Formation grouping optimization method for multi-node cluster cooperative positioning

Abstract

The invention discloses a formation grouping optimization method for multi-node cluster cooperative positioning, and the method comprises the following steps: setting a constraint condition which is more suitable for multi-node cooperative work, and guiding multiple nodes to carry out formation grouping based on a clustering algorithm; designing a multi-node grouping optimization method combining a clustering algorithm and an improved wolf pack algorithm (K-WPA); optimizing the population process of the wolf pack algorithm according to the clustering result; a measurement model is established in combination with sensors equipped for nodes, and an evaluation function of formation grouping is designed based on a Fisher information matrix. The K-WPA algorithm provided by the invention shows a stronger capability of solving a globally optimal solution in a dynamic grouping process. The K-WPA grouping optimization algorithm solves the problem of selection of cooperative nodes, effectively improves the grouping efficiency of the unmanned aerial vehicle cluster, and improves the positioning precision of the unmanned aerial vehicle cluster.

Description

Technical Field

[0001] The present invention relates to the field of navigation and positioning, and in particular to a formation grouping optimization method for multi-node cluster collaborative positioning. Background Art

[0002] As the modern battlefield develops towards systematization, informatization, intelligence and collaboration, the application limitations of single UAVs are becoming increasingly prominent in complex and ever-changing battlefield environments, while highly flexible distributed UAV clusters are showing high efficiency potential. Large-scale dense clusters will not only increase the complexity of network communication between nodes, but will also frequently cause problems such as communication distance exceeding the limit, thereby affecting the control effect and robustness of fixed formations. Therefore, implementing efficient dynamic formation grouping for dynamic multi-node clusters and selecting the optimal grouping to achieve high-precision collaborative positioning will provide necessary guarantees for the efficient completion of tasks when multi-node clusters are in collaborative combat.

[0003] In recent years, the real-time dynamic grouping technology of drone swarms has demonstrated extremely high practical value in multiple dimensions such as military strategy and commercial applications, and has attracted extensive research around the world. The patent application number 202311609090.X, "Method and device for attack defense of unmanned systems based on dynamic heterogeneous redundancy", discloses a device that can group drone swarms to prevent GPS spoofing, so as to ensure that the cluster has the ability to effectively detect navigation and positioning threats such as GPS spoofing attacks and ensure mission safety. The patent application number 202310995849.6, "Goal-oriented decentralized unmanned swarm dynamic formation method, equipment, medium and product for fragmented information", discloses a dynamic formation method that solves the problem of incomplete and fragmented information caused by limited cluster communication.

[0004] At present, the goal of dynamic formation grouping of clusters is mainly to improve the coordination and cooperation efficiency among members. However, the possible impact on the collaborative positioning accuracy of clusters is rarely considered in the grouping process. Therefore, it is urgent to develop a formation grouping optimization method for multi-node clusters to improve the collaborative positioning accuracy. Summary of the invention

[0005] Aiming at the problem of cooperative node selection during multi-node cooperative positioning, the present invention designs a formation grouping evaluation function of a multi-node cooperative system, and proposes an optimization algorithm (abbreviated as K-WPA) for formation grouping during multi-node cooperative positioning based on K-means and an improved wolf pack algorithm (WPA). By setting constraint conditions that are more in line with actual combat scenarios, the clustering grouping of multiple nodes is guided, and the grouping efficiency of the cluster is effectively improved. According to the clustering results, the variation process of the wolf pack algorithm is optimized to avoid falling into the problem of local optimal solution. Based on the Fisher information matrix, the objective function of the wolf pack algorithm is designed to complete the evaluation of the formation grouping optimization process.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] The formation grouping optimization method for multi-node cluster collaborative positioning includes the following steps: S1: for multi-node clusters, all nodes are equipped with Beidou satellite navigation sensors (BDS) and ultra-wideband ranging sensors (UWB); S2: using the K-means clustering method, combined with the designed constraints, to obtain the initial grouping class table matrix of the multi-node cluster; S3: according to the clustering results, the grouping class table matrix is ​​obtained, a formation grouping sample pool is generated, and some samples are extracted as the initial population of the wolf pack algorithm; S4: combining the sensor measurement model, Fisher information and Cramer-Rao lower bound, an evaluation function for evaluating the formation grouping is designed, and then the objective function of the wolf pack algorithm is generated; S5: through the formation grouping sample pool obtained by K-means based on the constraints, the mutation process of the wolf pack algorithm is optimized, and the improved wolf pack algorithm is used to optimize the formation grouping until the optimal collaborative grouping is iterated, thereby obtaining the optimal collaborative positioning accuracy.

