Large-scale unmanned aerial vehicle cluster sub-region cooperative positioning method based on network formation game

Abstract

This invention discloses a large-scale UAV swarm regional cooperative positioning method based on network formation game theory. First, for a large-scale UAV swarm, cooperative navigation is performed in different regions. Then, game theory rules are used to find the cooperative UAV set with the maximum utility, and the optimal connection strategy network structure is selected, allowing low-precision UAVs to adaptively select high-precision UAVs within the region for cooperative positioning. Finally, based on the updated cooperative UAV set, the belief propagation method is used to locate the low-precision UAVs. This invention expands the scale of the UAV swarm by dividing the large-scale swarm into regions and optimizing the cooperative UAV set for each region using network formation game theory. This allows the UAV to receive navigation information only within the cooperative region and adaptively select the optimal cooperative UAV, thereby reducing network connection complexity, maximizing UAV utility, and ensuring the positioning accuracy of the UAV swarm.

Description

Technical Field

[0001] This invention belongs to the field of positioning and navigation technology, specifically relating to a large-scale UAV swarm regional collaborative positioning method based on network-based game theory. Background Technology

[0002] In recent years, drone swarms have been widely used in both civilian and military fields. With the expanding applications of drones and the increasing number of drone swarms, large-scale drone collaborative operations have become an important future development direction. Large-scale drone swarms can flexibly adjust the distribution of drones as needed to adapt to different mission requirements and environmental changes. Compared to small swarms, large-scale drone swarms can share risk costs, and even if some drones are damaged, others can continue to perform their missions.

[0003] As the number of clusters increases, managing and controlling large-scale drones becomes more challenging. Traditional collaborative positioning strategies involve a large number of collaborative connections, and the complexity of collaborative computation increases exponentially, leading to problems such as long navigation and positioning times and severe network congestion. Summary of the Invention

[0004] Purpose of the invention: This invention proposes a large-scale UAV swarm regional collaborative positioning method based on network-based game theory. It adaptively finds the optimal collaborative connection selection strategy for a single UAV within its region, dividing the large swarm into different regional sub-swarms. While ensuring navigation accuracy, it effectively reduces computational complexity and communication overhead, achieving efficient and accurate navigation and positioning in complex environments.

[0005] Technical solution: The large-scale UAV swarm regional cooperative positioning method based on network-formed game theory described in this invention includes the following steps:

[0006] (1) Obtain the position, velocity, attitude of the UAV in the geodetic coordinate system and the relative measurement information between UAV clusters;

[0007] (2) Based on the circular coverage area, the UAV collaborative set is divided;

[0008] (3) Linearize the relative measurement information between UAVs using the linear regression method and calculate the linearization factor;

[0009] (4) Execute steps (5) to (8) according to the judgment condition of iteration time t; if iteration time t = 1, execute step (8) first, then execute steps (5) to (7); if iteration time t ≠ 1, execute steps (5) to (8) directly.

[0010] (5) Calculate the conditional mean square error reduced by UAV collaboration;

[0011] (6) Optimize the set of cooperative regions of the UAVs to be located based on game theory rules to construct a new network structure;

[0012] (7) Calculate the cost function and utility function of the UAV cooperative set, change the UAV cooperative connection relationship, and reorganize the cooperative network structure;

[0013] (8) The position status of UAVs in each sub-region is updated and fused according to the belief propagation algorithm;

[0014] (9) Repeat steps (1) to (8) to iteratively update the drone cluster positioning information until the iteration time t equals the preset time.

[0015] Furthermore, the implementation process of step (1) is as follows:

[0016] The drone swarm consists of a reference drone (a) and a drone to be located (b), as follows:

[0017] V=A∪B,A={1,...a},B={1,...,b}

[0018] Where A is the set of all reference UAVs and B is the set of all UAVs to be located. The reference UAVs obtain their own longitude, latitude and altitude based on the high-precision sensor devices and GNSS. The UAVs to be located rely only on the inertial navigation system to obtain their own position information and need the reference UAVs to assist in positioning.

[0019] The positions of the UAV to be located, i∈B, and the reference UAV, j∈A, are X and X, respectively. i =(x i ,y i ,z i ), X j =(x j ,y j ,z j The relative measurement information between the two drones is z. ij :

[0020]

[0021] Where, d ij Let θ be the relative distance between drone i and drone j. ij Let i be the relative azimuth angle between UAV i and UAV j. Let be the relative altitude angle between UAV i and UAV j.

