Unmanned aerial vehicle formation cooperative positioning method based on stochastic analysis in zero-trust scene

Abstract

The invention discloses an unmanned aerial vehicle formation cooperative positioning method based on stochastic analysis in a zero-trust scene. The method comprises the steps that each unmanned aerial vehicle calculates predicted motion state data; each unmanned aerial vehicle transmits the predicted motion state data to the updating stage of the own fusion center and the adjacent unmanned aerial vehicles; each unmanned aerial vehicle performs relative measurement on the adjacent unmanned aerial vehicles to obtain a measurement vector; each unmanned aerial vehicle detects the predicted motion state data transmitted by the adjacent unmanned aerial vehicle based on the measurement vector, and if the predicted motion state data is judged to be the predicted motion state data, subsequent operation is carried out; and each unmanned aerial vehicle performs data fusion updating on the predicted motion state data and predicted motion state data transmitted by the adjacent unmanned aerial vehicle based on the measurement vector to obtain state estimation in an updating stage. According to the invention, when the communication link of the unmanned aerial vehicle formation suffers from a malicious attack scene, a reliable and high-precision positioning result is provided for unmanned aerial vehicle formation control, and the flight safety of the unmanned aerial vehicle formation in a zero-trust scene is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of cooperative positioning of drone formations, and in particular to a method for cooperative positioning of drone formations based on random analysis in a zero-trust scenario. Background Art

[0002] With the rapid development of drone technology, drones are increasingly being used in a variety of fields, including military, civilian, and scientific research. However, when performing missions, drone fleets face numerous challenges in positioning accuracy, collaborative efficiency, and security, especially in complex and changing environments. Against this backdrop, the concept of zero-trust security has been introduced into drone collaborative positioning systems, becoming a new approach to addressing network security and positioning accuracy. The zero-trust security model effectively protects against potential internal and external threats, ensuring the security and stability of drone collaborative positioning systems. Through strict identity authentication and access control mechanisms, it prevents unauthorized access and data leakage, thereby ensuring data integrity and reliability, which helps improve the positioning accuracy and collaborative efficiency of drone collaborative positioning systems.

[0003] Existing UAV collaborative positioning methods mainly include extended Kalman filter algorithms, distributed Kalman filter algorithms, and autonomous positioning and mapping technologies. Among them, patent publication number CN117826866B discloses a multi-UAV collaborative positioning and formation control method based on UWB ranging. In a GNSS-denied environment without positioning systems such as GPS, this method calculates the relative position coordinates of multiple UAVs by solving the relative distance between them. Specifically, by obtaining the current inter-UAV distances to obtain a distance matrix, the relative position coordinates of multiple UAVs are uniquely determined in the leader-UAV system, thus achieving multi-UAV collaborative positioning in a GNSS-denied environment.

[0004] In the existing solutions mentioned above, cooperative drone positioning methods actually use the relative distances between drones to determine the relative position coordinates of multiple drones. Specifically, by obtaining the current inter-drone distances, a distance matrix is ​​generated, and the unique relative position coordinates of multiple drones in the leader-drone system are calculated. However, in harsh environments or those with limited communication, the measurement information and communication transmission between drones will be interfered with, resulting in inaccurate measurement data and reduced drone positioning accuracy. Summary of the Invention

[0005] The purpose of the present invention is to provide a drone formation collaborative positioning method based on random analysis in a zero-trust scenario, which incorporates the detection and judgment of communication loss or communication attack into the collaborative positioning of multiple drones, can reduce the drone's anti-attack capability in harsh environments, thereby improving the drone positioning accuracy.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] The UAV formation collaborative positioning method based on random analysis in a zero-trust scenario includes the following steps:

[0008] S1. Each drone calculates the predicted motion state data;

[0009] S2, each UAV transmits the predicted motion state data to its own fusion center and the adjacent UAVs;

[0010] S3, each UAV performs relative measurement on the adjacent UAV to obtain a measurement vector;

[0011] S4. Each UAV detects the predicted motion state data transmitted by the adjacent UAV based on the measurement vector and determines whether to continue transmitting the predicted motion state data for data fusion update. If the determination is no, the predicted motion state data of the UAV is used as the state estimate in the update phase. If the determination is yes, proceed to S5.