[0008] As a preferred solution of the present invention, S1 is specifically as follows: for a drone cluster system including multiple nodes, each node is equipped with UWB. BDS and UWB provide location information and distance information between drones for each drone respectively. All drones broadcast their own locations and receive the locations of other drones through a wireless network.

[0009] As a preferred solution of the present invention, S2 specifically includes: setting reasonable constraints to ensure that each sub-formation after grouping meets the actual application requirements, so as to improve the efficiency of the collaborative positioning formation grouping optimization. The specific constraints are:

[0010] 1) The number of nodes in each sub-team N k ∈[5,8].

[0011] 2) Nodes in a sub-team can communicate with each other, and the maximum communication distance is d max .

[0012] 3) Each node only participates in the collaborative positioning of one sub-formation.

[0013] Based on the above constraints, the improved K-means clustering grouping method obtains the clustering table matrix W as follows:

[0014]

[0015] In W, the row number is the sub-formation number, and the column number is the node number. If the node belongs to the sub-formation, it is represented by "1", otherwise, it is represented by "0". Therefore, the nodes in the class table matrix W are divided into two categories: nodes in only one cluster, such as node 2, node 3, node 4, node 6, node 9, node 11, node 15, node 17, node 18, node 19 and node 20; and nodes in multiple clusters, such as the remaining nodes in 20 nodes.

[0016] Design grouping table matrix W based on W * For nodes that belong to only one cluster, the node is directly assigned to the corresponding sub-team, and the column corresponding to the node remains unchanged; for nodes that belong to multiple clusters, the "0" in the column remains unchanged, and the position of "1" is represented by "*". Then the W corresponding to the above W matrix is * The matrix is

[0017]

[0018] The position of "*" can be filled with "1" or "0". When a "*" in a column is assigned a value of "1", the other "*" in the column will be assigned a value of "0". According to this rule, a formation grouping sample pool consisting of multiple combinations will be obtained.

[0019] As a preferred solution of the present invention, S3 is specifically:

[0020] Since the number of nodes in each sub-team is not fixed, N k ∈[5,8], so there are T seed formations in the UAV cluster grouping. |·| c Indicates rounding up. Each sub-formation corresponds to a grouping table matrix. The "*" in each grouping table matrix is ​​randomly assigned according to the rules, and the number of generated Each result is an individual of the population, which together constitutes a population size of 100, which is used as the initial population of the wolf pack algorithm.

[0021] As a preferred embodiment of the present invention, S4 is specifically:

[0022] First, establish the measurement model of the sensors in the system. In a drone cluster with N nodes,k nodes form the kth sub-formation. In this sub-formation, drone i (i=1,2,...,N k ) is They represent the northeast celestial coordinates of UAV i respectively.

[0023] The measurement model of UAV i measured by BDS is expressed as

[0024]

[0025] Among them, u i ={x i ,y i ,z i}, x i ,y i ,z i are the northeast celestial coordinates measured by BDS, h BDS is the theoretical measurement function of BDS, ε BDS is the measurement noise of BDS, is the BDS positioning error variance, which conforms to Gaussian white noise.

[0026] UWB measurement of drone i and drone j (j = 1, 2, .., N k The measurement model of distance information of &j≠i) is expressed as

[0027] D i,j =d i,j +ε UWB , (2)

[0028] Among them, ε UWB is the UWB ranging noise, is the UWB ranging error variance, which is consistent with Gaussian white noise. i,j is the theoretical distance between UAV i and UAV j, d i,j It is expressed as:

[0029]

[0030] In the kth sub-formation, establish the distance measurement equation Z between UAV i and other UAV nodes j i , Z i It is expressed as:

[0031]

[0032] The node position information is used as the state variable, and the Fisher information is used to predict the amount of state information that the sensor's measurement value can provide. The lower bound of the Cramer-Rao inequality is the inverse of the Fisher information matrix, which gives the theoretical lower bound of the unbiased estimator. is the measured position u i Based on Z i The unbiased estimate of the estimated position error covariance satisfies the Cramer-Rao inequality, that is,

[0033]

[0034] In the formula, J(u i ) represents the Fisher information matrix of node i:

