m ={(t1,x1,y1,z1),(t2,x2,y2,z2),…,(t i ,x i ,y i ,z i ),...,(t n ,x n ,y n ,z n )} (1)

[0010] Among them, Tr m represents the three-dimensional trajectory of UAV m, t i represents the time step, i represents the number of the trajectory point, (x i ,y i ,z i ) indicates that the UAV is at time step t i The three-dimensional spatial coordinates of the trajectory points under, n represents the number of trajectory points;

[0011] Set the minimum threshold of the three-dimensional trajectory length to δ L , if the length of the three-dimensional trajectory L<δ L , the three-dimensional trajectory is considered incomplete and deleted; calculate the average velocity v of the three-dimensional trajectory avg , if the average speed of a three-dimensional trajectory exceeds the reasonable range V avg , then the three-dimensional trajectory is considered to be wrong or abnormal, that is, if v avg >V avg , then delete the three-dimensional trajectory;

[0012] S1.2: Use cubic spline interpolation to smooth the 3D trajectory and unify the 3D trajectory to the same time dimension;

[0013] Specifically, based on the filtered three-dimensional trajectory, a cubic spline function S(t) is constructed, where t is the time step, to interpolate the missing trajectory points; then resampling is performed according to a uniform resampling time step Δt to generate trajectory points at the same time step;

[0014] The resampled trajectory points are expressed as:

[0015]

[0016] in, Represents the resampled trajectory points, t0 and t f are the start time and end time of the three-dimensional trajectory respectively;

[0017] S1.3: Normalize all three-dimensional trajectories to have the same dimension and range;

[0018] S1.4: Map the three-dimensional trajectory to the same large map through coordinate transformation;

[0019] For each trajectory point in the three-dimensional trajectory, the three-dimensional space coordinates (x i ,y i ,z i ), and map it to the coordinate system of the large map through the following matrix transformation formula:

[0020]

[0021] in, is the transformation matrix, b is the offset vector, (x global ,y global ,z global ) is the three-dimensional spatial coordinate of the trajectory point mapped to the large map;

[0022] S2: Cluster analysis is performed on the preprocessed three-dimensional trajectories to divide them into different UAV trajectory clusters;

[0023] S2.1: extracting trajectory points with large direction changes in the three-dimensional trajectory by calculating the changes in angles in the three-dimensional trajectory;

[0024] Assume that the three-dimensional trajectory consists of n trajectory points. The three-dimensional spatial coordinates of the trajectory points in the three-dimensional trajectory are expressed as (x1, y1, z1), (x2, y2, z2), …, (x n ,y n ,z n );

[0025] First, for every two adjacent trajectory points on the three-dimensional trajectory, construct a vector pointing from one trajectory point to the adjacent trajectory point

[0026]

[0027] Among them, (x i+1 ,y i+1 ,z i+1 ) are the three-dimensional spatial coordinates of adjacent trajectory points;

[0028] For two adjacent vectors and The angle θ between them is calculated using the dot product formula of the vectors:

[0029]

[0030] in, represents the dot product of two vectors, and is the modulus of the vector, and the formula is:

[0031]

[0032] For every two adjacent trajectory points on the three-dimensional trajectory, calculate the difference in their movement directions. The specific calculation formula is as follows:

[0033] Dir=1-cosθ (8)

[0034] Wherein, Dir represents the difference in the movement direction between two adjacent trajectory points. The value range of Dir is 0 to 2. The larger the value of Dir, the greater the change in the direction of the three-dimensional trajectory. The threshold Dir1 is set according to specific needs. When Dir>Dir1, the trajectory point is recorded, thereby extracting the trajectory point with a large change in direction in the three-dimensional trajectory;

[0035] S2.2: Calculate the similarity measure between the three-dimensional trajectories using the starting trajectory point, the ending trajectory point and the extracted trajectory points with large direction changes in the three-dimensional trajectory;

[0036] The two three-dimensional trajectories are expressed as follows:

[0037]

[0038] Among them, Tr1 and Tr2 are two three-dimensional trajectories, r i and j Respectively represent the trajectory points in the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2; i and j are the numbers of the trajectory points, n1 is the total number of the starting trajectory points, the ending trajectory points and the extracted trajectory points with large trajectory direction changes in the three-dimensional trajectory Tr1; n2 is the total number of the starting trajectory points, the ending trajectory points and the extracted trajectory points with large trajectory direction changes in the three-dimensional trajectory Tr2;

[0039] First, the distances from the starting point, the ending point, and the point with large direction change on the three-dimensional trajectory Tr1 to the nearest point on the three-dimensional trajectory Tr2 are calculated respectively. Then, the mean of the distances from the starting point, the ending point, and the point with large direction change on the three-dimensional trajectory Tr1 to the nearest point on the three-dimensional trajectory Tr2 is calculated. The mean of the distances from the starting point, the ending point, and the point with large direction change on the three-dimensional trajectory Tr2 to the nearest point on the three-dimensional trajectory Tr1 is obtained in the same way. The minimum value between the two is taken as the three-dimensional trajectory shape similarity between the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2. The calculation formula for the three-dimensional trajectory shape similarity is as follows:

[0040]

[0041] TSS(Tr1,Tr2) represents the three-dimensional trajectory shape similarity between the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2; d NNP (r i ,Tr2) represents the trajectory point r on the three-dimensional trajectory Tr1 i The distance to the nearest trajectory point on the three-dimensional trajectory Tr2, d NNP (s j ,Tr1) represents the trajectory point s on the three-dimensional trajectory Tr2 j The distance to the nearest trajectory point on the three-dimensional trajectory Tr1;

[0042] Secondly, for the starting trajectory point, the ending trajectory point and the trajectory point with large direction change on the three-dimensional trajectory Tr1, calculate the mean of the difference in motion direction between them and the nearest trajectory point on the three-dimensional trajectory Tr2. Similarly, calculate the mean of the difference in motion direction between the starting trajectory point, the ending trajectory point and the trajectory point with large direction change on the three-dimensional trajectory Tr2 and the nearest trajectory point on the three-dimensional trajectory Tr1. Take the minimum value of the two as the three-dimensional trajectory direction similarity. The three-dimensional trajectory direction similarity calculation formula is as follows:

