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

Abstract

The invention discloses a large-scale unmanned aerial vehicle cluster regional cooperative positioning method based on a network formation game, which comprises the following steps: firstly, carrying out regional cooperative navigation on a large-scale unmanned aerial vehicle cluster, then finding a cooperative unmanned aerial vehicle set with the maximum utility through a game rule, selecting an optimal connection strategy network structure, and carrying out cooperative navigation on the large-scale unmanned aerial vehicle cluster. The low-precision unmanned aerial vehicle can adaptively select the high-precision unmanned aerial vehicle in the region for cooperative positioning; and finally, positioning the low-precision unmanned aerial vehicle by using a belief propagation method according to the cooperative unmanned aerial vehicle set updated each time. According to the method, the scale of the unmanned aerial vehicle cluster is expanded, the large-scale cluster is subjected to region division, and the cooperative unmanned aerial vehicle set of the to-be-positioned unmanned aerial vehicles in each region is optimized through a network formation game method, so that the to-be-positioned unmanned aerial vehicles only need to receive navigation information in the cooperative region and adaptively select the optimal cooperative unmanned aerial vehicle; therefore, the network connection complexity is reduced, the effectiveness of the unmanned aerial vehicle is maximized, and the positioning precision of the unmanned aerial vehicle cluster is ensured.

Description

Technical Field

[0001] The present invention belongs to the field of positioning and navigation technology, and specifically relates to a large-scale unmanned aerial vehicle cluster regional collaborative positioning method based on network formation game. Background Art

[0002] In recent years, drone swarms have been widely used in civil and military fields. As the application scope of drones expands and the number of drone swarms increases, large-scale drone coordinated operations will become an important development direction in the future. Large-scale drone swarms can flexibly adjust the distribution of drones as needed to adapt to different mission requirements and environmental changes. Compared with small swarms, large-scale drone swarms can share risk costs, and other drones can continue to perform tasks when some drones are damaged.

[0003] As the number of clusters increases, there are challenges in managing and controlling large-scale drones. Traditional collaborative strategy positioning methods have a large number of collaborative connections, and the complexity of collaborative computing increases exponentially, resulting in problems such as long navigation and positioning time and serious network congestion. Summary of the invention

[0004] Purpose of the invention: The present invention proposes a large-scale UAV cluster regional collaborative positioning method based on network formation game, which adaptively finds the optimal collaborative connection selection strategy within a single UAV area, divides the large cluster into small clusters in different regions, effectively reduces the computational complexity and communication overhead while ensuring navigation accuracy, and realizes efficient and accurate navigation and positioning in complex environments.

[0005] Technical solution: The large-scale UAV cluster regional collaborative positioning method based on network formation game described in the present 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 the UAV clusters;

[0007] (2) Divide the UAV cooperative set based on the circular coverage area;

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

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

[0010] (5) Calculate the conditional mean square error of UAV collaborative reduction;

[0011] (6) Optimize the cooperative area set of the unmanned aerial vehicles to be located based on the game rules and build a new network structure;

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

[0013] (8) Update and integrate the position status of drones in each sub-area based on the belief propagation algorithm;

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

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

[0016] The drone cluster includes a reference drone and b drones to be positioned, which are:

[0017] V=A∪B,A={1,...a},B={1,...,b}

[0018] Among them, A is the set of all reference drones, and B is the set of all drones to be positioned. The reference drones obtain their own longitude, latitude and altitude based on the high-precision sensor devices and GNSS they are equipped with; the drones to be positioned only rely on the inertial navigation system to obtain their own position information, and need the reference drones to assist in positioning;

[0019] The positions of the UAV to be located, i∈B, and the reference UAV j∈A are respectively X 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] Among them, d ij is the relative distance between UAV i and UAV j, θ ij is the relative azimuth between UAV i and UAV j, is 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 time of cluster flight t0 = 1, the initial value of the posterior game linearization iteration iteration = 1, and the maximum number of cooperation for each UAV is k;