[0035]

[0036] In the formula, Σ -1 is the covariance matrix of UWB measurement noise, H i is the distance measurement equation Z i The Jacobian matrix of p(Z i |u i ) is the distance measurement equation Z of node i i About the node position u i The likelihood function of

[0037]

[0038]

[0039] Substituting formula (7) into formula (6), we can get the Fisher information matrix J(u i ), namely:

[0040]

[0041] J(u i ) is reduced from the number of cluster nodes N to the number of nodes N in the kth sub-team k . Calculate the Fisher information matrix of all nodes in the k-th sub-formation respectively, and get the Fisher information matrix of the k-th sub-formation.

[0042]

[0043] The grouping evaluation function of the kth sub-formation can be designed as ||F k ||2,||F k The larger the ||2 is, the greater the Fisher information is and the better the position prediction is.

[0044] Based on the Fisher information matrix of the sub-formation, the objective function of the cluster system can be obtained as:

[0045] f=||diag(F1,F2,...,F K )||2 (11)

[0046] As a preferred solution of the present invention, S5 is specifically:

[0047] The wolf pack algorithm continuously iterates and optimizes the obtained initial population to obtain the optimal grouping. The specific process is as follows:

[0048] (1) Set the step sizes of β wolf and γ wolf to S respectively. β and S γ . At the same time, set the mutation threshold and iteration stop condition.

[0049] (2) Check the constraints and calculate the result according to the objective function f = || diag(F1, F2, ..., F K )||2, calculate the objective function values ​​of all individuals in the population and divide all individuals into α wolves, β wolves and γ wolves.

[0050] (3) Determine whether the wolf pack algorithm meets the iteration stop condition, that is, α wolf continuously iterates n nonew No update, or the preset maximum number of iterations n is reached max If it is satisfied, then the optimal grouping is output and the process goes to step (5); if it is not satisfied, then the process goes to step (4).

[0051] (4) Population update: retain the individuals corresponding to the previous generation of α wolf. At the same time, β wolf and γ wolf approach α wolf with their own step lengths, and complete the mutation operation based on the comparison between the mutation probability and the mutation threshold. If the updated β wolf and γ wolf meet the constraints, retain these individuals; otherwise, remove these individuals and introduce new individuals from the grouped sample pool to form a new generation of population. Repeat steps (2) to (4).

[0052] (5) The output optimal formations are grouped and the positioning accuracy is solved using a collaborative positioning method based on a factor graph model.

[0053] Therefore, the present invention has the following beneficial effects: setting unmanned cluster grouping constraints that are more suitable for actual combat scenarios, guiding cluster grouping, and improving the efficiency of collaborative positioning formation grouping optimization; designing an evaluation function for evaluating formation grouping based on the node measurement model, Fisher information volume and Cramer-Rao lower bound, and obtaining the objective function of the wolf pack algorithm to accurately evaluate the quality of formation grouping; the cluster grouping sample pool selected by the K-means algorithm based on the constraint conditions guides the WPA algorithm to find the best solution, avoiding the problem of the WPA algorithm falling into the local optimal solution, and showing a stronger ability to solve the global optimal solution in the dynamic grouping process. The K-WPA grouping optimization algorithm solves the problem of selecting collaborative nodes, effectively improves the accuracy of collaborative positioning, and significantly improves the grouping efficiency of drone clusters. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a flow chart of the UAV swarm formation grouping method.

[0055] Figure 2 It is a traditional K-means clustering grouping diagram.

[0056] Figure 3 This is a detailed diagram of the process of β wolf approaching α wolf.

[0057] Figure 4 This is the optimal grouping result diagram based on K-WPA.

[0058] Figure 5 It is the comparison of the final values ​​of the objective functions of WPA and K-WPA.

[0059] Figure 6 This is a comparison chart of the time it takes to group algorithms. DETAILED DESCRIPTION

[0060] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0061] A formation grouping optimization method for multi-node collaborative positioning includes the following steps: S1: for a multi-node cluster, all nodes are equipped with Beidou satellite navigation sensors (BDS) and ultra-wideband ranging sensors (UWB); S2: using the K-means clustering method, combined with the designed constraints, to obtain the initial grouping class table matrix of the multi-node cluster; S3: obtaining the grouping class table matrix according to the clustering result, generating a formation grouping sample pool, and extracting the samples as the initial population of the wolf pack algorithm; S4: combining the sensor measurement model, Fisher information and Cramer-Rao lower bound, designing an evaluation function for evaluating the formation grouping, and then generating the objective function of the wolf pack algorithm; S5: optimizing the mutation process of the wolf pack algorithm through the formation grouping sample pool obtained by K-means based on the constraints, and using the improved wolf pack algorithm to optimize the formation grouping until the optimal collaborative grouping is iterated, thereby obtaining the optimal collaborative positioning accuracy.