[0022] Furthermore, the implementation process of step (2) is as follows:

[0023] Set the initial flight time of the swarm to t0 = 1, the initial value of the posterior game linearization iteration to iteration = 1, and the maximum number of collaborations per drone to k.

[0024] Given a graph G = (V, E), where E represents the connections between drones, and the communication range is r centered on the drone i to be located. i Define a circular region with a radius, and all reference UAVs within this region constitute the initial cooperative UAV set of UAV i.

[0025] The target drone i and the reference drone The relative distance d between ij Sort, select relative distance d ij The smallest k drones form a new cooperative set.

[0026] Furthermore, the implementation process of step (3) is as follows:

[0027] Using the Sigma point method to analyze measurement information Perform linear regression decomposition, selecting m sigma sampling points χ1,...,χ based on the UAV's position mean and covariance. m and weights ω1,...,ω m Sampling points Let i be the s-th sampling point at position i of the drone. Let be the s-th sampling point at position j of the UAV, based on sampling point χ s Calculate relative distance information relative azimuth and relative elevation angle but

[0028] Based on m sigma sampling points and Z s To obtain relative measurement information z ij The mean and covariance are expressed as follows:

[0029]

[0030] in,

[0031] Based on relative measurement information z ij The mean and variance are used to calculate the linearization parameter A of the relative measurement information. ij b ij and Ω ij Its expression is:

[0032] A ij =ω T (Λ ij) -1

[0033]

[0034] Ω ij =Φ-A ij Λ ij A ij T

[0035] Then the relative measurement information z ij It can be linearized as follows:

[0036]

[0037] in, Λ i Λ j Let be the covariance matrix of the UAV at positions i and j. To obey The zero-mean Gaussian distribution, To obey The zero-mean Gaussian distribution;

[0038] Based on relative measurement information z ij Define the linearization factor v ij Its expression is:

[0039]

[0040] The linearization factor v of the relative measurement information between UAV i and UAV j is calculated. ij ;

[0041] Repeat the above process until the relative measurement information between all drones in the cluster is linearized.

[0042] Furthermore, the implementation process of step (5) is as follows:

[0043] Based on the confidence propagation of the position covariance Λ of the drone i to be located and the reference drone j, the position covariance Λ before the update is made. i Λ j and linearization factor v ij Calculate the joint conditional mean square error matrix Its expression is:

[0044]

[0045] in:

[0046]

[0047] Based on location covariance as well as Calculate the conditional mean square error ω that is collaboratively reduced between the UAV i to be located and the reference UAV j. ij :

[0048]

[0049] Furthermore, the implementation process of step (6) is as follows:

[0050] (61) If the number of iterations for linearization of the posterior game is 1, the conditional mean square error of the drone i to be located and the reference drone j to be reduced collaboratively is... Sort from largest to smallest, and select ω. ij >0 corresponds to the first k drones Constructing a new regional collaborative set of drones All drones in the set and the drone i to be located form a new collaborative network structure, and step (8) is executed directly;

[0051] (62) If the number of iterations for linearization of the posterior game is greater than 1, then... Sort the data from largest to smallest, remove values ​​less than zero, and obtain the sorted vector ω. ij-sorted =[ω1,ω2,...,ω n ], where ω1>ω2>...>ω n >0;

[0052] (63) The benchmark drone Its in ω ij-sorted If there is a maximum value, it is merged into the regional collaborative set. Its expression is:

[0053]

[0054] (64) Based on the regional collaborative set For drones Its regional collaborative set The conditional mean square error ω is reduced to the minimum. ij Remove it from the regional collaborative set Separating from the middle yields a new set of regional cooperative sets. All drones in the set form a new collaborative network structure with drone i. According to (63) and (64), the collaborative set is in the optimal configuration, the network structure is in the simplest state, and the total number of collaborative drones is no greater than k.