[0024] Given a graph G = (V, E), E is the connection between drones, with the drone i to be located as the center and the communication range r i A circular area is defined with a radius of , and all the benchmark drones in this area constitute the initial cooperative drone set of drone i

[0025] Treating positioning drones and reference drones The relative distance d ij Sort and select relative distance d ij The smallest top k drones form a new collaborative set

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

[0027] Using the Sigma point method to measure information Perform linear regression decomposition and select m sigma sampling points χ1,...,χ according to the mean and covariance of the drone position m and weights ω1,...,ω m , where the sampling points is the sth sampling point at the position of UAV i, is the sth sampling point of the UAV j position, according to the sampling point χ s Calculate relative distance information Relative azimuth and relative altitude angle but

[0028] According to m sigma sampling points and Z s , obtain relative measurement information z ij The mean and covariance of are expressed as:

[0029]

[0030] in,

[0031] According to the relative measurement information z ij The mean and variance of the relative measurement information are calculated using the linearization parameter A ij , b ij and Ω ij , whose 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:

[0036]

[0037] in, Λ i , Λ j is the covariance matrix of the positions of drones i and j, To obey The zero-mean Gaussian distribution of To obey The zero-mean Gaussian distribution of

[0038] According to the relative measurement information z ij , define the linearization factor v ij , whose expression is:

[0039]

[0040] Calculate the linearization factor v of the relative measurement information between UAV i and UAV j 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] According to the position covariance Λ before the confidence propagation update of the UAV i to be located and the reference UAV j i ,Λ j and the linearization factor v ij , calculate the joint conditional mean square error matrix Its expression is:

[0044]

[0045] in:

[0046]

[0047] According to the position covariance as well as Calculate the conditional mean square error ω of the coordinated reduction of 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 of the posterior game linearization is 1, the conditional mean square error of the coordinated reduction of the positioning UAV i and the reference UAV j is Sort from large to small, select ω ij >0 corresponding to the first k drones Constitute a new regional collaborative collection of drones All drones in the set and the drone i to be located form a new collaborative network structure and directly execute step (8);

[0051] (62) If the number of linearized iterations of the posterior game is greater than 1, Sort from large to small, 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) Benchmark UAV Its ij-sorted There is a maximum value in Its expression is:

[0053]

[0054] (64) Based on regional coordination For drones Its regional collaborative collection There is a minimum reduced conditional mean square error ω ij , which is collected from the regional coordination Separate from the original data to obtain a new regional coordination set All drones in the set form a new collaborative network structure with drone i. According to (63) and (64), the collaborative set is guaranteed to be in the optimal composition, the network structure is in the simplest state, and the total number of collaborative drones is no more 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 cooperative UAVs n, n≤k, and its expression is:

[0057]

[0058] Among them, a i To increase the minimum cooperation benefit required for a cooperative UAV, a i =10, n is the number of cooperative drones in the cooperative set of drone i, The coordinated area r of UAV i i The number of all benchmark drones in the

[0059] (72) According to the collaborative set N →i , calculate the cost function C corresponding to the regional coordination set that has not been merged, separated and updated i (n), its expression is:

[0060]

[0061] According to the conditional mean square error ω reduced by the cooperation between drones ij And the cost function C i (n), calculate the utility function U corresponding to the regional coordination set that has not been merged, separated and updated i (G):

[0062]

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

[0064]

[0065] According to the conditional mean square error ω reduced by the cooperation between drones ij And the cost function Calculate the utility function corresponding to the regional coordination set after merging, separating and updating

[0066]

[0067] (74) Compare the utility functions obtained by (72) and (73). If Then the regional coordination set corresponding to the unmanned aerial vehicle i to be located is updated to The regional collaborative network structure is reorganized, otherwise the original regional collaborative set is retained and collaborative network structure; until the collaborative set after drone i is updated It has the largest utility function and the network structure is in the simplest state.