[0043]

[0044] Where TDS(Tr1,Tr2) represents the 3D trajectory direction similarity between 3D trajectory Tr1 and 3D trajectory Tr2; θ(r i ,s j ) represents the trajectory point r on the three-dimensional trajectory Tr1 i and the trajectory point s on the three-dimensional trajectory Tr2 j The angle between the moving directions is taken as the cosθ value to characterize the difference in the moving directions;

[0045] Finally, the 3D trajectory shape similarity and 3D trajectory direction similarity are normalized and combined to calculate the similarity measure between 3D trajectories. The calculation formula is as follows:

[0046]

[0047] Among them, d max is the maximum value of the three-dimensional trajectory shape similarity, S(Tr1,Tr2) is the similarity measure between three-dimensional trajectories, and its value range is [0, 1];

[0048] S2.3: Based on the similarity measurement between the three-dimensional trajectories, the improved HDBSCAN algorithm is used to perform cluster analysis on the preprocessed three-dimensional trajectories to obtain several UAV trajectory clusters;

[0049] The improved HDBSCAN algorithm improves the core distance in the original HDBSCAN algorithm to the trajectory core distance C k , the mutual reachability metric distance in the original HDBSCAN algorithm is improved to the mutual reachability metric distance d mreach-k ;

[0050] The trajectory core distance C k The calculation method is: calculate the custom distance function value between each two three-dimensional trajectories, for the three-dimensional trajectory Tr m , arrange the custom distance function values ​​between it and other three-dimensional trajectories in order from small to large, and take the kth custom distance function value as the trajectory core distance C k (Tr m );

[0051] The calculation formula of the custom distance function is as follows:

[0052] Dist(Tr1,Tr2)=1-S(Tr1,Tr2) (14)

[0053] Wherein, Dist(Tr1,Tr2) is the custom distance function value between the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2;

[0054] The trajectories can reach the metric distance between each other, and the specific formula is as follows:

[0055] d mreach-k (Tr1,Tr2)=max{C k (Tr1),C k (Tr2), Dist(Tr1, Tr2)} (15)

[0056] Among them, d mreach-k Represents the mutual reachability metric distance between two three-dimensional trajectories;

[0057] S3: Input each drone trajectory cluster into the pre-trained deep learning intent recognition network for intent recognition, and obtain the intent prediction result of each drone trajectory cluster;

[0058] S3.1: The cluster of UAV trajectories obtained after clustering τ = {Tr1, Tr2, …, Tr N All three-dimensional trajectories in} are input to the input layer, where Tr m ∈R T×4 , N is the number of three-dimensional trajectories in the UAV trajectory cluster, and T is the time step;

[0059] S3.2: Construct a graph structure based on the three-dimensional trajectories in the drone trajectory cluster;

[0060] S3.2.1: Take each drone corresponding to each 3D trajectory in the drone trajectory cluster as a node and initialize the node features. Each node m is initialized as a feature vector And construct the initial feature matrix

[0061] The feature vector represents the initial features of node m, where x avg ,y avg ,z avg is the mean of all three-dimensional spatial coordinates in the three-dimensional trajectory of the UAV corresponding to node m;

[0062] S3.2.2: Construct a weighted adjacency matrix A based on the similarity measure between the three-dimensional trajectories of the UAVs;

[0063] Specifically: Based on the similarity measurement S(Tr m ,Tr q ) construct a similarity matrix S, where the elements S mq =S(Tr m ,Tr q );Set similarity threshold s, if S mq is not less than the threshold s, then there is an edge between node m and node q, and the element A in the weighted adjacency matrix A mq is the similarity measure between three-dimensional trajectories; if there is no edge, then element A mq is 0;

[0064]

[0065] S3.2.3: Add self-loops to the weighted adjacency matrix A to obtain a weighted adjacency matrix after adding self-loops;

[0066] The adjacency matrix after adding the self-loop is: Where I is the identity matrix;

[0067] S3.2.4: Obtain the graph structure based on the initial feature matrix and the adjacency matrix after adding self-loops;

[0068] S3.3: Input the graph structure into a two-layer graph neural network, and realize feature sharing within the drone trajectory cluster through the two-layer graph neural network, that is, the feature vector of each node is aggregated with the feature vector of its neighboring nodes to generate group structure features;

[0069] In each layer of graph convolutional network, the node feature vector is updated according to the following formula:

[0070]

[0071] Among them, H (l+1) is the feature matrix of the l+1th layer, H (l) is the feature matrix of the lth layer, each row represents the feature vector of a node. For the initial layer, H (0) is the initial feature matrix; yes The degree matrix of is the element in the weighted adjacency matrix after adding the self-loop; W (l) is the weight matrix of the lth layer; σ is the nonlinear activation function ReLU;

[0072] S3.4: Input the three-dimensional trajectory in the drone trajectory cluster into the bidirectional GRU network, extract the time series feature sequence set of each three-dimensional trajectory in the drone trajectory cluster, and then obtain the time feature vector of the drone trajectory cluster;

[0073]

[0074] in, represents the output of the bidirectional GRU of the three-dimensional trajectory of UAV m at time step t, x t is the 3D trajectory of the GRU input at time step t. forward is the output of the forward GRU, GRU backward is the output of the backward GRU;

[0075] Finally, according to the output of the bidirectional GRU (Bi-GRU) at each time step in the three-dimensional trajectory, the time series feature set of UAV m is obtained. T is the number of time steps, and the time feature vector of the entire UAV trajectory cluster is obtained

[0076] S3.5: The time series feature set extracted by the bidirectional GRU network and the group structure features extracted by the graph neural network are fused through the fusion layer to obtain the fused features Then we get the fused feature matrix

