Formation grouping optimization method for multi-node cluster cooperative positioning

Abstract

The application discloses a kind of formation grouping optimization methods for multi-node cluster cooperative positioning, comprising the following steps: setting more constraint conditions that fit multi-node cooperative work, based on clustering algorithm guiding multi-node to form formation grouping;Design the multi-node grouping optimization method of combination (K-WPA) of clustering algorithm and improved wolf swarm algorithm;According to the population process of wolf swarm algorithm optimized by clustering result;Combined with the sensor equipped with node to establish measurement model, design the evaluation function of formation grouping based on Fisher information matrix.The K-WPA algorithm proposed in the application shows stronger ability to solve global optimal solution in dynamic grouping process.K-WPA grouping optimization algorithm solves the selection problem of cooperative node, effectively improves the grouping efficiency of unmanned aerial vehicle cluster, improves the positioning accuracy of 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 modern battlefields evolve toward systematization, informatization, intelligence, and collaboration, the limitations of single drones are becoming increasingly apparent in complex and ever-changing battlefield environments. Highly flexible distributed drone swarms, however, offer significant potential. Large, dense swarms not only increase the complexity of inter-node network communications but also frequently encounter problems such as communication distance limits, which in turn impact the control effectiveness and robustness of fixed formations. Therefore, implementing efficient dynamic formation grouping for dynamic multi-node swarms and selecting the optimal grouping for high-precision collaborative positioning will provide essential support for efficient mission completion during multi-node swarm coordinated operations.

[0003] In recent years, real-time dynamic grouping technology for drone swarms has demonstrated significant practical value in multiple dimensions, including military strategy and commercial applications, attracting extensive research worldwide. Patent application number 202311609090.X, "Method and Device for Unmanned System Attack Defense Based on Dynamic Heterogeneous Redundancy," discloses a device for grouping drone swarms to prevent GPS spoofing, ensuring the swarm's ability to effectively detect navigation and positioning threats such as GPS spoofing attacks and ensure mission safety. Patent application number 202310995849.6, "Goal-Oriented Decentralized Unmanned Swarm Dynamic Formation Method, Device, Medium, and Product for Fragmented Information," discloses a dynamic formation method that addresses the incomplete and fragmented information issues caused by limited swarm communication.

[0004] Currently, the goal of dynamic formation grouping in clusters is to improve the coordination and cooperation efficiency among members. However, the impact of this on the accuracy of cluster collaborative positioning is rarely considered during the grouping process. Therefore, it is urgent to develop an optimized formation grouping method for multi-node clusters to improve collaborative positioning accuracy. Summary of the Invention

[0005] Aiming at the problem of collaborative node selection during multi-node collaborative positioning, the present invention designs a formation grouping evaluation function for a multi-node collaborative system and proposes an optimization algorithm (abbreviated as K-WPA) for formation grouping during multi-node collaborative positioning based on K-means and an improved wolf pack algorithm (WPA). By setting constraints that are more suitable for actual combat scenarios, the clustering and grouping of multiple nodes are guided, effectively improving the grouping efficiency of the cluster. Based on the clustering results, the variation process of the wolf pack algorithm is optimized to avoid falling into the problem of local optimal solutions. 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] A 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: obtaining the grouping class table matrix based on the clustering results, generating a formation grouping sample pool, and extracting some 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 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.

[0008] As a preferred embodiment of the present invention, S1 specifically includes: for a multi-node drone swarm system, each node is equipped with a Beidou satellite navigation sensor and an ultra-wideband ranging sensor, which respectively provide location information for each drone and distance information between drones. All drones broadcast their own locations and receive the locations of other drones via 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-formation N k ∈[5,8].

[0011] 2) Nodes in a sub-fleet 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

[0014]

[0015] In W, the row number is the sub-cluster number, and the column number is the node number. If a node belongs to a sub-cluster, it is represented by a "1," otherwise it is represented by a "0." Therefore, the nodes in the cluster matrix W are divided into two categories: one is the node that belongs to only one cluster, and the other is the node that belongs to multiple clusters.

[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-formation, 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 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". Following this rule, a formation grouping sample pool consisting of various combinations will be obtained.