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

[0069] (81) Benchmark UAV The message transmission factor μ is used between the UAV i to be located. j→i The transferred position belief corrects the own position estimate, and its expression is:

[0070] μ j→i (X i )∝N(α j→i ,Γ j→i )

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

[0072] (82) If the cooperative relationship set of the unmanned aerial vehicle i to be located is There is only one drone inside According to the message passing factor μ j→i , for N(X i ,Λ i ) Apply Kalman filtering to obtain the accurate position estimate mean of the UAV i to be located and the covariance matrix

[0073] (83) If the initial cooperative relationship set of the UAV i to be located is When there are multiple drones in the The message transmission factor to the UAV i to be located is μ p→i , the estimated mean position of the UAV i to be located and the covariance matrix It is expressed by the following formula:

[0074]

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

[0076] (84) Repeat (81) to (83) until the position estimates of all drones in the cluster are and the covariance matrix Update completed;

[0077] (85) According to the updated UAV positions and covariances, the joint posterior probability density function between the two coordinated UAVs is calculated, and its expression is:

[0078]

[0079] in, is the joint posterior probability estimate mean of drone i and drone j, is the joint covariance matrix, let Linearization parameter A based on 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 filter update to obtain the mean of the joint posterior probability estimates of UAV i and UAV j and covariance

[0080] (86)iteration=iteration+1, if iteration is equal to the preset value, t=t+1.

[0081] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention enables low-precision UAVs to adaptively select the UAV with the most information in the area for collaborative positioning, rather than relying on all high-precision UAVs in the collaborative area; at the same time, it can cut off the connection between the faulty UAV and the low-precision UAV, select the optimal connection strategy structure, and significantly reduce the computational complexity and network traffic; compared with the traditional collaborative positioning method, the present invention divides the large cluster into small clusters in different areas, and the UAV to be positioned only needs to receive the navigation information of the UAVs in the area. This regionalized connection strategy enhances the fault tolerance of the system, significantly reduces the computational complexity and network traffic while ensuring the navigation and positioning accuracy of the UAV cluster, and is suitable for practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 is a flow chart of the present invention;

[0083] Figure 2 This is the traditional collaborative connection diagram of the drone cluster;

[0084] Figure 3 It is a cooperative connection diagram for the UAV cluster game;

[0085] Figure 4 It is the box plot of low-precision UAV error corresponding to different numbers of collaboration;

[0086] Figure 5 is the computation time corresponding to different numbers of collaborations. DETAILED DESCRIPTION

[0087] The present invention is further described in detail below with reference to the accompanying drawings.

[0088] like Figure 1As shown, the present invention proposes a large-scale UAV cluster regional collaborative positioning method based on network formation game, comprising the following steps:

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

[0090] Define the drone cluster as:

[0091] V=A∪B,A={1,...a},B={1,...,b}

[0092] It includes a reference drone and b drones to be positioned, where A is the set of all reference drones, B is the set of all drones to be positioned, and a+b=1000. The reference drone obtains its own longitude, latitude and altitude based on the high-precision sensor device and GNSS, while the drone to be positioned only relies on the inertial navigation system to obtain its own position information and needs the reference drone to assist in positioning.

[0093] The positions of drone i, i∈B and drone j, j∈A are X 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 , whose expression is:

[0094]

[0095] Among them, d ij is the relative distance between UAV i and UAV j, θ ij is the relative azimuth between UAV i and UAV j, is the relative altitude angle between UAV i and UAV j.

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

[0097] Step (2-1), set the initial time of cluster flight t0 = 1, the initial value of the posterior game linearization iteration iteration = 1, and the maximum number of cooperative units for each UAV is k.