[0077] S3.6: Use the graph pooling method to aggregate the fused features of all nodes into a global feature of the graph structure;

[0078] First, calculate the attention score of each node. The calculation formula for the attention score of node m is as follows:

[0079]

[0080] Among them, W att is the weight matrix, b att is the bias term;

[0081] Then, the attention score is used to perform weighted summation on the fused features of the nodes to generate the global features of the graph structure. The specific formula is as follows:

[0082]

[0083] S3.7: The global feature H of the graph structure graph Input to the fully connected layer, and map the probability distribution of each intention through the softmax function, and finally get the intention prediction result of the drone trajectory cluster. The specific formula is:

[0084]

[0085] in, is the predicted probability distribution, represents the probability that the input drone trajectory cluster belongs to intention c, where C is the total number of intentions, and W out and b out are the weight matrix and bias term of the fully connected layer respectively.

[0086] Compared with the prior art, the beneficial effects of the present invention are:

[0087] The present invention improves the stability and quality of data by preprocessing the three-dimensional trajectory to ensure its consistency in time and space dimensions, reduces noise interference, and makes the subsequent intention recognition process more accurate and reliable. Through the improved HDBSCAN algorithm, the present invention can effectively identify the direction information of the trajectory and dynamically adjust the clustering structure at different density levels, which makes the drone intention recognition in different group sizes and complex mission scenarios more accurate. Combined with the deep learning network, the present invention can better capture the temporal dependencies of the three-dimensional trajectory, improve the ability to parse complex behavior patterns in the intention recognition process, and thus improve the accuracy and reliability of the recognition results, especially in complex scenarios such as multi-drone collaborative operations, to achieve more effective recognition of drone cluster intentions, compared with the existing technology, greatly improving the performance of intention recognition. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 Flow chart of a method for intention recognition based on three-dimensional trajectory analysis of a drone cluster in an embodiment of the present invention;

[0089] Figure 2 A structural diagram of a deep learning intention recognition network in an embodiment of the present invention;

[0090] Figure 3 Schematic diagram of trajectory intention coding of a drone cluster in an embodiment of the present invention. DETAILED DESCRIPTION

[0091] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0092] like Figure 1 As shown, an intention recognition method based on three-dimensional trajectory analysis of drone clusters includes the following steps:

[0093] S1: Acquire a three-dimensional trajectory data set of a drone cluster and preprocess the three-dimensional trajectories therein to obtain a preprocessed three-dimensional trajectory data set; the three-dimensional trajectory data set of the drone cluster includes three-dimensional trajectories of multiple drones, and the three-dimensional trajectory of each drone includes a number of time steps and the three-dimensional spatial coordinates of the trajectory point at the time step;

[0094] S1.1: Obtain the three-dimensional trajectories of the drones in the drone cluster, obtain the three-dimensional trajectory dataset of the drone cluster, and screen the obtained three-dimensional trajectories, delete incomplete three-dimensional trajectories and abnormal three-dimensional trajectories to ensure the validity of the three-dimensional trajectories;

[0095] The three-dimensional trajectory of UAV m is:

[0096] T m ={(t1,x1,y1,z1),(t2,x2,y2,z2),...,(t i ,x i ,y i ,z i ),...,(t n ,x n ,y n ,z n )} (1)

[0097] Among them, Tr m represents the three-dimensional trajectory of UAV m, t i represents the time step, i represents the number of the trajectory point, (x i ,y i ,z i ) indicates that the UAV is at time step t i The three-dimensional spatial coordinates of the trajectory points under, n represents the number of trajectory points;

[0098] Set the minimum threshold of the three-dimensional trajectory length to δ L , if the length of the three-dimensional trajectory L<δ L , the three-dimensional trajectory is considered incomplete and has no analytical value, so it is deleted; the average velocity v of the three-dimensional trajectory is calculated. avg , if the average speed of a three-dimensional trajectory exceeds the reasonable range V avg , then the three-dimensional trajectory is considered to be wrong or abnormal, that is, if v avg >V avg , then delete the three-dimensional trajectory;

[0099] The average speed calculation formula is:

[0100]

[0101] Among them, d i Represents the distance between two adjacent trajectory points in the three-dimensional trajectory, t i+1 Indicates that i adjacent time steps;

[0102] S1.2: Use cubic spline interpolation to smooth the 3D trajectory to further remove noise and repair missing data, while unifying the 3D trajectory to the same time dimension;

[0103] Specifically, based on the filtered three-dimensional trajectory, a cubic spline function S(t) is constructed, where t is the time step, to interpolate the missing trajectory points and achieve smooth processing of the three-dimensional trajectory; then resampling is performed according to a unified resampling time step Δt to generate trajectory points at the same time step;

[0104] The resampled trajectory points are expressed as:

[0105]

[0106] in, Represents the resampled trajectory points, t0 and t f are the start time and end time of the three-dimensional trajectory respectively;

[0107] S1.3: To facilitate subsequent analysis and modeling, all three-dimensional trajectories are standardized to have the same dimension and range;

[0108] S1.4: If you want to analyze the trajectory intention of the drone cluster more comprehensively and accurately, you need to map the three-dimensional trajectories collected in different small areas to the same large map through coordinate transformation. For each trajectory point in the three-dimensional trajectory, the three-dimensional spatial coordinates (x i ,y i ,z i ), and map it to the coordinate system of the large map through the following matrix transformation formula;

[0109]

[0110] in, is the transformation matrix, b is the offset vector, (x global ,y global ,z global ) is the three-dimensional spatial coordinate of the trajectory point mapped to the large map;

[0111] S2: To achieve preliminary intent classification, improve the processing capability of 3D trajectories of drone clusters of different sizes, enhance the generalization of the model, and prepare for subsequent intent recognition, cluster analysis is performed on the pre-processed 3D trajectories, and the 3D trajectories of drones with similar behavior characteristics are divided into different drone trajectory clusters. The 3D trajectories in the drone trajectory cluster represent similar motion patterns of the drone cluster under specific conditions.