[0012] S5. Each UAV performs data fusion update on the predicted motion state data and the predicted motion state data transmitted by the adjacent UAVs based on the measurement vector to obtain a state estimate in the update stage.

[0013] Furthermore, in said S1, the motion state data is predicted The calculation is as follows:

[0014]

[0015] is the state vector of the drone in the last update phase, A i,k-1 is the state propagation matrix after linearization of the nonlinear function, B i,k-1 is the noise matrix, is the noise vector during the UAV flight.

[0016] Furthermore, the S1 also includes calculating the prediction covariance matrix of the drone and the predicted cross-covariance matrix

[0017]

[0018] is the prediction covariance matrix of the UAV in the last update phase, is the system noise covariance matrix, is the prediction mutual covariance matrix of the UAV in the last update phase, A j,k-1 is the state propagation matrix transmitted by adjacent UAVs at the previous moment.

[0019] Furthermore, the S2 also includes: the prediction covariance matrix of the drone and the predicted cross-covariance matrix The update phase transmitted to the fusion center will predict the covariance matrix Transmit to neighboring drones.

[0020] Furthermore, the S3 includes: S31, measuring the relative distance and azimuth angle between the UAV and the adjacent UAV; S32, constructing a relative distance-azimuth-height measurement model based on the UAV's flight pitch angle and the relative distance and azimuth angle between the UAV and the adjacent UAV, and obtaining the UAV's measurement vector Z ij,k =[x ij,k y ij,k z ij,k φ ij,k ] T , the relative distance-azimuth-altitude measurement model is as follows:

[0021]

[0022] d ij,k is the relative distance between the UAV and its neighboring UAVs, γ ij,k is the azimuth angle between the UAV and the adjacent UAV, γ ji,k is the relative azimuth angle of the UAV measured by the adjacent UAV, α ij,k is the flight pitch angle of the drone, x ij,k 、y ij,k 、z ij,k 、φ ij,k They are the x-axis relative coordinate, y-axis relative coordinate, z-axis relative coordinate and relative direction angle respectively;

[0023] Preferably, in S31, the relative distance and azimuth angle between the drone and adjacent drones are measured using an onboard sensor module of the drone.

[0024] Furthermore, in S4, a trust evaluator is set on the drone:

[0025]

[0026] λ ij,k is a binary decision variable of the trust evaluator, η ij,k is the threshold of the trust evaluator, Υ a ij,k is the pre-trigger condition of the trust evaluator, Z ij,k is the measurement vector of the UAV, It is the predicted motion state data of the drone Predicted status information transmitted to neighboring drones jointly estimated forecast measurement data;

[0027] When the binary decision variable λ of the trust evaluator ij,k = 0, the predicted motion state data of the drone is used As the optimal estimate in the update phase; otherwise, the predicted motion state data will continue to be transmitted for data fusion update.

[0028] Furthermore, in said S5, the state estimation of the update stage Through the state update equation we get:

[0029]

[0030] is the Kalman gain of the UAV.

[0031] Furthermore, the state estimation in the update phase and the posterior error covariance matrix of the update phase Associated, through the posterior error covariance matrix of the update stage Get the state estimate of the update phase The posterior error covariance matrix during the update phase The calculation is as follows:

[0032]

[0033] in:

[0034]

[0035] and H j,k denote the Jacobian matrix of the UAV and the Jacobian matrix of the adjacent UAVs, is the error vector of the prediction information, X i,k is the real motion state data of the drone, is the predicted motion state data of the adjacent UAV, R ij,k is the covariance matrix of the measurement noise, E(·) represents the expected value of two independent variables, ξ ij,k and are mutually independent random variables that obey the Bernoulli distribution, σ ij,k Indicates the error prediction state information transmitted by an adjacent UAV, The first mutual covariance matrix indicating the existence of attacks between adjacent drones, represents the mutual covariance matrix of normal communication between UAVs, The second mutual covariance matrix indicating the existence of attacks between adjacent drones, is the prior error covariance matrix of adjacent UAVs.