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

[0020] Since the number of nodes in each sub-formation is not fixed, N k ∈[5,8], so the number of drone cluster groupings is T seed formations. |·| 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 in the population, together forming 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 sensor in the system. In a drone cluster with N nodes, k The nodes form the kth sub-formation. In this sub-formation, drone i (i=1,2,...,N k)’s theoretical position information 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 the 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 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 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] Where, J(u i ) represents the Fisher information matrix of node i:

[0035]

[0036] Where, Σ -1 is the covariance matrix of UWB measurement noise, H i is the distance measurement equation Z i The Jacobian matrix, 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] Substituting formula (7) into formula (6), we can get the Fisher information matrix J(u i ), namely:

[0039]

[0040] J(u i ) is reduced from the number of cluster nodes N to the number of nodes N in the kth sub-formation 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. Let

[0041] 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.

[0042] Based on the Fisher information matrix of the sub-formation, the objective function of the cluster system can be obtained as:

[0043] f=||diag(F1,F2,...,F K )||2 (11)

[0044] As a preferred embodiment of the present invention, S5 is specifically:

[0045] The wolf pack algorithm continuously iterates and optimizes the initialized population to find the optimal grouping. The specific process is as follows:

[0046] (1) Set the step sizes of β wolf and γ wolf to be S respectively β and S γ . At the same time, set the mutation threshold and iteration stop condition.

[0047] (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.

[0048] (3) Determine whether the wolf pack algorithm meets the iteration stopping 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).

[0049] (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 respective step sizes, and complete the mutation operation based on the comparison of mutation probability and mutation threshold. If the updated β wolf and γ wolf meet the constraints, these individuals are retained; otherwise, these individuals are eliminated and new individuals are introduced from the grouped sample pool to form a new generation of population. Repeat steps (2) to (4).

[0050] (5) The output optimal formations are grouped and the positioning accuracy is solved using a collaborative positioning method based on a factor graph model.

[0051] 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 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

[0052] Figure 1 It is a flow chart of the UAV cluster formation grouping method.

[0053] Figure 2 It is a traditional K-means clustering grouping diagram.

[0054] Figure 3 This is a detailed diagram of the process of β wolf approaching α wolf.

[0055] Figure 4 This is the optimal grouping result diagram based on K-WPA.

[0056] Figure 5 It is the comparison of the final values ​​of the objective functions of WPA and K-WPA.

[0057] Figure 6 This is a comparison chart of the time it takes to group the algorithms. DETAILED DESCRIPTION

[0058] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0059] 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 designed constraints, to obtain the initial grouping class table matrix of the multi-node cluster; S3: obtaining the grouping class table matrix based on the clustering results, 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.

[0060] The advantages of the present invention are: 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.

[0061] Example:

[0062] The design concept of this invention is: a formation grouping optimization method for multi-node collaborative positioning. It sets unmanned cluster grouping constraints that are more suitable for actual combat scenarios to guide cluster grouping and obtain an initial cluster grouping sample pool. Based on the node measurement model, Fisher information, and Cramer-Rao lower bound, an evaluation function for evaluating formation grouping is designed to obtain the objective function of the wolf pack algorithm. The cluster grouping sample pool selected by the constrained K-means algorithm guides the WPA algorithm to find the optimal grouping. WPA iterates to find the optimal grouping.

[0063] 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 as follows:

[0064] (1) Collect the location information output by the BeiDou satellite navigation sensor (BDS) carried by the node.

[0065] (2) Generate the initial clustering sample pool based on K-means constraints. First, set reasonable constraints to guide clustering. The specific constraints are:

[0066] 1) The number of nodes in each sub-formation N k ∈[5,8].

[0067] 2) Nodes in a sub-fleet can communicate with each other, and the maximum communication distance is d max .

[0068] 3) Each node only participates in the collaborative positioning of one sub-formation.

[0069] Based on the above constraints, the improved K-means clustering method is specifically as follows:

[0070] Set the class table matrix W to be K×N in dimension = [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

[0071]

[0072] According to constraint 2), considering the actual communication range, in order to improve 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

[0073]

[0074] When the node position u t and cluster center c k The distance is less than or equal to When ut Must be in the kth cluster; when u t and c k The distance is greater than d max , then u t It 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 greater the distance, the smaller the probability that node t is in the kth cluster. The value of ρ is

[0075]

[0076] Although the traditional K-means clustering method satisfies constraint 3), that is, each node is assigned to the nearest cluster, this method has uniqueness and is prone to falling into local optimality. To address this, the following improvements are made:

[0077]

[0078] Improved δ kt This makes it so that nodes are no longer divided into a single cluster, but can belong to multiple clusters, increasing the possibility of more grouping.