[0112] S2.1: extracting trajectory points with large direction changes in the three-dimensional trajectory by calculating the changes in angles in the three-dimensional trajectory;

[0113] Assume that the three-dimensional trajectory consists of n trajectory points. The three-dimensional spatial coordinates of the trajectory points in the three-dimensional trajectory are expressed as (x1, y1, z1), (x2, y2, z2), …, (xn ,y n ,z n );

[0114] First, for every two adjacent trajectory points on the three-dimensional trajectory, construct a vector pointing from one trajectory point to the adjacent trajectory point

[0115]

[0116] Among them, (x i+1 ,y i+1 ,z i+1 ) are the three-dimensional spatial coordinates of adjacent trajectory points;

[0117] For two adjacent vectors and The angle θ between them is calculated using the dot product formula of the vectors:

[0118]

[0119] in, represents the dot product of two vectors, and is the modulus of the vector, and the formula is:

[0120]

[0121] For the convenience of comparison, for every two adjacent trajectory points on the three-dimensional trajectory, the difference in their movement directions is calculated. The specific calculation formula is as follows:

[0122] Dir=1-cosθ (8)

[0123] Wherein, Dir represents the difference in the movement direction between two adjacent trajectory points. The value range of Dir is 0 to 2. The larger the value of Dir, the greater the change in the direction of the three-dimensional trajectory. The threshold Dir1 is set according to specific needs. When Dir>Dir1, the trajectory point is recorded, thereby extracting the trajectory point with a large change in direction in the three-dimensional trajectory;

[0124] S2.2: Calculate the similarity measure between the three-dimensional trajectories using the starting trajectory point, the ending trajectory point and the extracted trajectory points with large direction changes in the three-dimensional trajectory;

[0125] The three-dimensional trajectory similarity measurement method proposed in this paper is a comprehensive trajectory similarity measurement method constructed by three-dimensional trajectory shape similarity (Trajectory Shape Similarity, TSS) and three-dimensional trajectory direction similarity (Trajectory Direction Similarity, TDS), which comprehensively measures the similarity between two trajectories from two aspects: spatial shape and motion direction:

[0126] For the convenience of calculation, the present invention respectively takes the starting trajectory point, the ending trajectory point of the three-dimensional trajectory and the trajectory point with a large change in trajectory direction extracted in S2.1 to calculate the similarity between the three-dimensional trajectories. The specific two three-dimensional trajectories are expressed as follows:

[0127]

[0128] Among them, Tr1 and Tr2 are two three-dimensional trajectories, r i and j Respectively represent the trajectory points in the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2; i and j are the numbers of the trajectory points, n1 is the total number of the starting trajectory points, the ending trajectory points and the extracted trajectory points with large trajectory direction changes in the three-dimensional trajectory Tr1; n2 is the total number of the starting trajectory points, the ending trajectory points and the extracted trajectory points with large trajectory direction changes in the three-dimensional trajectory Tr2;

[0129] First, the distances from the starting point, the ending point and the point with large direction change on the three-dimensional trajectory Tr1 to the nearest point on the three-dimensional trajectory Tr2 (called the nearest neighbor distance points, NNP) are calculated respectively. Then, the mean of the distances from the starting point, the ending point and the point with large direction change on the three-dimensional trajectory Tr1 to the nearest point on the three-dimensional trajectory Tr2 is calculated. The mean of the distances from the starting point, the ending point and the point with large direction change on the three-dimensional trajectory Tr2 to the nearest point on the three-dimensional trajectory Tr1 is obtained in the same way. The minimum value between the two is taken as the three-dimensional trajectory shape similarity between the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2. The calculation formula of the three-dimensional trajectory shape similarity is as follows:

[0130]

[0131] TSS(Tr1,Tr2) represents the three-dimensional trajectory shape similarity between the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2; d NNP (r i ,Tr2) represents the trajectory point r on the three-dimensional trajectory Tr1 i The distance to the nearest trajectory point on the three-dimensional trajectory Tr2, d NNP (sj ,Tr1) represents the trajectory point s on the three-dimensional trajectory Tr2 j The distance to the nearest trajectory point on the three-dimensional trajectory Tr1;

[0132] Secondly, for the starting trajectory point, the ending trajectory point and the trajectory point with large direction change on the three-dimensional trajectory Tr1, the mean of the difference in motion direction between them and the nearest trajectory point on the three-dimensional trajectory Tr2 is calculated. Similarly, the mean of the difference in motion direction between the starting trajectory point, the ending trajectory point and the trajectory point with large direction change on the three-dimensional trajectory Tr2 and the nearest trajectory point on the three-dimensional trajectory Tr1 is calculated. The minimum value of the two is taken as the three-dimensional trajectory direction similarity, which represents the difference in the motion direction of the three-dimensional trajectory. The three-dimensional trajectory direction similarity calculation formula is as follows:

[0133]

[0134] Where TDS(Tr1,Tr2) represents the 3D trajectory direction similarity between 3D trajectory Tr1 and 3D trajectory Tr2; θ(r i ,s j ) represents the trajectory point r on the three-dimensional trajectory Tr1 i and the trajectory point s on the three-dimensional trajectory Tr2 j The angle between the moving directions is taken as the cosθ value to characterize the difference in the moving directions;

[0135] Finally, considering that the two key features of 3D trajectory shape similarity and 3D trajectory direction similarity have equal influence on 3D trajectory similarity, in order to achieve flexible adjustment in different scenarios, the 3D trajectory shape similarity and 3D trajectory direction similarity are normalized and combined to comprehensively analyze the influence on 3D trajectory similarity and ensure more accurate 3D trajectory comparison. The calculation formula of the similarity measure between 3D trajectories is as follows:

[0136]