[0055] Furthermore, the implementation process of step (7) is as follows:

[0056] (71) Cost function C i(n) is modeled as an increasing function relative to the number of cooperating drones n, n≤k, and its expression is:

[0057]

[0058] Among them, a i To increase the minimum cooperative benefit required for a collaborative drone, a i =10, where n is the number of cooperating drones in the cooperative set of drone i. For drone i collaborative area r i The total number of all benchmark drones in the country;

[0059] (72) Based on the cooperative set N →i Calculate the cost function C corresponding to the regional collaborative set that has not undergone merging, separation, and updating. i (n), whose expression is:

[0060]

[0061] Based on the reduced conditional mean square error ω of inter-UAV collaboration ij and cost function C i (n), calculate the utility function U corresponding to the region collaborative set that has not undergone merging, separation, and updating. i (G):

[0062]

[0063] (73) Based on the cooperative set Calculate the cost function corresponding to the regional collaborative set after merging, separating, and updating.

[0064]

[0065] Based on the reduced conditional mean square error ω of inter-UAV collaboration ij and cost function Calculate the utility function corresponding to the regional collaborative set after merging, separating, and updating.

[0066]

[0067] (74) Compare the utility functions obtained in (72) and (73), if Then the region cooperative set corresponding to the drone i to be located is updated to The regional collaborative network structure should be reorganized; otherwise, the original regional collaborative set should be retained. and cooperative network structure; until the updated cooperative set of drone i. It has the highest utility function, and the network structure is in its simplest state.

[0068] Furthermore, the implementation process of step (8) is as follows:

[0069] (81) Reference UAV The message passing factor μ is used to communicate with the drone i to be located. j→i The expression for correcting one's own position estimate by transmitting position beliefs is as follows:

[0070] μ j→i (X i )∝N(α j→i ,Γ j→i )

[0071] in R ij The relative measurement noise covariance matrix;

[0072] (82) If the set of cooperative relationships of the UAV i to be located is... There is only one drone inside. Based on message passing factor μ j→i For N(X) i ,Λ i By applying Kalman filtering, the mean of the accurate position estimate of the UAV i to be located is obtained. Covariance Matrix

[0073] (83) If the initial cooperative relationship set of the UAV i to be located is... When there are multiple drones inside, the drones The message passing factor to the drone i to be located is μ p→i The mean of the estimated position of the drone i to be located Covariance Matrix It can be expressed by the following formula:

[0074]

[0075] pass The Kalman filter continuously updates the position estimate of the drone i to be located;

[0076] (84) Repeat (81) to (83) until the positions of all drones in the cluster are estimated. Covariance Matrix Update complete;

[0077] (85) Based on the updated UAV positions and covariances, calculate the joint posterior probability density function between each pair of cooperative UAVs, the expression of which is:

[0078]

[0079] in, Let the mean of the joint posterior probability estimate for drones i and j be given. Let be the joint covariance matrix. Based on the linearization parameter A of the relative measurement information ij b ij Ω ij and relative measurement information z ij The relative measurement noise covariance matrix R ij ,right and Perform Kalman filtering to update and obtain the mean of the joint posterior probability estimates for UAV i and UAV j. Covariance

[0080] (86) iteration = iteration + 1. If iteration equals the preset value, t = t + 1.

[0081] Beneficial Effects: Compared with existing technologies, the beneficial effects of this invention are as follows: This invention enables low-precision UAVs to adaptively select the UAV with the richest information in the region for cooperative positioning, rather than relying on all high-precision UAVs in the cooperative region; at the same time, it can sever the connection between faulty UAVs and low-precision UAVs, select the optimal connection strategy structure, and significantly reduce computational complexity and network traffic; compared with traditional cooperative positioning methods, this invention divides large clusters into small clusters in different regions, and the UAV to be positioned only needs to receive navigation information from UAVs in its own region. This regionalized connection strategy enhances the fault tolerance of the system, and significantly reduces computational complexity and network traffic while ensuring the navigation and positioning accuracy of the UAV cluster, making it suitable for practical applications. Attached Figure Description

[0082] Figure 1 This is a flowchart of the present invention;

[0083] Figure 2 This is a traditional collaborative connection diagram for drone swarms.

[0084] Figure 3 A diagram illustrating the collaborative connection relationships in a drone swarm game;

[0085] Figure 4 Low-precision UAV error box plots for different numbers of coordinated operations;

[0086] Figure 5 The computation time corresponds to different numbers of collaborations. Detailed Implementation

[0087] The present invention will now be described in further detail with reference to the accompanying drawings.