[0036] Furthermore, the predicted state information of the adjacent UAV Through modeling, we get:

[0037]

[0038] The prior error covariance matrix of the adjacent UAVs Through modeling, we get:

[0039]

[0040] is the predicted motion state data transmitted by the drone, ξ ij,k and are mutually independent random variables that obey the Bernoulli distribution, σ ij,k and ψ ij,k Represent the error prediction state information and error covariance matrix transmitted by an adjacent UAV respectively;

[0041] When ij,k =1, each UAV can normally receive the predicted motion state data and predicted covariance matrix of the adjacent UAVs in the UAV formation;

[0042] When ij,k =0 and When σ ij,k and ψ ij,k Tampering with the received predicted motion state data and predicted covariance matrix of adjacent drones in the drone formation;

[0043] When ij,k =0 and When , the UAV can no longer obtain any information from the adjacent UAVs in the UAV formation, and the predicted motion state data of the UAV is used as the state estimation in the update phase.

[0044] Furthermore, for the posterior error covariance matrix in the update phase and The correlation is unknown and the expected operation cannot be obtained The analytical solution for and The two vectors introduce the following inequality:

[0045]

[0046] Substitute the inequality into the posterior error covariance matrix in the update phase In the calculation formula, we get:

[0047]

[0048] in:

[0049] n1=1+ε1+ε2

[0050] n2=ε3+ε+4

[0051] n3=ε5+ε6

[0052]

[0053] Represents ξ ij,k =1, express The probability of Yes and expectations, is the ij,k and , ε1, ε2, ε3, ε4, ε5, ε6, ε7 are different values ​​corresponding to the substitution of inequalities;

[0054] Compute the posterior error covariance matrix The minimum upper limit of

[0055] Will Both sides Taking the derivative, we get:

[0056]

[0057] in:

[0058]

[0059] The Kalman gain Substitute into the state update equation to obtain the state estimate in the update phase

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] Each drone in the drone formation of the present invention has a local fusion center, and multiple local fusion centers construct a drone formation collaborative positioning architecture, thereby effectively reducing the dependence on the global fusion center and improving the robustness of the positioning architecture.

[0062] The present invention targets DoS attacks and FDI attacks that may occur in zero-trust scenarios. A trust evaluator is used to determine whether to use information transmitted by adjacent drones for location updates, thereby improving the robustness of the positioning architecture against high-intensity attacks.

[0063] The present invention establishes a collaborative positioning method based on random analysis on UAVs, fuses the measurement vectors and predicted motion state data of the UAVs and the predicted motion state data transmitted by adjacent UAVs, and realizes high-precision positioning of the UAV formation.

[0064] Compared with traditional distributed positioning methods, the present invention can provide reliable and high-precision positioning results for drone formation control when the communication link of the drone formation is subjected to malicious attacks, ensuring the flight safety of the drone formation in zero-trust scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0066] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0067] like Figure 1 As shown, the present invention provides a UAV formation collaborative positioning method based on random analysis in a zero-trust scenario, comprising the following steps:

[0068] S1. Each drone calculates the predicted motion state data;

[0069] S2, each UAV transmits the predicted motion state data to its own fusion center and the adjacent UAVs;

[0070] S3, each UAV performs relative measurement on the adjacent UAV to obtain a measurement vector;

[0071] S4. Each UAV detects the predicted motion state data transmitted by the adjacent UAV based on the measurement vector and determines whether to continue transmitting the predicted motion state data for data fusion update. If the determination is no, the predicted motion state data of the UAV is used as the state estimate in the update phase. If the determination is yes, proceed to S5.

[0072] S5. Each UAV performs data fusion update on the predicted motion state data and the predicted motion state data transmitted by the adjacent UAVs based on the measurement vector to obtain a state estimate in the update stage.

[0073] In S1, the predicted motion state data of the drone is obtained according to the kinematic model state equation and the internal sensor. The calculation is as follows:

[0074]

[0075] is the state vector of the drone in the last update phase, A i,k-1 is the state propagation matrix after linearization of the nonlinear function, B i,k-1 is the noise matrix, is the noise vector during the UAV flight.