[0137] Among them, d max is the maximum value of the three-dimensional trajectory shape similarity, S(Tr1, Tr2) is the similarity measure between three-dimensional trajectories, and its value range is [0, 1]. The closer it is to 1, the more similar the two three-dimensional trajectories are. On the contrary, the smaller the value, the greater the difference between the three-dimensional trajectories. When the two three-dimensional trajectories move in exactly the same direction, the trajectory similarity measure is mainly determined by the three-dimensional trajectory shape similarity; when the two three-dimensional trajectories move in completely opposite directions, This results in S(Tr1, Tr2) = 0, indicating that the three-dimensional trajectories are extremely different;

[0138] S2.3: Based on the similarity measurement between three-dimensional trajectories, the improved HDBSCAN (Hierarchical Density-Based Spatial Clustering of Applications with Noise) algorithm is used to perform cluster analysis on the three-dimensional trajectories of the pre-processed drone cluster, and several drone trajectory clusters with similar behavior patterns are obtained, which effectively reveals the collaborative combat characteristics of the drone group and provides an important basis for subsequent intention recognition;

[0139] The improved HDBSCAN algorithm improves the core distance in the original HDBSCAN algorithm to the trajectory core distance C k , the mutual reachability distance in the original HDBSCAN algorithm is improved to the mutual reachability distance d mreach-k ;

[0140] The trajectory core distance C k The calculation method is: calculate the custom distance function value between each two three-dimensional trajectories, for the three-dimensional trajectory Tr m , arrange the custom distance function values ​​between it and other three-dimensional trajectories in order from small to large, and take the kth custom distance function value as the trajectory core distance C k (Tr m ), where the default value of k is consistent with the minimum cluster size (min_cluster_size) parameter;

[0141] The custom distance function is defined based on the similarity measurement between three-dimensional trajectories, so that it satisfies that the smaller the custom distance, the more similar the three-dimensional trajectories are. The calculation formula of the custom distance function is as follows:

[0142] Dist(Tr1,Tr2)=1-S(Tr1,Tr2) (14)

[0143] Wherein, Dist(Tr1,Tr2) is the custom distance function value between the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2;

[0144] The trajectories are mutually reachable metric distances, which are used to disperse low-density trajectories (with high trajectory core distances). The specific formula is as follows:

[0145] d mreach-k (Tr1,Tr2)=max{C k (Tr1),C k (Tr2), Dist(Tr1, Tr2)} (15)

[0146] Among them, dmreach-k Represents the mutual reachability metric distance between two three-dimensional trajectories;

[0147] S3: Input each drone trajectory cluster into the pre-trained deep learning intent recognition network for intent recognition, and obtain the intent prediction result of each drone trajectory cluster;

[0148] There are significant differences in the intentions of the targets represented by different drone trajectory clusters. Therefore, a trajectory intention recognition method based on deep learning is proposed. The three-dimensional trajectories in different drone trajectory clusters are input into the network for recognition, and the intention of the final drone trajectory cluster is output, such as Figure 2 and Figure 3 As shown, the intentions include attack, retreat, electronic jamming, surveillance, reconnaissance, feint, transportation, etc. The specific steps are as follows:

[0149] S3.1: The cluster of UAV trajectories obtained after clustering τ = {Tr1, Tr2, …, Tr N All three-dimensional trajectories in} are input to the input layer, where Tr m ∈R T×4 , N is the number of three-dimensional trajectories in the UAV trajectory cluster, T is the time step (trajectory sequence length), and 4 means that each trajectory point includes both the time step and the three-dimensional space coordinates;

[0150] S3.2: Construct a graph structure based on the three-dimensional trajectories in the drone trajectory cluster;

[0151] S3.2.1: Take each drone corresponding to each 3D trajectory in the drone trajectory cluster as a node and initialize the node features. Each node (corresponding to a drone) m is initialized as a feature vector And construct the initial feature matrix

[0152] The feature vector represents the initial features of node m, where x avg ,y avg ,z avg is the mean of all three-dimensional spatial coordinates in the three-dimensional trajectory of the UAV corresponding to node m;

[0153] S3.2.2: Construct a weighted adjacency matrix A based on the similarity measure between the three-dimensional trajectories of the UAVs;

[0154] Specifically: Based on the similarity measurement S(Tr m ,Tr q ) construct a similarity matrix S, where the elements S mq =S(Tr m ,Tr q);Set similarity threshold s, if S mq is not less than the threshold s, then there is an edge between node m and node q, and the element A in the weighted adjacency matrix A mq is the similarity measure between three-dimensional trajectories; if there is no edge, then element A mq is 0;

[0155]

[0156] S3.2.3: To ensure that each node can contain its own information during the feature aggregation process, a self-loop is added to the weighted adjacency matrix A so that each node can be aggregated with its own information to obtain a weighted adjacency matrix after adding the self-loop;

[0157] The adjacency matrix after adding the self-loop is: Where I is the identity matrix;

[0158] S3.2.4: Obtain the graph structure based on the initial feature matrix and the adjacency matrix after adding self-loops;

[0159] S3.3: In order to enable the network to extract the group behavior characteristics of the drone trajectory cluster, the graph structure is input into a two-layer graph neural network (GNN). The two-layer graph neural network is used to realize feature sharing within the drone trajectory cluster, that is, the feature vector of each node is aggregated with the feature vector of its neighboring nodes to generate group structure features;

[0160] In GCN (graph convolutional network), the node feature vector update of each layer follows the following formula:

[0161]

[0162] Among them, H (l+1) is the feature matrix of the l+1th layer, H (l) is the feature matrix of the lth layer, each row represents the feature vector of a node. For the initial layer, H (0) is the initial feature matrix; yes The degree matrix of is the element in the weighted adjacency matrix after adding the self-loop; W (l) is the weight matrix of the lth layer, which needs to be learned through training; σ is the nonlinear activation function ReLU;

[0163] In a two-layer GCN, the feature update formulas for layer 1 and layer 2 are as follows:

[0164]