[0062] The advantages of the present invention are: setting unmanned cluster grouping constraints that are more suitable for actual combat scenarios, guiding cluster grouping, so as to improve the efficiency of collaborative positioning formation grouping optimization; designing an evaluation function for evaluating formation grouping based on the node measurement model, Fisher information and Cramer-Rao lower bound, and obtaining the objective function of the wolf pack algorithm to accurately evaluate the quality of formation grouping; the cluster grouping sample pool screened out by the K-means algorithm based on the constraint conditions guides the WPA algorithm to find the best solution, avoiding the problem of the WPA algorithm falling into the local optimal solution, and showing a stronger ability to solve the global optimal solution in the dynamic grouping process. The K-WPA grouping optimization algorithm solves the problem of selecting collaborative nodes, effectively improves the accuracy of collaborative positioning, and significantly improves the grouping efficiency of drone clusters.

[0063] Example:

[0064] The design concept of the present invention is: a formation grouping optimization method for multi-node collaborative positioning. Set unmanned cluster grouping constraints that are more suitable for actual combat scenarios, guide cluster grouping, and obtain an initial cluster grouping sample pool; based on the node measurement model, Fisher information and Cramer-Rao lower bound, design an evaluation function for evaluating formation grouping, and obtain the objective function of the wolf pack algorithm; based on the cluster grouping sample pool selected by the K-means algorithm under the constraints, guide the WPA algorithm to find the best, and WPA iterates to find the optimal grouping.

[0065] Next, combine Figure 1 The flowchart of the UAV cluster formation grouping method shown in the figure introduces the K-WPA formation grouping optimization method for multi-node cluster collaborative positioning. The specific implementation steps are:

[0066] (1) Collect the location information output by the Beidou satellite navigation sensor (BDS) carried by the node.

[0067] (2) Generate the initial clustering sample pool based on K-means constraints. First, set reasonable constraints to guide clustering. The specific constraints are:

[0068] 1) The number of nodes in each sub-team N k ∈[5,8].

[0069] 2) Nodes in a sub-team can communicate with each other, and the maximum communication distance is d max .

[0070] 3) Each node only participates in the collaborative positioning of one sub-formation.

[0071] Based on the above constraints, the specific contents of the improved K-means clustering grouping method are as follows:

[0072] Set the class table matrix W = [δ kt ]. According to constraint 1), considering the number of nodes in the sub-formation, limiting the minimum number of nodes in each cluster, we have

[0073]

[0074] According to constraint 2), considering the actual communication range, in order to increase the probability that the drone nodes in each cluster can measure the distance between each other, the element δ in the class table matrix is ​​set kt for

[0075]

[0076] When the node position u t and cluster center c k The distance is less than or equal to When t must be in the kth cluster; when u t and c k The distance is greater than d max , then u t must not be in cluster k; when u t and c k The distance is greater than and less than or equal to d max When setting the parameter ρ, u t and c k The larger the distance, the smaller the probability that node t is in the kth cluster. The value of ρ is

[0077]

[0078] Although the traditional K-means clustering method satisfies constraint 3), that is, each node is divided into a single nearest cluster, this method has uniqueness and is prone to fall into local optimality. The following improvements are made to this:

[0079]

[0080] Improved δ kt This makes the nodes no longer classified into a single cluster, but can belong to multiple clusters, increasing the possibility of more grouping.

[0081] Figure 2 Represents the grouping graph obtained by traditional K-means clustering, Figure 2 Taking the cluster of 20 nodes shown in the figure as an example, the clustering table matrix W is obtained by the above-mentioned K-means clustering method based on constraints:

[0082]

[0083] In W, the row number is the sub-formation number, and the column number is the node number. If the node belongs to the sub-formation, it is represented by "1", otherwise, it is represented by "0". Therefore, the nodes in the class table matrix W are divided into two categories: nodes in only one cluster, such as node 2, node 3, node 4, node 6, node 9, node 11, node 15, node 17, node 18, node 19 and node 20; and nodes in multiple clusters, such as the remaining nodes in 20 nodes.