[0076] During the UAV formation flight, the UAV state is mainly composed of position coordinates and attitude angles. i,k =[x i,k y i,k z i,k φ i,k ] T ,i=1,2,...,N is the state quantity of the i-th UAV, where (x i,k ,y i,k ,z i,k ) represents the absolute position coordinates of the i-th UAV, i.e., the real motion state data of the UAV, φ i,k Represents the heading angle of the i-th UAV. The state equation of the kinematic model of the UAV formation is expressed as follows:

[0077]

[0078] Δt represents the flight sampling interval of the UAV, v i,k-1 and ω i,k-1 They represent the linear velocity and angular velocity of the drone, respectively, which are measured by internal sensors. (x i,k-1 ,y i,k-1 ,z i,k-1 ) represents the absolute position coordinates of the i-th UAV at the last moment, and the formula can also be expressed as x i,k =f(x i,k-1 ,u i,k-1 ,w i,k-1 ).

[0079] The S1 also includes calculating the prediction covariance matrix of the drone and the predicted cross-covariance matrix

[0080]

[0081] is the prediction covariance matrix of the UAV in the last update phase, is the system noise covariance matrix, is the prediction mutual covariance matrix of the UAV in the last update phase, Aj,k-1 is the state propagation matrix transmitted by adjacent UAVs at the previous moment.

[0082] Drones will predict motion status data The update phase of the fusion center is passed to the other adjacent drones. Because the update phase of the drone requires the predicted state of the local drone, the drone will pass the predicted motion state data Prediction covariance matrix and the forecast cross-covariance matrix The update phase is passed to the fusion center. Other drones adjacent to the drone also need to use the predicted motion state data. and the forecast covariance matrix This will then also be passed on to neighboring drones.

[0083] The step S3 performs relative measurement of each UAV to its adjacent UAVs to obtain a measurement vector, specifically including:

[0084] S31. Measure the relative distance and azimuth angle between the UAV and the adjacent UAVs; preferably, use an onboard sensor module of the UAV to measure the relative distance and azimuth angle between the UAV and the adjacent UAVs.

[0085] S32, construct a relative distance-azimuth-height measurement model based on the flight pitch angle of the UAV and the relative distance and azimuth angle between the UAV and the adjacent UAV, and obtain the measurement vector Z of the UAV ij,k =[x ij,k y ij,k z ij,k φ ij,k ] T , the relative distance-azimuth-altitude measurement model is as follows:

[0086]

[0087] d ij,k is the relative distance between the UAV and its neighboring UAVs, γ ij,k is the azimuth angle between the UAV and the adjacent UAV, γ ji,k is the relative azimuth angle of the UAV measured by the adjacent UAV, α ij,k is the flight pitch angle of the drone, x ij,k 、y ij,k 、z ij,k 、φ ij,k They are the relative coordinates of the x-axis, the relative coordinates of the y-axis, the relative coordinates of the z-axis and the relative direction angle.

[0088] However, during the UAV communication transmission process, it may be affected by malicious network attacks or communication restrictions, resulting in DoS attacks and FDI attacks on the transmitted status information. To this end, in S4, a trust evaluator is set up on the UAV to detect the predicted motion state data transmitted by other adjacent UAVs to determine whether to continue transmitting the predicted motion state data for data fusion and update.

[0089] The trust evaluator is designed as follows:

[0090]

[0091] λ ij,k is a binary decision variable of the trust evaluator, η ij,k is the threshold of the trust evaluator, Υ a ij,k is the pre-trigger condition of the trust evaluator, Z ij,k is the measurement vector of the UAV, It is the predicted motion state data of the drone Predicted status information transmitted to neighboring drones Jointly estimated forecast measurements.

[0092] Predicted status information of drones passing adjacent drones Estimated predicted measurement data Should be consistent with the measurement vector Z ij,k Keep consistent, and the difference between the two Should be less than the threshold η ij,k . When||Υ a ij,k ||≤η ij,k When λ ij,k =1, indicating that the predicted state information transmitted by the adjacent drone at the current moment is reliable and there is no attack. The predicted motion state data is used. Predicted status information of neighboring drones and the measurement vector Z ij,k Perform data fusion to locate the UAV with high precision; otherwise, λ ij,k =0, indicating that the predicted state information transmitted by the adjacent drone at the current moment is under attack, then the transmitted predicted state information will be discarded, and the drone will interrupt the state update and use its own predicted motion state data As the positioning result and the input information for the next moment, the predicted motion state data of the drone is used as the optimal estimate in the update phase.