[0165] Through the update of the first layer, the node feature matrix H (1 ) already contains neighborhood information, which integrates the features of each node and its neighboring nodes; the second layer aggregates the neighborhood information again to obtain the output feature matrix of the two-layer GCN As a group structural feature;

[0166] S3.4: Input the 3D trajectory in the drone trajectory cluster into the bidirectional GRU network. The Bi-GRU can simultaneously capture the forward and backward dependencies of the 3D trajectory to better capture the global 3D trajectory change characteristics, thereby effectively learning the change pattern of the 3D trajectory over time, extracting the time series feature sequence set of each 3D trajectory in the drone trajectory cluster, and then obtaining the time feature vector of the drone trajectory cluster;

[0167]

[0168] in, represents the output of the bidirectional GRU of the three-dimensional trajectory of UAV m at time step t, x t is the 3D trajectory of the GRU input at time step t. forward is the output of the forward GRU, GRU backward is the output of the backward GRU;

[0169] Finally, according to the output of the bidirectional GRU (Bi-GRU) at each time step in the three-dimensional trajectory, the time series feature set of UAV m is obtained. T is the number of time steps, and the time feature vector of the entire UAV trajectory cluster is obtained

[0170] S3.5: The time series feature set extracted by the bidirectional GRU network and the group structure features extracted by the GCN are fused through the fusion layer to reconstruct a feature representation containing richer information, which is convenient for further analysis of the drone cluster intention and obtain the fused feature Then we get the fused feature matrix

[0171] S3.6: Use the graph pooling method to aggregate the fused features of all nodes into a global feature of a graph structure;

[0172] First, calculate the attention score of each node. The calculation formula for the attention score of node m is as follows:

[0173]

[0174] Among them, W att is the weight matrix, b attis a bias term, and softmax is used to normalize the attention scores of all nodes;

[0175] Then, the attention score is used to perform weighted summation on the fused features of the nodes to generate the global features of the graph structure. The specific formula is as follows:

[0176]

[0177] S3.7: The global feature H of the graph structure graph Input to the fully connected layer, and map the probability distribution of each intention through the softmax function, and finally get the intention prediction result of the drone trajectory cluster. The specific formula is:

[0178]

[0179] in, is the predicted probability distribution, which contains the probability of each intent, where represents the probability that the input drone trajectory cluster belongs to intention c, C is the total number of intentions, and W out and b out They are the weight matrix and bias term of the fully connected layer respectively. Through softmax, the network outputs the intention classification result corresponding to the drone trajectory cluster, and finally identifies the target's behavioral intention;

[0180] The training method of the pre-trained deep learning intent recognition network in this embodiment is:

[0181] In order to identify the intent of drone trajectory clusters, it is first necessary to annotate each drone trajectory cluster in the drone cluster. Specifically, for each drone trajectory cluster, an intention label is manually assigned, and the intent categories include but are not limited to attack, retreat, electronic interference, surveillance, reconnaissance, feint, transportation, etc. After the labeling is completed, the data set is divided into training set, validation set and test set, usually with 70% of the data used for training, 15% for validation, and 15% for testing.

[0182] During the training process, each batch of training samples is first forward propagated. The drone trajectory cluster is input into the model, calculated layer by layer, and finally the predicted intent of the trajectory cluster is output. In order to evaluate the degree of match between the model's prediction results and the true labels, the cross entropy loss function is used to calculate the loss, as follows:

[0183]

[0184] Among them, y c shows the true label of the cth class, is the model's predicted probability for that category.

[0185] Next, the back-propagation algorithm is used to calculate the gradient of the loss to each layer parameter, and the model parameters are updated through the Adam optimizer to gradually minimize the loss. After each training round, the model performance is evaluated using the validation set data, and the validation loss and accuracy are recorded. When the validation loss no longer decreases significantly within multiple consecutive training rounds, the early stopping strategy is applied to terminate the training to prevent overfitting.

[0186] After training is completed, the model is evaluated on the test set, and indicators such as accuracy, precision, recall, and F1-score are calculated to comprehensively evaluate the generalization performance of the model. According to the performance on the validation set, hyperparameters (such as learning rate and regularization coefficient) are adjusted if necessary, and the model is retrained. Finally, the optimal model is selected for actual deployment.

[0187] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An intention recognition method based on three-dimensional trajectory analysis of drone clusters, characterized in that: The steps include: S1: Obtain a three-dimensional trajectory data set of a drone cluster and preprocess the three-dimensional trajectories therein to obtain a preprocessed three-dimensional trajectory; the three-dimensional trajectory data set of the drone cluster includes three-dimensional trajectories of multiple drones, and the three-dimensional trajectory of each drone includes a number of time steps and the three-dimensional spatial coordinates of the trajectory point at the time step; S2: Cluster analysis is performed on the preprocessed three-dimensional trajectories to divide them into different UAV trajectory clusters; S3: Input each drone trajectory cluster into the pre-trained deep learning intent recognition network for intent recognition to obtain the intent prediction result of each drone trajectory cluster.