[0088] like Figure 1As shown, this invention proposes a large-scale UAV swarm regional cooperative positioning method based on network-based game theory, comprising the following steps:

[0089] Step 1: Obtain the position, velocity, attitude of the UAV in the geodetic coordinate system, as well as the relative measurement information between UAV clusters, including relative distance information and relative angle information.

[0090] Define drone swarms as:

[0091] V=A∪B,A={1,...a},B={1,...,b}

[0092] The dataset includes 'a' reference UAVs and 'b' UAVs to be located, where A is the set of all reference UAVs and B is the set of all UAVs to be located, and a + b = 1000. The reference UAVs obtain their longitude, latitude, and altitude using their high-precision sensors and GNSS, while the UAVs to be located rely solely on their inertial navigation systems and require the assistance of the reference UAVs for positioning.

[0093] The locations of drones i, i∈B and j, j∈A are X respectively. i =(x i ,y i ,z i ), X j =(x j ,y j ,z j The relative measurement information between the two drones is z. ij Its expression is:

[0094]

[0095] Where, d ij Let θ be the relative distance between drone i and drone j. ij Let i be the relative azimuth angle between UAV i and UAV j. Let be the relative altitude angle between UAV i and UAV j.

[0096] Step 2, dividing the UAV cooperative set based on circular coverage, includes the following specific steps:

[0097] Step (2-1): Set the initial flight time of the cluster to t0 = 1, the initial value of the posterior game linearization iteration to iteration = 1, and the maximum number of collaborations for each drone to be k.

[0098] Step (2-2): Given a graph G = (V, E), where E represents the connections between UAVs, and the communication range is r with UAV i as the center. iDefine a circular region with a radius, and all reference UAVs within this region constitute the initial cooperative UAV set of UAV i.

[0099] Step (2-3) involves examining the drone i and drone i obtained in step (1-2). The relative distance d between ij Sort, select relative distance d ij The smallest k drones form a new cooperative set.

[0100] Step 3: Linearize the relative measurement information between UAVs using linear regression and calculate the linearization factor, including the following specific steps:

[0101] Step (3-1), use the Sigma point method to analyze the measurement information. Perform linear regression decomposition, selecting m sigma sampling points χ1,...,χ based on the UAV's position mean and covariance. m and weights ω1,...,ω m Sampling points Let i be the s-th sampling point at position i of the drone. Let be the s-th sampling point at position j of the UAV, based on sampling point χ s Calculate relative distance information relative azimuth and relative elevation angle but

[0102] Based on m sigma sampling points and Z s To obtain relative measurement information z ij The mean and covariance are expressed as follows:

[0103]

[0104] in,

[0105] Step (3-3): Based on the relative measurement information z obtained in step (3-2) ij The mean and variance are used to calculate the linearization parameter A of the relative measurement information. ij b ij and Ω ij Its expression is:

[0106] A ij =ψ T (Λ ij ) -1

[0107]

[0108] Ω ij =Φ-A ij Λ ij A ij T

[0109] Then the relative measurement information z ij It can be linearized as follows:

[0110]

[0111] in, Λ i Λ j Let be the covariance matrix of the UAV at positions i and j. To obey The zero-mean Gaussian distribution, To obey It follows a zero-mean Gaussian distribution.

[0112] Step (3-4): Based on the relative measurement information z obtained in step (3-3) ij Define the linearization factor v ij Its expression is:

[0113]

[0114] The linearization factor v of the relative measurement information between UAV i and UAV j is calculated. ij Step (3-5): Repeat steps (3-1) to (3-4) until the relative measurement information between all UAVs in the cluster is linearized.