[0093] If an attack is detected and the attack persists, the drone is positioned using the predicted motion state data. As the best estimate in the update phase until no attack is detected, the drone status information is updated again, that is, the predicted motion state data is used Predicted status information of neighboring drones and the measurement vector Z ij,k Perform data fusion.

[0094] It can also be expressed as the following formula:

[0095]

[0096] (x i,k ,y i,k ,z i,k ) represents the absolute position coordinates of the i-th UAV, i.e., the real motion state data of the UAV, φ i,k represents the heading angle of the i-th UAV, represents the position coordinate information in the coordinate system transmitted by the adjacent UAV j, Represents the azimuth angle information transmitted by the adjacent UAV j.

[0097] Continue to transmit the predicted status information of neighboring drones that have not been attacked and are considered reliable through the evaluation of the trust evaluator Combine it with the drone’s predicted motion state data and the measurement vector Z ij,k Fusion, get the state estimate of the update stage State estimation during the update phase Through the state update equation we get:

[0098]

[0099] is the Kalman gain of the UAV.

[0100] In the ordinary Kalman filter algorithm, the error covariance matrix The calculation is as follows:

[0101]

[0102] To update the estimated value and the true value x i,k The difference between The updated estimate of the present invention is use replace renew Again and The error covariance matrix can be obtained by taking the transpose of

[0103] In the state update equation, the predicted state information of the adjacent UAVs Through modeling, we get:

[0104]

[0105] And in the state update equation, the prediction covariance matrix of adjacent drones is Updated by modeling to the prior error covariance matrix

[0106]

[0107] is the predicted motion state data transmitted by the drone, ξ ij,k and are mutually independent random variables that obey the Bernoulli distribution, σ ij,k and ψ ij,k They represent the error prediction state information and error covariance matrix transmitted by adjacent UAVs respectively.

[0108] According to ξ ij,k and Different values ​​of will result in several modeling situations, which will cause the information received by each UAV local fusion center to be different. The specific situations are as follows:

[0109] When ij,k =1, each UAV can normally receive the predicted motion state data and predicted covariance matrix of the adjacent UAVs in the UAV formation;

[0110] When ij,k =0 and When σ ij,k and ψ ij,k The received predicted motion state data and predicted covariance matrix of adjacent drones in the drone formation are tampered with. This is an FDI attack, and the attack occurs on the communication link between drones.

[0111] When ij,k =0 and When the UAV is no longer able to obtain any information from the adjacent UAVs in the UAV formation, this is a DoS attack on the communication link between UAVs. At this time, the predicted motion state data of the UAV is used as the state estimation in the update phase.

[0112] Will Substitute the error covariance matrix In the update phase, the posterior error covariance matrix is ​​obtained

[0113]

[0114] in:

[0115]

[0116] and H j,k denote the Jacobian matrix of the UAV and the Jacobian matrix of the adjacent UAVs, is the error vector of the prediction information, X i,k is the real motion state data of the drone, is the predicted motion state data of the adjacent UAV, R ij,k is the covariance matrix of the measurement noise, E(·) represents the expected value of two independent variables, ξ ij,k and are mutually independent random variables that obey the Bernoulli distribution, σ ij,k Indicates the error prediction state information transmitted by an adjacent UAV, The first mutual covariance matrix indicating the existence of attacks between adjacent drones, represents the mutual covariance matrix of normal communication between UAVs, The second mutual covariance matrix indicating the existence of attacks between adjacent drones, is the prior error covariance matrix of adjacent UAVs.

[0117] For the update phase, the posterior error covariance matrix is and The correlation is unknown and the expected operation cannot be obtained For any two vectors x and y, there exists a scalar Satisfy the equation: xy T +yx T ≤εxx T +ε -1 yy T .