[0079] Figure 2 Represents the grouping graph obtained by traditional K-means clustering, with Figure 2 Taking the cluster of 20 nodes shown in the figure as an example, the clustering matrix W is obtained by the above-mentioned K-means clustering method based on the constraint conditions.

[0080]

[0081] In W, the row number is the sub-cluster number, and the column number is the node number. If a node belongs to a sub-cluster, it is represented by a "1," otherwise it is represented by a "0." Therefore, the nodes in the cluster matrix W are divided into two categories: one is the node that belongs to only one cluster, and the other is the node that belongs to multiple clusters.

[0082] 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-formation, 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

[0083]

[0084] During subsequent grouping optimization, the "*" position can be filled with either "1" or "0." When a "*" in a column is assigned a value of "1," the remaining "*" in that column are assigned a value of "0." Following this rule, a pool of formation grouping samples consisting of various combinations is obtained, providing guidance for subsequent search for the optimal grouping that meets the constraints.

[0085] (3) Based on the constraint condition, the K-means clustering method 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 the number of drone cluster groupings is T seed formations. |·| 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. When the number of drone cluster nodes is 20, 30 and 50 respectively, the iteration step size S is set. β 1,1,1,S respectively γ 3, 4, 5 respectively; variable step length S mu =2,3,4, mutation threshold p v =0.5.

[0086] (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:

[0087] First, establish the measurement model of the sensor in the system. In a drone cluster with N nodes, k The nodes form the kth sub-formation. In this sub-formation, drone i (i=1,2,...,N k )’s theoretical position information is They represent the northeast celestial coordinates of UAV i respectively.

[0088] The measurement model of UAV i measured by BDS is expressed as

[0089]

[0090] Among them, u i ={x i ,y i ,z i}, x i ,y i ,zi 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.

[0091] UWB measurement of drone i and drone j (j=1,2,..,N k The measurement model of the distance information of &j≠i) is expressed as

[0092] D i,j =d i,j +ε UWB , (5)

[0093] 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 Expressed as:

[0094]

[0095] In the kth sub-formation, establish the distance measurement equation Z between UAV i and other UAV nodes j i , Z i Expressed as:

[0096]

[0097] 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

[0098]

[0099] Where, J(u i ) represents the Fisher information matrix of node i:

[0100]

[0101] Where, Σ -1 is the covariance matrix of UWB measurement noise, Hi is the distance measurement equation Z i The Jacobian matrix, 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

[0102]

[0103] Substituting formula (7) into formula (6), we can get the Fisher information matrix J(u i ), namely:

[0104]

[0105] J(u i ) is reduced from the number of cluster nodes N to the number of nodes N in the kth sub-formation 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. Let

[0106] 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.

[0107] Based on the Fisher information matrix of the sub-formation, the objective function of the cluster system can be obtained as:

[0108] f=||diag(F1,F2,...,F K )||2 (14)

[0109] (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.

[0110] (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.

[0111] (7) Population update: retain the individuals corresponding to the previous generation of α wolves. At the same time, β wolves are updated with a smaller step size S. βApproaching the α wolf, gradually optimizing itself; the γ wolf takes a larger step size S γ Move 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-formation numbers to which the above nodes belong in the α wolf are extracted, and these nodes in the β wolf or γ wolf are organized into corresponding sub-formations.

[0112] When S β = 1, the specific process of β wolf approaching α wolf is as follows Figure 3 As shown in Figure 2, the randomly selected node belonging to multiple clusters is node 5. Node 5 in wolf α is in sub-formation 1. Therefore, node 5 in wolf β is incorporated into sub-formation 1, completing the approach operation of wolf β with a step length of 1.

[0113] Then add mutation operations to all individuals of β wolf and γ wolf, set the mutation probability, and improve the probability of solving the global optimal solution. Sample mutation probability p mu for

[0114]

[0115] 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 Nodes are mutated. The selected mutated nodes are randomly assigned to the remaining available sub-formations; otherwise, they remain unchanged. The updated β-wolves and γ-wolves are checked to see if they meet the constraints. Those that meet all the constraints are retained; those that do not are removed, and new individuals are introduced from the grouped sample pool to form the next generation of the population.