[0084] Design grouping table matrix W based on W * For nodes that belong to only one cluster, the node is directly assigned to the corresponding sub-team, and the column corresponding to the node remains unchanged; for nodes that belong to multiple clusters, the "0" in the column remains unchanged, and the position of "1" is represented by "*". Then the W corresponding to the above W matrix is * The matrix is

[0085]

[0086] In the subsequent grouping optimization process, the position of "*" can be filled with "1" or "0". When a "*" in a column is assigned a value of "1", the other "*" in the column will be assigned a value of "0". According to this rule, a formation grouping sample pool consisting of multiple combinations will be obtained, which will provide guidance for the subsequent search for the optimal grouping that meets the constraints.

[0087] (3) The K-means clustering method based on constraints is used to obtain the grouped sample pool. Since the number of nodes in each sub-formation is not fixed, N k ∈[5,8], so there are T seed formations in the UAV cluster grouping. |·| c Indicates rounding up. Each sub-formation corresponds to a grouping table matrix. The "*" in each grouping table matrix is ​​randomly assigned according to the rules, and the number of generated Each result is used as an individual of the population, and together they form a population size of 100, which is used as the initial population of the wolf pack algorithm. When the number of nodes in the drone cluster is 20, 30, and 50, respectively, the iteration step size S is set. β They are 1,1,1,S respectively. γ 3, 4, 5 respectively; variable step length S mu =2,3,4, mutation threshold p v =0.5.

[0088] (4) Check whether the individuals in the population meet all the constraints, and calculate the objective function value of each individual by the objective function. The objective function is obtained by combining the node measurement model, Fisher information and Cramer-Rao lower bound. The specific steps are as follows:

[0089] First, establish the measurement model of the sensors in the system. In a drone cluster with N nodes, k nodes form the kth sub-formation. In this sub-formation, drone i (i=1,2,...,N k ) is They represent the northeast celestial coordinates of UAV i respectively.

[0090] The measurement model of UAV i measured by BDS is expressed as

[0091]

[0092] Among them, u i ={x i ,y i ,z i}, x i ,y i ,z i are the northeast celestial coordinates measured by BDS, h BDS is the theoretical measurement function of BDS, ε BDS is the measurement noise of BDS, is the BDS positioning error variance, which conforms to Gaussian white noise.

[0093] UWB measurement of drone i and drone j (j = 1, 2, .., N k The measurement model of distance information of &j≠i) is expressed as

[0094] D i,j =d i,j +ε UWB, (5)

[0095] Among them, ε UWB is the UWB ranging noise, is the UWB ranging error variance, which is consistent with Gaussian white noise. i,j is the theoretical distance between UAV i and UAV j, d i,j It is expressed as:

[0096]

[0097] In the kth sub-formation, establish the distance measurement equation Z between UAV i and other UAV nodes j i , Z i It is expressed as:

[0098]

[0099] The node position information is used as the state variable, and the Fisher information is used to predict the amount of state information that the sensor's measurement value can provide. The lower bound of the Cramer-Rao inequality is the inverse of the Fisher information matrix, which gives the theoretical lower bound of the unbiased estimator. is the measured position u i Based on Z i The unbiased estimate of the estimated position error covariance satisfies the Cramer-Rao inequality, that is,

[0100]

[0101] In the formula, J(u i ) represents the Fisher information matrix of node i:

[0102]

[0103] In the formula, Σ -1 is the covariance matrix of UWB measurement noise, H i is the distance measurement equation Z i The Jacobian matrix of p(Z i |u i ) is the distance measurement equation Z of node i i About the node position u i The likelihood function of

[0104]

[0105]

[0106] Substituting formula (7) into formula (6), we can get the Fisher information matrix J(u i ), namely:

[0107]

[0108] J(u i ) is reduced from the number of cluster nodes N to the number of nodes N in the kth sub-team k . Calculate the Fisher information matrix of all nodes in the k-th sub-formation respectively, and get the Fisher information matrix of the k-th sub-formation.

[0109]

[0110] The grouping evaluation function of the kth sub-formation can be designed as ||F k ||2,||F k The larger the ||2 is, the greater the Fisher information is and the better the position prediction is.