[0118] To this end, the present invention and Two vectors introduce an inequality:

[0119]

[0120] Substitute the above inequality into the posterior error covariance matrix of the update phase In the calculation formula, we get:

[0121]

[0122] in:

[0123] n1=1+ε1+ε2

[0124] n2=ε3+ε4

[0125] n3=ε5+ε6

[0126]

[0127] Represents ξ ij,k =1, express The probability of Yes and expectations, is the ij,k and , ε1, ε2, ε3, ε4, ε5, ε6, ε7 are different values ​​corresponding to the substitution of inequalities.

[0128] Then, by solving the variable optimization problem, we can solve the posterior error covariance matrix Minimum upper limit:

[0129]

[0130] Then Both sides Taking the derivative, we get:

[0131]

[0132] in:

[0133]

[0134] Finally, the Kalman gain Substitute into the state update equation and calculate the state estimate of the update phase The state estimation in the update phase This is the positioning result.

[0135] Finally, it should be noted that the above embodiments are merely preferred embodiments of the present invention and are intended to illustrate the technical solutions of the present invention, rather than limiting them, and certainly not limiting the patent scope of the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features therein may be replaced by equivalents. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention. In other words, any changes or refinements made to the main design concept and spirit of the present invention that have no substantive significance, provided that the technical problems they solve are still consistent with those of the present invention, should be included in the protection scope of the present invention. In addition, the direct or indirect application of the technical solutions of the present invention to other related technical fields should also be included in the patent protection scope of the present invention.

Claims

1. A UAV formation collaborative positioning method based on random analysis in zero-trust scenarios, characterized by: The following steps are involved: S1. Each drone calculates the predicted motion state data; S2, each UAV transmits the predicted motion state data to its own fusion center and the adjacent UAVs in the update phase; S3, each UAV performs relative measurement on the adjacent UAV to obtain a measurement vector; S4. Each UAV detects the predicted motion state data transmitted by the adjacent UAV based on the measurement vector and determines whether to continue transmitting the predicted motion state data for data fusion update. If the determination is no, the predicted motion state data of the UAV is used as the state estimate in the update phase. If the determination is yes, proceed to S5. S5. Each UAV performs data fusion update on the predicted motion state data and the predicted motion state data transmitted by the adjacent UAVs based on the measurement vector to obtain a state estimate in the update stage.

2. The UAV formation collaborative positioning method based on random analysis in a zero-trust scenario according to claim 1 is characterized in that: In S1, the motion state data is predicted The calculation of is as follows: is the state vector of the drone in the last update phase, A i,k-1 is the state propagation matrix after linearization of the nonlinear function, B i,k-1 is the noise matrix, is the noise vector during the UAV flight.

3. The UAV formation collaborative positioning method based on random analysis in a zero-trust scenario according to claim 2 is characterized in that: The S1 also includes calculating the prediction covariance matrix of the drone and the predicted cross-covariance matrix is the prediction covariance matrix of the UAV in the last update phase, is the system noise covariance matrix, is the prediction mutual covariance matrix of the UAV in the last update phase, A j,k-1 is the state propagation matrix transmitted by adjacent UAVs at the previous moment.

4. The UAV formation collaborative positioning method based on random analysis in a zero-trust scenario according to claim 3 is characterized in that: Said S2 also includes: transforming the prediction covariance matrix of the UAV into and the predicted cross-covariance matrix The update phase transmitted to the fusion center will predict the covariance matrix Transmit to neighboring drones.

5. The UAV formation collaborative positioning method based on random analysis in a zero-trust scenario according to claim 4 is characterized in that: The S3 includes: S31, measuring the relative distance and azimuth angle between the UAV and the adjacent UAV; S32, constructing a relative distance-azimuth-height measurement model based on the UAV's flight pitch angle and the relative distance and azimuth angle between the UAV and the adjacent UAV, and obtaining the UAV's measurement vector Z ij,k =[x ij,k y ij,k z ij,k φ ij,k ] T , the relative distance-azimuth-altitude measurement model is as follows: d ij,k is the relative distance between the UAV and its neighboring UAVs, γ ij,k is the azimuth angle between the UAV and the adjacent UAV, γ ji,k is the relative azimuth angle of the UAV measured by the adjacent UAV, α ij,k is the flight pitch angle of the drone, x ij,k 、y ij,k 、z ij,k 、φ ij,k They are the x-axis relative coordinate, y-axis relative coordinate, z-axis relative coordinate and relative direction angle respectively; Preferably, in S31, the relative distance and azimuth angle between the drone and adjacent drones are measured using an onboard sensor module of the drone.