[0116] (8) The output optimal formations are grouped and the positioning accuracy is solved using a collaborative positioning method based on a factor graph model.

[0117] 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.

[0118] (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 UAV was equipped with BDS and UWB. All UAVs could broadcast and receive location information through wireless network. The UAV clusters with 20, 30, and 50 nodes were respectively located in 350*350*300 (m3 )、400*400*350(m 3 )、500*500*400(m 3 ) in the three-dimensional space, and randomly generate the initial position to ensure the minimum safety distance d min =80 (m), the drones moved in random directions at speeds of 0 to 10 m / s, simulating the flexible motion trajectory of a real-world combat drone swarm. The total simulation time was 1500 s. The measurement noise of the drone sensors was set to Gaussian white noise. The specific sensor parameter configuration is shown in Table 1.

[0119] Table 1: Sensor parameter configuration

[0120]

[0121] (10) Perform optimization simulation verification

[0122] 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 values ​​of the optimal grouping results of the two algorithms are compared as shown in the figure below. Figure 5 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.

[0123] (11) Perform positioning accuracy simulation verification

[0124] The positioning accuracy of the nodes in the grouped sub-formation 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.

[0125] Table 2: Comparison of drone position estimation errors

[0126]

[0127]

[0128] 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.

[0129] (12) Perform packet rate verification

[0130] 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 grouping method, other processes and parameters are consistent. The simulation comparison of the grouping time of the two algorithms is as follows: Figure 6 As shown. Figure 6It can be seen that the K-WPA grouping method takes less time to run and has better results than WPA. Specifically, when optimizing the grouping of drones with 20 nodes, K-WPA has a 95% probability of completing it within 0.186 seconds; when optimizing the grouping of drones with 30 nodes, it has a 95% probability of completing it within 0.213 seconds; and when optimizing the grouping of drones with 50 nodes, it has a 95% probability of completing it within 0.412 seconds.

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 the K-means clustering method and combining the designed constraints, we can obtain the initial grouping matrix of the multi-node cluster. 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. A formation grouping optimization method for multi-node cluster collaborative positioning according to claim 1, characterized in that: In S1, all nodes are equipped with Beidou satellite navigation sensors and ultra-wideband ranging sensors to provide location information for each drone and distance information between drones; 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 to obtain the initial grouping table matrix of the multi-node cluster and generate the initial clustering group sample pool; the specific constraints are: 1) The number of nodes in each sub-formation N k ∈[5,8]; 2) Nodes in a sub-fleet 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 In W, the row number is the sub-cluster number, and the column number is the node number. If a node belongs to a sub-cluster, it is represented by "1", otherwise it is represented by "0". Therefore, the nodes in the cluster matrix W are divided into two categories: one is the nodes in only one cluster, and the other is the nodes in multiple clusters. 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-formation, 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, characterized in that: In S3, a grouping table matrix is ​​obtained based on 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 the number of drone cluster groupings is T seed formations. |·| 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, the objective function value of all individuals in the initial population of the wolf pack algorithm is calculated by the objective function, which is obtained by combining the sensor measurement model, Fisher information and Cramer-Rao lower bound: First, the measurement model of the sensor in the system is established. In a drone cluster with N nodes, N k nodes form the kth sub-formation; UAV i (i=1,2,...,N k )’s theoretical position information 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 is consistent with Gaussian white noise; UWB measurement of drone i and drone j (j=1,2,..,N k The measurement model of the 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 Expressed as: In the kth sub-formation, establish the distance measurement equation Z between UAV i and other UAV nodes j i , Z i 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: Where, J(u i ) represents the Fisher information matrix of node i: Where, Σ -1 is the covariance matrix of UWB measurement noise, H i is the distance measurement equation Z i The Jacobian matrix, 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-formation 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 the ||2, the greater the Fisher information and the better the position prediction. 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 wolf pack algorithm's mutation process is optimized by using the formation grouping sample pool obtained by K-means based on the constraint conditions. The improved wolf pack algorithm is used to optimize the initial population 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 be 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 )||2Calculate the objective function value 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 stopping condition, that is, α wolf continuously iterates n nonew No update, or the preset maximum number of iterations n is reached max ; If satisfied, then output the optimal grouping and go to step (5); if not satisfied, then go to step (4); (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 respective step sizes, 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, these individuals are retained; otherwise, these individuals are eliminated and new individuals are introduced 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.

Images