[0111] Based on the Fisher information matrix of the sub-formation, the objective function of the cluster system can be obtained as:

[0112] f=||diag(F1,F2,...,F K )||2 (14)

[0113] (5) All individuals are divided into α wolves (optimal solution), β wolves (suboptimal solution) and γ wolves (poor solution). The individuals that meet all constraints and have the best objective function value are α wolves, representing the current optimal grouping; the individuals that meet all constraints except α wolves are β wolves, representing the suboptimal grouping; the individuals that do not meet the constraints are γ wolves.

[0114] (6) Determine whether the iteration stop condition is met, that is, α wolf continuously iterates n nonew = 15 times without update, or the preset maximum number of iterations n is reached max = 100. If it is satisfied, the optimal formation grouping is output; if it is not satisfied, the population is updated.

[0115] (7) Population update: retain the individuals corresponding to the previous generation of wolf α. At the same time, wolf β updates with a smaller step size S β Approaching wolf α, gradually optimizing itself; wolf γ takes a larger step size S γ Get closer to wolf α and explore a wider search space. β or S γ The specific process of approaching is: randomly select S from the grouping table matrix β or S γ Nodes belonging to multiple clusters are extracted, the sub-team numbers to which the above nodes belong in the α wolf are extracted, and these nodes in the β wolf or γ wolf are assigned to the corresponding sub-teams.

[0116] When S β= 1, the specific process of β wolf approaching α wolf is as follows Figure 3 As shown in the figure, the randomly selected node belonging to multiple clusters is node 5. Node 5 in α wolf is in sub-formation 1. Therefore, node 5 of β wolf is incorporated into sub-formation 1, completing the approach operation of β wolf with a step length of 1.

[0117] Then add mutation operations to all individuals of β wolf and γ wolf, set the mutation probability, and increase the probability of solving the global optimal solution. Sample mutation probability p mu for

[0118]

[0119] Among them, n iter is the number of iterations. If the mutation probability p mu Greater than the mutation threshold p v , then randomly select S belonging to multiple clusters in the grouping table matrix mu The nodes selected for mutation are randomly assigned to the remaining available sub-teams; otherwise, they remain unchanged. Check whether the updated β wolf and γ wolf meet the constraints, and keep the corresponding individuals that meet all the constraints; remove the individuals that do not meet the constraints, and introduce new individuals from the grouped sample pool to form a new generation of population.

[0120] (8) The output optimal formations are grouped and the positioning accuracy is solved using a collaborative positioning method based on a factor graph model.

[0121] against Figure 2 The 20 randomly distributed nodes shown in the figure are processed using the K-WPA-based algorithm, and the output optimal grouping result is as follows Figure 4 shown.

[0122] (9) Simulation environment construction: The K-WPA algorithm was verified based on MATLAB. The northeast sky coordinate system was used as the navigation coordinate system. Each drone was equipped with BDS and UWB. All drones could broadcast and receive location information through wireless networks. The drone clusters with 20, 30, and 50 nodes were located in 350*350*300 (m 3 )、400*400*350(m 3 )、500*500*400(m 3 ) in the three-dimensional space, and the initial position is randomly generated while ensuring the minimum safety distance d min = 80 (m), it moves in random directions at a speed of 0 to 10 m / s to simulate the flexible motion trajectory of a real combat drone cluster. The total simulation time is 1500 s. The sensor measurement noise of the drone is set to Gaussian white noise. The specific sensor parameter configuration is shown in Table 1.

[0123] Table 1: Sensor parameter configuration

[0124]

[0125] (10) Perform optimization simulation verification

[0126] The final values ​​of the objective functions of WPA and K-WPA are calculated to analyze the performance of the two algorithms at different drone cluster sizes. When the number of cluster nodes is 50, the objective function value comparison of the optimal grouping results of the two algorithms is shown in the figure below: Figure 5 As shown in the figure, during the entire simulation period, the final value of the objective function of K-WPA is higher than that of WPA, and the optimization effect is better.

[0127] (11) Perform positioning accuracy simulation verification

[0128] The positioning accuracy of the nodes in the sub-formation after grouping is analyzed, and the positioning effects of cluster grouping (K), fixed grouping (FG), WPA grouping, and K-WPA grouping are compared and verified by calculating the UAV position estimation error.