[0098] Step (2-2), given a graph G = (V, E), E is the connection between drones, with drone i as the center and communication range r iA circular area is defined with a radius of , and all the benchmark drones in this area constitute the initial cooperative drone set of drone i

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

[0100] Step 3, linearizing the relative measurement information between drones using a linear regression method and calculating a linearization factor, includes the following specific steps:

[0101] Step (3-1), use the Sigma point method to calculate the measured information Perform linear regression decomposition and select m sigma sampling points χ1,...,χ according to the mean and covariance of the drone position m and weights ω1,...,ω m , where the sampling points is the sth sampling point at the position of UAV i, is the sth sampling point of the UAV j position, according to the sampling point χ s Calculate relative distance information Relative azimuth and relative altitude angle but

[0102] According to m sigma sampling points and Z s , obtain relative measurement information z ij The mean and covariance of are expressed as:

[0103]

[0104] in,

[0105] Step (3-3), based on the relative measurement information z obtained in step (3-2) ij The mean and variance of the relative measurement information are calculated using the linearization parameter A ij 、b ij and Ω ij , whose 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:

[0110]

[0111] in, Λ i , Λ j is the covariance matrix of the positions of drones i and j, To obey The zero-mean Gaussian distribution of To obey 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 , whose expression is:

[0113]

[0114] Calculate the linearization factor v of the relative measurement information between UAV i and UAV j ij ; Step (3-5), repeat steps (3-1) to (3-4) until the relative measurement information between all drones in the cluster is linearized.

[0115] Step 4, executing steps (5) to (8) according to the judgment condition of the self-increment variable time t, includes the following specific steps:

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

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

[0118] Step 5, calculating the conditional mean square error of UAV collaborative reduction, includes the following specific steps:

[0119] Step (5-1), update the position covariance Λ before the confidence propagation of 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 drone i and drone j obtained in step (8) And the joint conditional mean square error matrix obtained according to step (5-1) Calculate the conditional mean square error ω of the collaborative reduction of UAV i and UAV j ij , whose expression is:

[0124]

[0125] Step 6, based on the game rules, optimize the cooperative area set of the drones to be located and build a new network structure, including the following specific steps:

[0126] Step (6-1), if the number of iterations of the posterior game linearization is 1, the conditional mean square error of the coordinated reduction of UAV i and UAV j obtained in step (5-2) is Sort from large to small, select ω ij >0 corresponding to the first k drones Constitute a new regional collaborative collection of drones All drones in the set form a new collaborative network structure with drone i, skipping steps (6-2) to (7) and directly executing step (8).

[0127] Step (6-2), if the number of iterations of the posterior game linearization is > 1, the conditional mean square error of the coordinated reduction of UAV i and UAV j obtained in step (5-2) is Sort from large to small, remove values ​​less than zero, and obtain the sorted vector ωij-sorted =[ω1,ω2,...,ω n ], where ω1>ω2>...>ω n >0.

[0128] Step (6-3), place the drone Its ij-sorted There is a maximum value in Its expression is:

[0129]

[0130] Step (6-4), based on the regional collaborative collection For drones Its regional collaborative collection There is a minimum reduced conditional mean square error ω ij , which is collected from the regional coordination Separate from the original data to obtain a new regional coordination set 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 guaranteed to be in the optimal composition, the network structure is in the simplest state, and the total number of collaborative drones is no more than k.

[0131] Step 7, calculating the cost function and utility function of the UAV collaborative set, changing the UAV collaborative connection relationship, and reorganizing the collaborative 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 cooperative UAVs n, n≤k, and its expression is:

[0133]

[0134] Among them, a i To increase the minimum cooperation benefit required for a cooperative UAV, a i =10, n is the number of cooperative drones in the cooperative set of drone i, The coordinated area r of UAV i i The number of all baseline drones within.

[0135] Step (7-2), according to the collaborative set N obtained in step (2-3) →i , calculate the cost function C corresponding to the regional coordination set that has not been merged, separated and updated i (n), its expression is:

[0136]

[0137] The conditional mean square error ω of the cooperative reduction between drones obtained according to step (5-2) ij , and the cost function C i (n), calculate the utility function U corresponding to the regional coordination set that has not been merged, separated and updated i (G), its expression is:

[0138]

[0139] Step (7-3), based on 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 the cooperative reduction between drones obtained according to step (5-2) ij , and the cost function Calculate the utility function U corresponding to the regional collaborative set after merging, separating and updating i + (G), its expression is:

[0142]

[0143] Step (7-4), compare the utility functions obtained in step (7-2) and step (7-3), if Then the regional coordination set corresponding to UAV i is updated to The regional collaborative network structure is reorganized, otherwise the original regional collaborative set is retained and collaborative network structures.