6. The UAV formation collaborative positioning method based on random analysis in a zero-trust scenario according to claim 5 is characterized in that: In S4, a trust evaluator is set on the drone: λ ij,k is a binary decision variable of the trust evaluator, η ij,k is the threshold of the trust evaluator, Υ a ij,k is the pre-trigger condition of the trust evaluator, Z ij,k is the measurement vector of the UAV, It is the predicted motion state data of the drone Predicted status information transmitted to neighboring drones jointly estimated forecast measurement data; When the binary decision variable λ of the trust evaluator ij,k = 0, the predicted motion state data of the drone is used As the optimal estimate in the update phase; otherwise, the predicted motion state data will continue to be transmitted for data fusion update.

7. The UAV formation collaborative positioning method based on random analysis in a zero-trust scenario according to claim 6 is characterized in that: In S5, the state estimation of the update stage Through the state update equation we get: is the Kalman gain of the UAV.

8. The UAV formation collaborative positioning method based on random analysis in a zero-trust scenario according to claim 7 is characterized in that: The state estimation in the update phase and the posterior error covariance matrix in the update phase Associated, through the posterior error covariance matrix of the update stage Get the state estimate of the update phase The posterior error covariance matrix during the update phase The calculation of is as follows: in: and H j,k denote the Jacobian matrix of the UAV and the Jacobian matrix of the adjacent UAVs, is the error vector of the prediction information, X i,k is the real motion state data of the drone, is the predicted motion state data of the adjacent UAV, R ij,k is the covariance matrix of the measurement noise, E(·) represents the expected value of two independent variables, ξ ij,k and are mutually independent random variables that obey the Bernoulli distribution, σ ij,k Indicates the error prediction state information transmitted by an adjacent UAV, The first mutual covariance matrix indicating the existence of attacks between adjacent drones, represents the mutual covariance matrix of normal communication between UAVs, The second mutual covariance matrix indicating the existence of attacks between adjacent drones, is the prior error covariance matrix of adjacent UAVs.

9. The UAV formation collaborative positioning method based on random analysis in a zero-trust scenario according to claim 8 is characterized in that: Predicted state information of the adjacent UAV Through modeling, we get: The prior error covariance matrix of the adjacent UAVs Through modeling, we get: is the predicted motion state data transmitted by the drone, ξ ij,k and are mutually independent random variables that obey the Bernoulli distribution, σ ij,k and ψ ij,k Represent the error prediction state information and error covariance matrix transmitted by an adjacent UAV respectively; When ij,k =1, each UAV can normally receive the predicted motion state data and predicted covariance matrix of the adjacent UAVs in the UAV formation; When ij,k =0 and When σ ij,k and ψ ij,k Tampering with the received predicted motion state data and predicted covariance matrix of adjacent drones in the drone formation; When ij,k =0 and When , the UAV can no longer obtain any information from the adjacent UAVs in the UAV formation, and the predicted motion state data of the UAV is used as the state estimation in the update phase.

10. The UAV formation collaborative positioning method based on random analysis in a zero-trust scenario according to claim 8 is characterized in that: For the update phase, the posterior error covariance matrix is and The correlation is unknown and the expected operation cannot be obtained The analytical solution for and The two vectors introduce the following inequality: Substitute the inequality into the posterior error covariance matrix in the update phase In the calculation formula, we get: in: n1=1+ε1+ε2 n2=ε3+ε+4 n3=ε5+ε6 Represents ξ ij,k =1, express The probability of Yes and expectations, is the ij,k and , ε1, ε2, ε3, ε4, ε5, ε6, ε7 are different values ​​corresponding to the substitution of inequalities; Compute the posterior error covariance matrix The minimum upper limit of Will Both sides Taking the derivative, we get: in: The Kalman gain Substitute into the state update equation to obtain the state estimate in the update phase

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