[0129] Table 2: Comparison of UAV position estimation errors

[0130]

[0131]

[0132] It can be seen from Table 2 that the node position estimation error is the largest after FG grouping; the node position estimation error is second after K grouping and WPA grouping; and the position estimation error is the smallest after K-WPA grouping.

[0133] (12) Perform packet rate verification

[0134] The K-WPA algorithm is compared with the WPA algorithm. The entire time period of the simulated UAV cluster movement is selected for analysis. Except for the difference in the grouping method, other processes and parameters are consistent. The simulation comparison of the time spent on grouping of the two algorithms is as follows: Figure 6 As shown. Figure 6 It can be seen that the K-WPA grouping method takes less time to run the algorithm and has better results than WPA. Specifically, when K-WPA optimizes the grouping of drone clusters with 20 nodes, there is a 95% probability that it will be completed within 0.186s; when K-WPA optimizes the grouping of drone clusters with 30 nodes, there is a 95% probability that it will be completed within 0.213s; when K-WPA optimizes the grouping of drone clusters with 50 nodes, there is a 95% probability that it will be completed within 0.412s.

Claims

1. A formation grouping optimization method for multi-node cluster collaborative positioning, characterized in that: The following steps are involved: S1: For multi-node clusters, all nodes are equipped with BeiDou satellite navigation sensors (BDS) and ultra-wideband ranging sensors (UWB); S2: Using K-means clustering method and combining the designed constraints, we can obtain the initial grouping table matrix of multi-node clusters; S3: Obtain the grouping table matrix based on the clustering results, generate a formation grouping sample pool, and extract some samples as the initial population of the wolf pack algorithm; S4: Combining the sensor measurement model, Fisher information and Cramer-Rao lower bound, an evaluation function for evaluating formation grouping is designed to generate the objective function of the wolf pack algorithm; S5: Through the formation grouping sample pool obtained by K-means based on constraint conditions, the mutation process of the wolf pack algorithm is optimized, and the improved wolf pack algorithm is used to optimize the formation grouping until the optimal collaborative grouping is iterated, thereby obtaining the optimal collaborative positioning accuracy.

2. The formation grouping optimization method for multi-node cluster collaborative positioning according to claim 1 is characterized in that: In S1, all nodes are equipped with BDS and UWB, which respectively provide location information and distance information between drones for each drone; all drones broadcast their own locations and receive the locations of other drones through wireless networks.

3. The formation grouping optimization method for multi-node cluster collaborative positioning according to claim 1, characterized in that: In S2, the K-means clustering method is used to set reasonable constraints, obtain the initial grouping table matrix of the multi-node cluster, and generate the initial clustering grouping sample pool; the specific constraints are: 1) The number of nodes in each sub-team N k ∈[5,8]; 2) Nodes in a sub-team can communicate with each other, and the maximum communication distance is d max ; 3) Each node only participates in the collaborative positioning of one sub-formation; Based on the above constraints, the improved K-means clustering grouping method obtains the clustering table matrix W as follows: In W, the row number is the sub-formation number, and the column number is the node number; if the node belongs to the sub-formation, it is represented by "1", otherwise, it is represented by "0"; therefore, the nodes in the class table matrix W are divided into two categories: nodes in only one cluster, such as node 2, node 3, node 4, node 6, node 9, node 11, node 15, node 17, node 18, node 19 and node 20; and nodes in multiple clusters, such as the remaining nodes in 20 nodes; Design grouping table matrix W based on W * ; For nodes that belong to only one cluster, the node is directly assigned to the corresponding sub-team, and the column corresponding to the node remains unchanged; for nodes that belong to multiple clusters, the "0" in the column remains unchanged, and the position of "1" is represented by "*". Then the W corresponding to the above W matrix is * The matrix is Among them, the position of "*" can be filled with "1" or "0"; when a "*" in a column is assigned a value of "1", the other "*" in the column will be assigned a value of "0"; according to this rule, a formation grouping sample pool composed of multiple combinations will be obtained.

4. The formation grouping optimization method for multi-node cluster collaborative positioning according to claim 3 is characterized in that: In S3, a grouping table matrix is ​​obtained according to clustering, a formation grouping sample pool is generated, and some samples are extracted as the initial population of the wolf pack algorithm; since the number of nodes in each sub-formation is not fixed, N k ∈[5,8], so there are T seed formations in the UAV cluster grouping. |·| c Indicates rounding up; each sub-formation corresponds to a grouping table matrix, and the "*" in each grouping table matrix is ​​randomly assigned according to the rules, and the number of generated The grouping results; each result is an individual of the population, together forming a population size of 100, which is used as the initial population of the wolf pack algorithm.