2. The method for intention recognition based on three-dimensional trajectory analysis of drone clusters according to claim 1 is characterized in that: S1 specifically includes: S1.1: Obtain the three-dimensional trajectories of the drones in the drone cluster, obtain the three-dimensional trajectory dataset of the drone cluster, and filter the obtained three-dimensional trajectories to delete incomplete three-dimensional trajectories and abnormal three-dimensional trajectories; The three-dimensional trajectory of UAV m is: Tr m {(t1,x1,y1,z1),(t2,x2,y2,z2),…,(t i , x i ,y i ,z i ),…,(t n , x n ,y n ,z n )} (1) Among them, Tr m represents the three-dimensional trajectory of UAV m, t i represents the time step, i represents the number of the trajectory point, (x i ,y i ,z i ) indicates that the UAV is at time step t i The three-dimensional spatial coordinates of the trajectory points under, n represents the number of trajectory points; Set the minimum threshold of the three-dimensional trajectory length to δ L , if the length of the three-dimensional trajectory L<δ L , the three-dimensional trajectory is considered incomplete and deleted; calculate the average velocity v of the three-dimensional trajectory avg , if the average speed of a three-dimensional trajectory exceeds the reasonable range V avg , then the three-dimensional trajectory is considered to be wrong or abnormal, that is, if v avg >V avg , then delete the three-dimensional trajectory; S1.2: Use cubic spline interpolation to smooth the 3D trajectory and unify the 3D trajectory to the same time dimension; Specifically, based on the filtered three-dimensional trajectory, a cubic spline function S(t) is constructed, where t is the time step, to interpolate the missing trajectory points; then resampling is performed according to a uniform resampling time step Δt to generate trajectory points at the same time step; The resampled trajectory points are expressed as: in, Represents the resampled trajectory points, t0 and t f are the start time and end time of the three-dimensional trajectory respectively; S1.3: Normalize all three-dimensional trajectories to have the same dimension and range; S1.4: Map the three-dimensional trajectory to the same large map through coordinate transformation; For each trajectory point in the three-dimensional trajectory, the three-dimensional space coordinates (x i ,y i ,z i ), and map it to the coordinate system of the large map through the following matrix transformation formula: in, is the transformation matrix, b is the offset vector, (x global ,y global ,z global ) is the three-dimensional spatial coordinate of the trajectory point mapped to the large map.

3. The method for intention recognition based on three-dimensional trajectory analysis of drone clusters according to claim 2 is characterized in that: S2 specifically includes: S2.1: extracting trajectory points with large direction changes in the three-dimensional trajectory by calculating the changes in angles in the three-dimensional trajectory; S2.2: Calculate the similarity measure between the three-dimensional trajectories using the starting trajectory point, the ending trajectory point and the extracted trajectory points with large direction changes in the three-dimensional trajectory; S2.3: Based on the similarity measurement between three-dimensional trajectories, the improved HDBSCAN algorithm is used to perform cluster analysis on the preprocessed three-dimensional trajectories to obtain several UAV trajectory clusters.

4. The method for intention recognition based on three-dimensional trajectory analysis of drone clusters according to claim 3 is characterized in that: S2.1 specifically includes: Assume that the three-dimensional trajectory consists of n trajectory points. The three-dimensional spatial coordinates of the trajectory points in the three-dimensional trajectory are expressed as (x1, y1, z1), (x2, y2, z2), …, (x n ,y n ,z n ); First, for every two adjacent trajectory points on the three-dimensional trajectory, construct a vector pointing from one trajectory point to the adjacent trajectory point Among them, (x i+1 ,y i+1 ,z i+1 ) are the three-dimensional spatial coordinates of adjacent trajectory points; For two adjacent vectors and The angle θ between them is calculated using the dot product formula of the vectors: in, represents the dot product of two vectors, and is the modulus of the vector, and the formula is: For every two adjacent trajectory points on the three-dimensional trajectory, calculate the difference in their movement directions. The specific calculation formula is as follows: Dir=1-cosθ (8) Among them, Dir represents the difference in movement direction between two adjacent trajectory points. The value range of Dir is 0 to 2. The larger the value of Dir, the greater the change in direction of the three-dimensional trajectory. The threshold Dir1 is set according to specific needs. When Dir>Dir1, the trajectory point is recorded, thereby extracting the trajectory points with large direction changes in the three-dimensional trajectory.

5. The method for intention recognition based on three-dimensional trajectory analysis of drone clusters according to claim 4 is characterized in that: S2.2 specifically includes: The two three-dimensional trajectories are expressed as follows: Among them, Tr1 and Tr2 are two three-dimensional trajectories, r i and j Respectively represent the trajectory points in the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2; i and j are the numbers of the trajectory points, n1 is the total number of the starting trajectory points, the ending trajectory points and the extracted trajectory points with large trajectory direction changes in the three-dimensional trajectory Tr1; n2 is the total number of the starting trajectory points, the ending trajectory points and the extracted trajectory points with large trajectory direction changes in the three-dimensional trajectory Tr2; First, the distances from the starting point, the ending point, and the point with large direction change on the three-dimensional trajectory Tr1 to the nearest point on the three-dimensional trajectory Tr2 are calculated respectively. Then, the mean of the distances from the starting point, the ending point, and the point with large direction change on the three-dimensional trajectory Tr1 to the nearest point on the three-dimensional trajectory Tr2 is calculated. The mean of the distances from the starting point, the ending point, and the point with large direction change on the three-dimensional trajectory Tr2 to the nearest point on the three-dimensional trajectory Tr1 is obtained in the same way. The minimum value between the two is taken as the three-dimensional trajectory shape similarity between the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2. The calculation formula for the three-dimensional trajectory shape similarity is as follows: TSS(Tr1,Tr2) represents the three-dimensional trajectory shape similarity between the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2; d NNP (r i ,Tr2) represents the trajectory point r on the three-dimensional trajectory Tr1 i The distance to the nearest trajectory point on the three-dimensional trajectory Tr2, d NNP (s j ,Tr1) represents the trajectory point s on the three-dimensional trajectory Tr2 j The distance to the nearest trajectory point on the three-dimensional trajectory Tr1; Secondly, for the starting trajectory point, the ending trajectory point and the trajectory point with large direction change on the three-dimensional trajectory Tr1, calculate the mean of the difference in motion direction between them and the nearest trajectory point on the three-dimensional trajectory Tr2. Similarly, calculate the mean of the difference in motion direction between the starting trajectory point, the ending trajectory point and the trajectory point with large direction change on the three-dimensional trajectory Tr2 and the nearest trajectory point on the three-dimensional trajectory Tr1. Take the minimum value of the two as the three-dimensional trajectory direction similarity. The three-dimensional trajectory direction similarity calculation formula is as follows: Where TDS(Tr1,Tr2) represents the 3D trajectory direction similarity between 3D trajectory Tr1 and 3D trajectory Tr2; θ(r i ,s j ) represents the trajectory point r on the three-dimensional trajectory Tr1 i and the trajectory point s on the three-dimensional trajectory Tr2 j The angle between the moving directions is taken as the cosθ value to characterize the difference in the moving directions; Finally, the 3D trajectory shape similarity and 3D trajectory direction similarity are normalized and combined to calculate the similarity measure between 3D trajectories. The calculation formula is as follows: Among them, d max is the maximum value of the three-dimensional trajectory shape similarity, S(Tr1, Tr2) is the similarity measure between three-dimensional trajectories, and its value range is [0, 1].