[0115] Step 4: Execute steps (5) to (8) based on the judgment condition of the auto-incrementing variable time t, including the following specific steps:

[0116] In step (4-1), if the iteration time t = 1, then first execute step (8) to obtain the covariance matrix of all UAVs. Then execute steps (5) to (7) to calculate the reduction in conditional mean square error ω after UAV cooperative positioning. ij Calculate the cost function C i (n) and utility function U i (G), Update the drone regional cooperative set

[0117] In step (4-2), if the iteration time t≠1, then directly execute steps (5) to (8) to calculate the reduced conditional mean square error ω after UAV cooperative localization. ij Calculate the cost function C i(n) and utility function U i (G), Update the drone regional cooperative set

[0118] Step 5, calculate the conditional mean square error reduction due to UAV collaboration, including the following specific steps:

[0119] Step (5-1) updates the position covariance Λ before confidence propagation based on UAV i and UAV j. i Λ j And the linearization factor v obtained according to step (3-4) ij Calculate the joint conditional mean square error matrix Its expression is:

[0120]

[0121] in,

[0122]

[0123] Step (5-2), based on the updated position covariance of UAV i and UAV j obtained in step (8) and the joint conditional mean square error matrix obtained from step (5-1) Calculate the conditional mean square error ω reduced by UAV i and UAV j in a coordinated manner. ij Its expression is:

[0124]

[0125] Step 6: Optimize the set of cooperative regions for the UAVs to be located based on game theory rules, and construct a new network structure, including the following specific steps:

[0126] Step (6-1): If the posterior game linearization iteration number is 1, then the conditional mean square error of the joint reduction of UAV i and UAV j obtained in step (5-2) is calculated. Sort from largest to smallest, and select ω. ij >0 corresponds to the first k drones Constructing a new regional collaborative set of drones All drones in the set form a new collaborative network structure with drone i. Skip step (6-2) to step (7) and directly execute step (8).

[0127] Step (6-2): If the number of iterations for linearization of the posterior game is greater than 1, then the conditional mean square error of the joint reduction of UAV i and UAV j obtained in step (5-2) is calculated. Sort the data from largest to smallest, remove values ​​less than zero, and obtain the sorted vector ω.ij-sorted =[ω1,ω2,...,ω n ], where ω1>ω2>...>ω n >0.

[0128] Step (6-3), take the drone Its in ω ij-sorted If there is a maximum value, it is merged into the regional collaborative set. Its expression is:

[0129]

[0130] Step (6-4), based on the regional collaborative set For drones Its regional collaborative set The conditional mean square error ω is reduced to the minimum. ij Remove it from the regional collaborative set Separating from the middle yields a new set of regional cooperative sets. All drones in the set form a new collaborative network structure with drone i. According to steps (6-3) and (6-4), the collaborative set is in the optimal configuration, the network structure is in the simplest state, and the total number of collaborative drones is no greater than k.

[0131] Step 7: Calculate the cost function and utility function of the UAV cooperative set, modify the UAV cooperative connection relationships, and reorganize the cooperative network structure, including the following specific steps:

[0132] Step (7-1), cost function C i (n) is modeled as an increasing function relative to the number of cooperating drones n, n≤k, and its expression is:

[0133]

[0134] Among them, a i To increase the minimum cooperative benefit required for a collaborative drone, a i =10, where n is the number of cooperating drones in the cooperative set of drone i. For drone i collaborative area r i The total number of all benchmark drones in the country.

[0135] Step (7-2), based on the cooperative set N obtained in step (2-3) →i Calculate the cost function C corresponding to the regional collaborative set that has not undergone merging, separation, and updating. i (n), whose expression is:

[0136]

[0137] The conditional mean square error ω of inter-UAV cooperation reduced based on step (5-2) ij and cost function C i (n), calculate the utility function U corresponding to the region collaborative set that has not undergone merging, separation, and updating. i (G), whose expression is:

[0138]

[0139] Step (7-3) involves using the collaborative set obtained in step (6-4). Calculate the cost function corresponding to the regional collaborative set after merging, separating, and updating. Its expression is:

[0140]

[0141] The conditional mean square error ω of inter-UAV cooperation reduced based on step (5-2) ij and cost function Calculate the utility function U corresponding to the regional collaborative set after merging, separating, and updating. i + (G), whose expression is:

[0142]

[0143] Step (7-4): Compare the utility functions obtained in steps (7-2) and (7-3). If... Then the region cooperative set corresponding to UAV i is updated to The regional collaborative network structure should be reorganized; otherwise, the original regional collaborative set should be retained. And collaborative network structure.

[0144] Step (7-5), repeat steps (6-2) to (7-4) until the updated cooperative set of UAV i. It has the highest utility function, and the network structure is in its simplest state.