5. The formation grouping optimization method for multi-node cluster collaborative positioning according to claim 4, characterized in that: In S4, for all individuals in the initial population of the wolf pack algorithm, the objective function value is calculated through the objective function, and the objective function is obtained by combining the sensor measurement model, the Fisher information amount and the Cramer-Rao lower bound: First, the measurement model of the sensor in the system is established. In a drone cluster with N nodes, k nodes form the kth sub-formation; in this sub-formation, drone i (i=1,2,...,N k ) is They represent the northeast celestial coordinates of UAV i respectively; The measurement model of UAV i measured by BDS is expressed as Among them, u i ={x i ,y i ,z i }, x i ,y i ,z i are the northeast celestial coordinates measured by BDS, h BDS is the theoretical measurement function of BDS, ε BDS is the measurement noise of BDS, is the BDS positioning error variance, which conforms to Gaussian white noise; UWB measurement of drone i and drone j (j = 1, 2, .., N k The measurement model of distance information of &j≠i) is expressed as: D i,j =d i,j +e UWB , Among them, ε UWB is the UWB ranging noise, is the UWB ranging error variance, which is consistent with Gaussian white noise; d i,j is the theoretical distance between UAV i and UAV j, d i,j It is expressed as: In the kth sub-formation, establish the distance measurement equation Z between UAV i and other UAV nodes j i , Z i It is expressed as: The node position information is used as the state variable, and the Fisher information is used to predict the amount of state information that the sensor's measurement value can provide. The lower bound of the Cramer-Rao inequality is the inverse of the Fisher information matrix, which gives the theoretical lower bound of the unbiased estimator. is the measured position u i Based on Z i The unbiased estimate of , the estimated position error covariance satisfies the Cramer-Rao inequality, that is: In the formula, J(u i ) represents the Fisher information matrix of node i: In the formula, Σ -1 is the covariance matrix of UWB measurement noise, H i is the distance measurement equation Z i The Jacobian matrix of p(Z i |u i ) is the distance measurement equation Z of node i i About the node position u i The likelihood function of H i Substitution The Fisher information matrix J(u i ), namely: J(u i ) is reduced from the number of cluster nodes N to the number of nodes N in the kth sub-team k ; Calculate the Fisher information matrix of all nodes in the k-th sub-formation respectively, and get the Fisher information matrix of the k-th sub-formation. The grouping evaluation function of the kth sub-formation can be designed as ||F k ||2,||F k The larger ||2 is, the greater the Fisher information is, and the better the position prediction is; Based on the Fisher information matrix of the sub-formation, the objective function of the cluster system can be obtained as: f=||diag(F1,F2,...,F K )||2。 6. The formation grouping optimization method for multi-node cluster collaborative positioning according to claim 5, characterized in that: In S5, the variation process of the wolf pack algorithm is optimized by using the formation grouping sample pool obtained by K-means based on the constraint condition, and the initial population is optimized by using the improved wolf pack algorithm until the optimal collaborative grouping is iterated, thereby obtaining the optimal collaborative positioning accuracy; the specific process is as follows: (1) Set the step sizes of β wolf and γ wolf to S respectively. β and S γ ,At the same time, set the mutation threshold and iteration stop condition; (2) Check the constraints and calculate the result according to the objective function f = || diag(F1, F2, ..., F K )||2 Calculate the objective function values ​​of all individuals in the population and divide all individuals into α wolves, β wolves and γ wolves; (3) Determine whether the wolf pack algorithm meets the iteration stop condition, that is, α wolf continuously iterates n nonew No update, or the preset maximum number of iterations n is reached max ; If satisfied, output the optimal grouping and go to step (5); if not satisfied, go to step (4); (4) Population update: retain the individuals corresponding to the previous generation of wolf α, and at the same time, wolf β and wolf γ approach wolf α with their own step lengths, and complete the mutation operation based on the comparison between the mutation probability and the mutation threshold; if the updated wolf β and wolf γ meet the constraints, retain these individuals; otherwise, remove these individuals and introduce new individuals from the grouped sample pool to form a new generation of population; repeat steps (2) to (4); (5) The output optimal formations are grouped and the positioning accuracy is solved using a collaborative positioning method based on a factor graph model.

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