6. The method for intention recognition based on three-dimensional trajectory analysis of drone clusters according to claim 5 is characterized in that: The improved HDBSCAN algorithm described in S2.3 improves the core distance in the original HDBSCAN algorithm to the trajectory core distance C k , the mutual reachability metric distance in the original HDBSCAN algorithm is improved to the mutual reachability metric distance d mreach-k ; The trajectory core distance C k The calculation method is: calculate the custom distance function value between each two three-dimensional trajectories, for the three-dimensional trajectory Tr m , arrange the custom distance function values ​​between it and other three-dimensional trajectories in order from small to large, and take the kth custom distance function value as the trajectory core distance C k (Tr m ); The calculation formula of the custom distance function is as follows: Dist(Tr1,Tr2)=1-S(Tr1,Tr2) (14) Wherein, Dist(Tr1,Tr2) is the custom distance function value between the three-dimensional trajectory Tr1 and the three-dimensional trajectory Tr2; The trajectories can reach the metric distance between each other, and the specific formula is as follows: d mreach-k (Tr1,Tr2)=max{C k (Tr1),C k (Tr2),Dist(Tr1,Tr2)} (15) Among them, d mreach-k Represents the mutual reachability metric distance between two 3D trajectories.

7. The method for intention recognition based on three-dimensional trajectory analysis of drone clusters according to claim 6 is characterized in that: S3 specifically includes: S3.1: The cluster of UAV trajectories obtained after clustering τ = {Tr1, Tr2, …, Tr N All three-dimensional trajectories in} are input to the input layer, where Tr m ∈R T×4 , N is the number of three-dimensional trajectories in the UAV trajectory cluster, and T is the time step; S3.2: Construct a graph structure based on the three-dimensional trajectories in the drone trajectory cluster; S3.3: Input the graph structure into a two-layer graph neural network, and realize feature sharing within the drone trajectory cluster through the two-layer graph neural network, that is, the feature vector of each node is aggregated with the feature vector of its neighboring nodes to generate group structure features; In each layer of graph convolutional network, the node feature vector is updated according to the following formula: Among them, H (l+1) is the feature matrix of the l+1th layer, H (l) is the feature matrix of the lth layer, each row represents the feature vector of a node. For the initial layer, H (0) is the initial feature matrix; yes The degree matrix of is the element in the weighted adjacency matrix after adding the self-loop; W (l) is the weight matrix of the lth layer; σ is the nonlinear activation function ReLU; S3.4: Input the three-dimensional trajectory in the drone trajectory cluster into the bidirectional GRU network, extract the time series feature sequence set of each three-dimensional trajectory in the drone trajectory cluster, and then obtain the time feature vector of the drone trajectory cluster; in, represents the output of the bidirectional GRU of the three-dimensional trajectory of drone m at time step t, x t is the 3D trajectory of the GRU input at time step t. forward is the output of the forward GRU, GRU backward is the output of the backward GRU; Finally, according to the output of the bidirectional GRU (Bi-GRU) at each time step in the three-dimensional trajectory, the time series feature set of UAV m is obtained. T is the number of time steps, and the time feature vector of the entire UAV trajectory cluster is obtained S3.5: The time series feature set extracted by the bidirectional GRU network and the group structure features extracted by the graph neural network are fused through the fusion layer to obtain the fused features Then we get the fused feature matrix S3.6: Use the graph pooling method to aggregate the fused features of all nodes into a global feature of the graph structure; First, calculate the attention score of each node. The calculation formula for the attention score of node m is as follows: Among them, W att is the weight matrix, b att is the bias term; Then, the attention score is used to perform weighted summation on the fused features of the nodes to generate the global features of the graph structure. The specific formula is as follows: S3.7: The global feature H of the graph structure graph Input to the fully connected layer, and map the probability distribution of each intention through the softmax function, and finally get the intention prediction result of the drone trajectory cluster. The specific formula is: in, is the predicted probability distribution, represents the probability that the input drone trajectory cluster belongs to intention c, where C is the total number of intentions, and W out and b out are the weight matrix and bias term of the fully connected layer respectively.

8. The method for intention recognition based on three-dimensional trajectory analysis of drone clusters according to claim 7 is characterized in that: S3.2 specifically includes: S3.2.1: Take each drone corresponding to each 3D trajectory in the drone trajectory cluster as a node and initialize the node features. Each node m is initialized as a feature vector And construct the initial feature matrix The feature vector represents the initial features of node m, where x avg ,y avg ,z avg is the mean of all three-dimensional spatial coordinates in the three-dimensional trajectory of the UAV corresponding to node m; S3.2.2: Construct a weighted adjacency matrix A based on the similarity measure between the three-dimensional trajectories of the UAVs; Specifically: Based on the similarity measurement S(Tr m ,Tr q ) construct a similarity matrix S, where the elements S mq =S(Tr m ,Tr q );Set similarity threshold s, if S mq is not less than the threshold s, then there is an edge between node m and node q, and the element A in the weighted adjacency matrix A mq is the similarity measure between three-dimensional trajectories; if there is no edge, then element A mq is 0; S3.2.3: Add self-loops to the weighted adjacency matrix A to obtain a weighted adjacency matrix after adding self-loops; The adjacency matrix after adding the self-loop is: Where I is the identity matrix; S3.2.4: Obtain the graph structure based on the initial feature matrix and the adjacency matrix after adding self-loops.

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