[0145] Step 8: Update and fuse the UAV position status in each sub-region according to the belief propagation algorithm, including the following specific steps:

[0146] Step (8-1), Drone The message passing factor μ is used to communicate with drone i. j→i The expression for correcting one's own position estimate by transmitting position beliefs is as follows:

[0147] μ j→i (X i )∝N(α j→i ,Γ j→i )

[0148] in R ij This is the relative measurement noise covariance matrix.

[0149] Step (8-2), if the set of cooperative relationships of UAV i There is only one drone inside. Based on the message passing factor μ between drone i and drone j j→i For N(X) i ,Λ i By applying Kalman filtering, the mean of the accurate position estimate of UAV i is obtained. Covariance Matrix

[0150] Step (8-3), if the initial cooperative relationship set of UAV i When there are multiple drones inside, the drones The message passing factor to drone i is μ p→i Mean position estimate of drone i Covariance Matrix It can be expressed by the following formula:

[0151]

[0152] pass The Kalman filter continuously updates the position estimate of UAV i.

[0153] Step (8-4): Repeat steps (8-1) through (8-3) until the positions of all drones in the cluster are estimated. Covariance Matrix Update complete.

[0154] Step (8-5): Based on the updated UAV positions and covariance, calculate the joint posterior probability density function between each pair of cooperative UAVs, the expression of which is:

[0155]

[0156] in, Let the mean of the joint posterior probability estimate for drones i and j be given. Let be the joint covariance matrix. The linearization parameter A based on the relative measurement information obtained in step (3-3) ij b ij Ω ij and relative measurement information z ij The relative measurement noise covariance matrix R ij ,right and Perform Kalman filtering to update and obtain the mean of the joint posterior probability estimates for UAV i and UAV j. Covariance

[0157] Step (8-6), iteration = iteration + 1. If iteration equals the preset value, t = t + 1.

[0158] Step 9: Repeat steps 1 to 8 to iteratively update the drone cluster positioning information until the iteration time t equals the preset time.

[0159] To verify the effectiveness of this invention, digital simulation analysis was conducted. The simulation used 1000 drones, including 600 high-precision drones and 400 low-precision drones. Figure 2 This is a traditional collaborative connection graph. Figure 3 This is a graph showing the collaborative connections in a game theory context. Figure 4 Box plots of low-precision UAV errors corresponding to different numbers of coordinated operations. Figure 5 The computation time corresponds to different numbers of collaborations. Figure 2 and Figure 3 The connection relationship between two low-precision drones from a drone swarm was demonstrated. Figure 2 and Figure 3 It can be seen that traditional cooperative connection methods result in complex cooperative connection networks with a large number of connections and high communication overhead between UAVs, while game-theoretic cooperative connection methods result in simpler cooperative connection networks with fewer connections and lower communication overhead between UAVs. Figure 4 and Figure 5 As can be seen, compared with traditional cooperative connection methods, the method of this invention, when each low-precision UAV collaborates with only one high-precision UAV, results in a positioning accuracy loss of only 1.84% and a computational efficiency improvement of 89.3%. Compared with traditional cooperative connection methods, when the method of this invention allows each low-precision UAV to collaborate with a maximum of three high-precision UAVs, the positioning error loss is 0.35% and the computational efficiency is improved by 81.9%. As the number of collaborating UAVs increases, the rate of decrease in positioning error slows down, while the computational efficiency still significantly improves. Therefore, it is evident that when increasing the size of the UAV swarm, using the method of this invention to divide the collaborative area and utilize network-based game theory to select the collaborative connection strategy can significantly improve the navigation efficiency of the UAV swarm, reduce unnecessary information transmission, improve navigation real-time performance, and simultaneously ensure positioning accuracy, demonstrating significant application value.

[0160] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for regional collaborative positioning of large-scale UAV swarms based on network-based game theory, characterized in that, Includes the following steps: (1) Obtain the position, velocity, attitude of the UAV in the geodetic coordinate system and the relative measurement information between UAV clusters; (2) Based on the circular coverage area, the UAV collaborative set is divided; (3) Linearize the relative measurement information between UAVs using the linear regression method and calculate the linearization factor; (4) Execute steps (5) to (8) according to the judgment condition of iteration time t; if iteration time t = 1, execute step (8) first, then execute steps (5) to (7); if iteration time t ≠ 1, execute steps (5) to (8) directly. (5) Calculate the conditional mean square error reduced by UAV collaboration; (6) Optimize the set of cooperative regions of the UAVs to be located based on game theory rules to construct a new network structure; (7) Calculate the cost function and utility function of the UAV cooperative set, change the UAV cooperative connection relationship, and reorganize the cooperative network structure; (8) The position status of UAVs in each sub-region is updated and fused according to the belief propagation algorithm; (9) Repeat steps (1) to (8) to iteratively update the drone cluster positioning information until the iteration time t equals the preset time.