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

[0145] Step 8, based on the belief propagation algorithm, the updated fusion of the position status of the UAVs in each sub-area is realized, including the following specific steps:

[0146] Step (8-1), drone The message transmission factor μ is used between drone i and drone i. j→i The transferred position belief corrects the own position estimate, and its expression is:

[0147] μ j→i (X i )∝N(α j→i ,Γ j→i )

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

[0149] Step (8-2), if the cooperative relationship set of drone i There is only one drone inside According to the message transmission factor μ between UAV i and UAV j j→i , for N(X i ,Λ i ) Apply Kalman filtering to obtain the accurate position estimate mean of UAV i and the covariance matrix

[0150] Step (8-3), if the initial collaborative relationship set of drone i is When there are multiple drones in the The message transmission factor to UAV i is μ p→i , the estimated mean position of UAV i and the covariance matrix It can be expressed by the following formula:

[0151]

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

[0153] Step (8-4), repeat steps (8-1) to (8-3) until the positions of all drones in the cluster are estimated. and the covariance matrix Update completed.

[0154] Step (8-5), based on the updated UAV positions and covariances, calculate the joint posterior probability density function between the two cooperative UAVs, which is expressed as:

[0155]

[0156] in, is the joint posterior probability estimate mean of drone i and drone j, is the joint covariance matrix, let The linearization parameter A of the relative measurement information obtained according to 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 filter update to obtain the mean of the joint posterior probability estimates of UAV i and UAV j and covariance

[0157] Step (8-6), iteration=iteration+1, if iteration is equal to the preset value, t=t+1.

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

[0159] In order to verify the effectiveness of the present invention, a digital simulation analysis is conducted, in which 1000 drones are used, including 600 high-precision drones and 400 low-precision drones. Figure 2 This is a traditional collaborative connection diagram. Figure 3 It is the game collaborative connection relationship diagram. Figure 4 It is the box plot of low-precision UAV error corresponding to different numbers of collaborations. Figure 5 is the computation time corresponding to different numbers of collaborations. Figure 2 and Figure 3 Two low-precision drones in the drone cluster are extracted to display the connection relationship. Figure 2 and Figure 3 It can be seen that the cooperative connection network relationship corresponding to the traditional cooperative connection method is complex, the number of connections is large, and the communication overhead between drones is large. The cooperative connection network relationship corresponding to the game cooperative connection is simple, the number of connections is small, and the communication overhead between drones is small. Figure 4 and Figure 5 It can be seen that compared with the traditional collaborative connection method, the positioning accuracy of the method of the present invention only loses 1.84% when each low-precision drone only cooperates with one high-precision drone, and the computing efficiency is improved by 89.3%. Compared with the traditional collaborative connection method, when the method of the present invention is used to make each low-precision drone cooperate with up to three high-precision drones, the positioning error loss is 0.35%, and the computing efficiency is improved by 81.9%. As the number of collaborations increases, the decline in positioning error slows down, while the computing efficiency is still significantly improved. It can be seen that when the scale of the drone cluster is increased, the method of the present invention is used to divide the collaborative area, and the network is used to form a game to select the collaborative connection strategy. After that, the navigation efficiency of the drone cluster can be significantly improved, unnecessary information transmission can be reduced, and the real-time performance of navigation can be improved. At the same time, the positioning accuracy is guaranteed, and it has good application value.