2. The method for large-scale UAV swarm regional collaborative positioning based on network-formed game theory as described in claim 1, characterized in that, The implementation process of step (1) is as follows: The drone swarm consists of a reference drone (a) and a drone to be located (b), as follows: V=A∪B,A={1,...a},B={1,...,b} Where A is the set of all reference UAVs and B is the set of all UAVs to be located. The reference UAVs obtain their own longitude, latitude and altitude based on the high-precision sensor devices and GNSS they are equipped with. The drone to be located relies solely on its inertial navigation system to obtain its own position information, and requires a reference drone for assistance in positioning. The positions of the UAV to be located, i∈B, and the reference UAV, j∈A, are X and X, respectively. i =(x i ,y i ,z i ), X j =(x j ,y j ,z j The relative measurement information between the two drones is z. ij : Where, d ij Let θ be the relative distance between drone i and drone j. ij Let i be the relative azimuth angle between UAV i and UAV j. Let be the relative altitude angle between UAV i and UAV j.

3. The method for large-scale UAV swarm regional collaborative positioning based on network-formed game theory as described in claim 1, characterized in that, The implementation process of step (2) is as follows: Set the initial flight time of the swarm to t0 = 1, the initial value of the posterior game linearization iteration to iteration = 1, and the maximum number of collaborations per drone to k. Given a graph G = (V, E), where E represents the connections between drones, and the communication range is r centered on the drone i to be located. i Define a circular region with a radius, and all reference UAVs within this region constitute the initial cooperative UAV set of UAV i. The target drone i and the reference drone The relative distance d between ij Sort, select relative distance d ij The smallest k drones form a new cooperative set.

4. The method for large-scale UAV swarm regional collaborative positioning based on network-formed game theory as described in claim 1, characterized in that, The implementation process of step (3) is as follows: Using the Sigma point method to analyze measurement information Perform linear regression decomposition, selecting m sigma sampling points χ1,…,χ based on the UAV's position mean and covariance. m and weights ω1,…,ω m Sampling points Let i be the s-th sampling point at position i of the drone. Let be the s-th sampling point at position j of the UAV, based on sampling point χ s Calculate relative distance information relative azimuth and relative elevation angle but Based on m sigma sampling points and Z s To obtain relative measurement information z ij The mean and covariance are expressed as follows: in, Based on relative measurement information z ij The mean and variance are used to calculate the linearization parameter A of the relative measurement information. ij b ij and Ω ij Its expression is: A ij =ψ T (L ij ) -1 Oh ij =Φ-A ij L ij A ij T Then the relative measurement information z ij It can be linearized as follows: in, Λ i Λ j Let be the covariance matrix of the UAV at positions i and j. To obey The zero-mean Gaussian distribution, To obey The zero-mean Gaussian distribution; Based on relative measurement information z ij Define the linearization factor v ij Its expression is: The linearization factor v of the relative measurement information between UAV i and UAV j is calculated. ij ; Repeat the above process until the relative measurement information between all drones in the cluster is linearized.

5. The method for large-scale UAV swarm regional collaborative positioning based on network-based game theory according to claim 1, characterized in that, The implementation process of step (5) is as follows: Based on the confidence propagation of the position covariance Λ of the drone i to be located and the reference drone j, the position covariance Λ before the update is made. i Λ j and linearization factor v ij Calculate the joint conditional mean square error matrix Its expression is: in: Based on location covariance as well as Calculate the conditional mean square error ω that is collaboratively reduced between the UAV i to be located and the reference UAV j. ij :