[0160] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A large-scale UAV cluster regional collaborative positioning method based on network formation game, characterized in that: The following steps are involved: (1) Obtain the position, velocity, attitude of the UAV in the geodetic coordinate system and the relative measurement information between the UAV clusters; (2) Divide the UAV cooperative set based on the circular coverage area; (3) Linearize the relative measurement information between UAVs using linear regression method and calculate the linearization factor; (4) Execute steps (5) to (8) according to the judgment condition of the iteration time t; if the iteration time t=1, first execute step (8), then execute steps (5) to (7); if the iteration time t≠1, directly execute steps (5) to (8); (5) Calculate the conditional mean square error of UAV collaborative reduction; (6) Optimize the cooperative area set of the unmanned aerial vehicles to be located based on the game rules and build a new network structure; (7) Calculate the cost function and utility function of the UAV collaborative set, change the UAV collaborative connection relationship, and reorganize the collaborative network structure; (8) Update and integrate the position status of drones in each sub-area based on the belief propagation algorithm; (9) Repeat steps (1) to (8) to iteratively update the positioning information of the drone cluster until the iteration time t is equal to the preset time.

2. According to the large-scale UAV cluster regional collaborative positioning method based on network formation game according to claim 1, it is characterized in that: The implementation process of step (1) is as follows: The drone cluster includes a reference drone and b drones to be positioned, which are: V=A∪B,A={1,...a},B={1,...,b} Among them, A is the set of all reference drones, and B is the set of all drones to be positioned. The reference drones obtain the longitude, latitude, and altitude of their own locations based on the high-precision sensor devices and GNSS they are equipped with; The UAV to be positioned only relies on the inertial navigation system to obtain its own position information and requires the reference UAV to assist in positioning; The positions of the UAV to be located, i∈B, and the reference UAV j∈A are respectively X 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 : Among them, d ij is the relative distance between UAV i and UAV j, θ ij is the relative azimuth between UAV i and UAV j, is the relative altitude angle between UAV i and UAV j.

3. According to the large-scale UAV cluster regional collaborative positioning method based on network formation game according to claim 1, it is characterized in that: The implementation process of step (2) is as follows: Set the initial time of cluster flight t0 = 1, the initial value of the posterior game linearization iteration iteration = 1, and the maximum number of cooperation for each UAV is k; Given a graph G = (V, E), E is the connection between drones, with the drone i to be located as the center and the communication range r i A circular area is defined with a radius of , and all the benchmark drones in this area constitute the initial cooperative drone set of drone i Treating positioning drones and reference drones The relative distance d ij Sort and select relative distance d ij The smallest top k drones form a new collaborative set 4. The method for large-scale UAV cluster regional collaborative positioning based on network formation game according to claim 1 is characterized in that: The implementation process of step (3) is as follows: Using the Sigma point method to measure information Perform linear regression decomposition and select m sigma sampling points χ1,…,χ according to the mean and covariance of the drone position m and weights ω1,…,ω m , where the sampling points is the sth sampling point at the position of UAV i, is the sth sampling point of the UAV j position, according to the sampling point χ s Calculate relative distance information Relative azimuth and relative altitude angle but According to m sigma sampling points and Z s , obtain relative measurement information z ij The mean and covariance of are expressed as: in, According to the relative measurement information z ij The mean and variance of the relative measurement information are calculated using the linearization parameter A ij , b ij and Ω ij , whose 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: in, Λ i , Λ j is the covariance matrix of the positions of drones i and j, To obey The zero-mean Gaussian distribution of To obey The zero-mean Gaussian distribution of According to the relative measurement information z ij , define the linearization factor v ij , whose expression is: Calculate the linearization factor v of the relative measurement information between UAV i and UAV j 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 cluster regional collaborative positioning based on network formation game according to claim 1 is characterized in that: The implementation process of step (5) is as follows: According to the position covariance Λ before the confidence propagation update of the UAV i to be located and the reference UAV j i ,Λ j and the linearization factor v ij , calculate the joint conditional mean square error matrix Its expression is: in: According to the position covariance as well as Calculate the conditional mean square error ω of the coordinated reduction of the UAV i to be located and the reference UAV j ij :