6. The method for large-scale UAV swarm regional collaborative positioning based on network-formed game theory according to claim 1, characterized in that, The implementation process of step (6) is as follows: (61) If the number of iterations for linearization of the posterior game is 1, the conditional mean square error of the drone i to be located and the reference drone j to be reduced collaboratively is... Sort from largest to smallest, and select ω. ij >0 corresponds to the first k drones Constructing a new regional collaborative set of drones All drones in the set and the drone i to be located form a new collaborative network structure, and step (8) is executed directly; (62) If the number of iterations for linearization of the posterior game is greater than 1, then... Sort the data from largest to smallest, remove values ​​less than zero, and obtain the sorted vector ω. ij-sorted =[ω1,ω2,...,ω n ], where, ω1>ω2>...>ω n >0; (63) The benchmark drone Its in ω ij-sorted If there is a maximum value, it is merged into the regional collaborative set. Its expression is: (64) Based on the regional collaborative set For drones Its regional collaborative set The conditional mean square error ω is reduced to the minimum. ij Remove it from the regional collaborative set Separating from the middle yields a new set of regional cooperative sets. All drones in the set form a new collaborative network structure with drone i. According to (63) and (64), the collaborative set is in the optimal configuration, the network structure is in the simplest state, and the total number of collaborative drones is no greater than k.

7. The method for large-scale UAV swarm regional collaborative positioning based on network-formed game theory according to claim 1, characterized in that, The implementation process of step (7) is as follows: (71) Cost function C i (n) is modeled as an increasing function relative to the number of cooperating drones n, n≤k, and its expression is: Among them, a i To increase the minimum cooperative benefit required for a collaborative drone, a i =10, where n is the number of cooperating drones in the cooperative set of drone i. For drone i collaborative area r i The total number of all benchmark drones in the country; (72) Based on the cooperative set N →i Calculate the cost function C corresponding to the regional collaborative set that has not undergone merging, separation, and updating. i (n), whose expression is: Based on the reduced conditional mean square error ω of inter-UAV collaboration ij and cost function C i (n), calculate the utility function U corresponding to the region collaborative set that has not undergone merging, separation, and updating. i (G): (73) Based on the cooperative set Calculate the cost function corresponding to the regional collaborative set after merging, separating, and updating. Based on the reduced conditional mean square error ω of inter-UAV collaboration ij and cost function Calculate the utility function corresponding to the regional collaborative set after merging, separating, and updating. (74) Compare the utility functions obtained in (72) and (73), if Then the region cooperative set corresponding to the drone i to be located is updated to The regional collaborative network structure should be reorganized; otherwise, the original regional collaborative set should be retained. and cooperative network structure; until the updated cooperative set of drone i. It has the highest utility function, and the network structure is in its simplest state.

8. The method for large-scale UAV swarm regional collaborative positioning based on network-formed game theory according to claim 1, characterized in that, The implementation process of step (8) is as follows: (81) Reference UAV The message passing factor μ is used to communicate with the drone i to be located. j→i The expression for correcting one's own position estimate by transmitting position beliefs is as follows: m j→i (X i )∝N(α j→i ,C j→i ) in R ij The relative measurement noise covariance matrix; (82) If the set of cooperative relationships of the UAV i to be located is... There is only one drone inside. Based on message passing factor μ j→i For N(X) i ,Λ i By applying Kalman filtering, the mean of the accurate position estimate of the UAV i to be located is obtained. Covariance Matrix (83) If the initial cooperative relationship set of the UAV i to be located is... When there are multiple drones inside, the drones The message passing factor to the drone i to be located is μ p→i The mean of the estimated position of the drone i to be located Covariance Matrix It can be expressed by the following formula: pass The Kalman filter continuously updates the position estimate of the drone i to be located; (84) Repeat (81) to (83) until the positions of all drones in the cluster are estimated. Covariance Matrix Update complete; (85) Based on the updated UAV positions and covariances, calculate the joint posterior probability density function between each pair of cooperative UAVs, the expression of which is: in, Let the mean of the joint posterior probability estimate for drones i and j be given. Let be the joint covariance matrix. Based on the linearization parameter A of the relative measurement information ij b ij Ω ij and relative measurement information z ij The relative measurement noise covariance matrix R ij ,right and Perform Kalman filtering to update and obtain the mean of the joint posterior probability estimates for UAV i and UAV j. Covariance (86) iteration = iteration + 1. If iteration equals the preset value, t = t + 1.

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