6. The method for large-scale UAV cluster regional collaborative positioning based on network formation game according to claim 1 is characterized in that: The implementation process of step (6) is as follows: (61) If the number of iterations of the posterior game linearization is 1, the conditional mean square error of the coordinated reduction of the positioning UAV i and the reference UAV j is Sort from large to small, select ω ij >0 corresponding to the first k drones Constitute a new regional collaborative collection of drones All drones in the set and the drone i to be located form a new collaborative network structure and directly execute step (8); (62) If the number of linearized iterations of the posterior game is greater than 1, Sort from large to small, remove values ​​less than zero, and obtain the sorted vector ω ij-sorted =[ω1,ω2,...,ω n ], where, ω1>ω2>...>ω n >0; (63) Benchmark UAV Its ij-sorted There is a maximum value in Its expression is: (64) Based on regional coordination For drones Its regional collaborative collection There is a minimum reduced conditional mean square error ω ij , which is collected from the regional coordination Separate from the original data to obtain a new regional coordination set All drones in the set form a new collaborative network structure with drone i. According to (63) and (64), the collaborative set is guaranteed to be in the optimal composition, the network structure is in the simplest state, and the total number of collaborative drones is no more than k.

7. The method for large-scale UAV cluster regional collaborative positioning based on network formation game according to claim 1 is 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 cooperative UAVs n, n≤k, and its expression is: Among them, a i To increase the minimum cooperation benefit required for a cooperative UAV, a i =10, n is the number of cooperative drones in the cooperative set of drone i, The coordinated area r of UAV i i The number of all benchmark drones in the (72) According to the collaborative set N →i , calculate the cost function C corresponding to the regional coordination set that has not been merged, separated and updated i (n), its expression is: According to the conditional mean square error ω reduced by the cooperation between drones ij And the cost function C i (n), calculate the utility function U corresponding to the regional coordination set that has not been merged, separated and updated i (G): (73) According to the collaborative set Calculate the cost function corresponding to the regional coordination set after merging, separating and updating According to the conditional mean square error ω reduced by the cooperation between drones ij And the cost function Calculate the utility function corresponding to the regional coordination set after merging, separating and updating (74) Compare the utility functions obtained by (72) and (73). If Then the regional coordination set corresponding to the unmanned aerial vehicle i to be located is updated to The regional collaborative network structure is reorganized, otherwise the original regional collaborative set is retained and collaborative network structure; until the collaborative set after drone i is updated It has the largest utility function and the network structure is in the simplest state.

8. The method for large-scale UAV cluster regional collaborative positioning based on network formation game according to claim 1 is characterized in that: The implementation process of step (8) is as follows: (81) Benchmark UAV The message transmission factor μ is used between the UAV i to be located. j→i The transferred position belief modifies the own position estimate, and its expression is: m j→i (X i )∝N(α j→i ,C j→i ) in R ij is the relative measurement noise covariance matrix; (82) If the cooperative relationship set of the unmanned aerial vehicle i to be located is There is only one drone inside According to the message passing factor μ j→i , for N(X i ,Λ i ) Apply Kalman filtering to obtain the accurate position estimate mean of the UAV i to be located and the covariance matrix (83) If the initial cooperative relationship set of the UAV i to be located is When there are multiple drones in the The message transmission factor to the UAV i to be located is μ p→i , the estimated mean position of the UAV i to be located and the covariance matrix It is expressed by the following formula: pass The secondary Kalman filter continuously updates the position estimate of the UAV i to be located; (84) Repeat (81) to (83) until the position estimates of all drones in the cluster are and the covariance matrix Update completed; (85) According to the updated UAV positions and covariances, the joint posterior probability density function between the two coordinated UAVs is calculated, and its expression is: in, is the joint posterior probability estimate mean of drone i and drone j, is the joint covariance matrix, let Linearization parameter A based on 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 filter update to obtain the mean of the joint posterior probability estimates of UAV i and UAV j and covariance (86)iteration=iteration+1, if iteration is equal to the preset value, t=t+1.

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