Information security-oriented unmanned aerial vehicle trajectory optimization method

Abstract

The invention relates to an unmanned aerial vehicle trajectory optimization method for information security, and belongs to the technical field of communication. The method comprises the following steps: establishing a system framework comprising multiple users, an unmanned aerial vehicle, a no-fly zone, an eavesdropper and a target; thirdly, establishing an unmanned aerial vehicle mobile model and a multi-user channel model, and defining performance indexes; then, according to the eavesdropper position and channel characteristics, an interference model is established to reduce the eavesdropping effect, and meanwhile, the safe distance between the unmanned aerial vehicles is ensured; on the basis, an optimization problem with the goals of maximizing the communication rate and the coverage rate and minimizing the eavesdropping effect is constructed. A block coordinate descent method is adopted to decompose the problem, and a continuous convex approximation technology is combined for iterative solution. And by alternately optimizing the trajectory of the unmanned aerial vehicle and updating variables and constraints, it is ensured that the algorithm is converged to be globally optimal. According to the method, the task execution efficiency and safety are improved, and the method has important theoretical and application values.

Description

Technical Field

[0001] The invention belongs to the field of communication technology and relates to an information security-oriented unmanned aerial vehicle trajectory optimization method. Background Art

[0002] With the rapid development of Unmanned Aerial Vehicle (UAV) technology, its application in the fields of communication, security, logistics, perception, etc. has gradually deepened. Especially in the field of wireless communication, drones have become an important choice for aerial base stations, communication relays, and dynamic hotspots due to their flexible deployment, efficient coverage, and three-dimensional mobility. However, with the widespread application of drone communication networks, their security issues in complex environments have gradually become prominent, especially in terms of physical layer security (PLS).

[0003] Physical layer security is a technical means to improve the confidentiality of communication systems by utilizing the characteristics of wireless channels. Traditional cryptography-based security methods have high requirements for efficient computing and key management, while physical layer security optimizes the characteristics of wireless channels and suppresses the receiving signals of eavesdroppers at the hardware level, thereby enhancing the security of communication networks. This method is particularly suitable for the multiple challenges brought about by dynamic location changes and complex environments in drone communication networks.

[0004] In practical applications, drone communication networks face many security threats. For example, malicious eavesdroppers attempt to intercept sensitive information between communication base station drones and ground users by deploying eavesdropping drones or ground eavesdropping devices. To deal with such threats, jamming drones are usually introduced to reduce the signal-to-interference-plus-noise ratio (SINR) of eavesdroppers by transmitting jamming signals, thereby enhancing the system's anti-eavesdropping capability. At the same time, base station drones need to optimize their flight trajectories to improve communication rates and coverage, avoid no-fly zones in dynamic environments, and maintain a minimum safe distance between drones. However, current research has mostly focused on single-task optimization, ignoring the synergy between communication and jamming tasks. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a method for optimizing the trajectory of unmanned aerial vehicles for information security. A communication base station unmanned aerial vehicle (UAV-M) and a jamming unmanned aerial vehicle (UAV-J) are deployed in the system respectively, and the multi-user communication quality and eavesdropping jamming capability during the communication process are modeled and optimized. By jointly optimizing the multi-objective model, the communication rate, the perception coverage performance, and the effect of minimizing the eavesdropping of the eavesdropper are maximized. By optimizing the flight trajectory of the two unmanned aerial vehicles, the collaborative performance of the communication and jamming tasks is guaranteed, and the possibility of eavesdropping is reduced, thereby effectively enhancing the physical layer security of the system.

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

[0007] A method for optimizing the trajectory of a drone for information security, the method comprising the following steps:

[0008] S1: Establish a system framework based on a network scenario that includes multiple communication users, a base station drone, a jamming drone, a no-fly zone, multiple eavesdroppers, and detection targets;

[0009] S2: Under the system framework, the mobility model and no-fly zone of the base station drone and the jammer drone are established. According to the mission requirements of the base station drone, a multi-user channel model is established, and the communication rate and coverage rate that measure the size of the perception capability are defined;

[0010] S3: Based on the location and channel characteristics of the eavesdropper, a jamming model for the jamming drone is established to reduce the effect of the eavesdropper's eavesdropping, while ensuring a safe distance between the jamming drone and the base station drone;

[0011] S4: According to the communication model and the perception model, an optimization problem is established with the objective function of maximizing the achievable communication rate and the coverage of the perception target and minimizing the eavesdropper's eavesdropping effect;

[0012] S5: The optimization problem is decomposed into two sub-problems by block coordinate descent technique and solved iteratively by continuous convex approximation technique in subsequent steps;

[0013] S6: Under the condition of fixed interference drone trajectory, optimize the trajectory Q of the base station drone with the goal of maximizing communication rate and perception coverage M ;

[0014] S7: Under the condition of fixed base station drone trajectory, the trajectory Q of the jamming drone is optimized with the goal of minimizing the eavesdropper's eavesdropping effect. J , introduce auxiliary variables, use continuous convex approximation technology to transform non-convex objective functions and constraints into convex optimization problems, and combine solvers to iteratively solve them;

[0015] S8: By alternately optimizing the UAV trajectory between sub-problems and iteratively updating the auxiliary variables and constraints, the optimization algorithm is ensured to converge to the global optimal solution within a limited number of iterations.

[0016] Further, in step S1, in the established dual-UAV assisted interaceptive integrated system framework, the base station UAV provides services for K single-antenna users, while sensing targets in the environment, and the jamming UAV transmits jamming signals to confuse eavesdroppers, thereby protecting the communication security of the base station UAV within the flight time T.

[0017] Further, in step S2, the flight time T is divided into N time periods of equal length δt , that is, T = Nδ t , where it is determined that the drone is in each time period δ t The position remains unchanged, then the trajectories of the base station drone M and the interference drone J in the time period T are expressed as:

[0018] q M [n] = [x M [n],y M [n],z M [n]] T

[0019] q J [n] = [x J [n],y J [n],z J [n]] T

[0020] Among them, x M [n],y M [n],z M [n] represents the three-dimensional coordinates of the base station drone in the nth time period, x J [n],y J [n],z J [n] represents the three-dimensional coordinates of the base station drone in the nth time period, The following mobility constraints are met:

[0021] ||q M [n+1]-q M [n]|| 2 ≤D 2 ,n=1,…,N-1,

[0022] ||q M [1]-q M0 || 2 ≤D 2 ,q M [N] = q MF ,

[0023] ||q J [n+1]-q J [n]|| 2 ≤D 2 ,n=1,…,N-1,

[0024] ||q J [1]-q J0 || 2 ≤D 2 ,q J [N] = q JF ,

[0025] H min ≤z M [n]≤H max ,

[0026] H min ≤z J [n]≤H max ,

[0027] Where D = Vδ t represents the maximum distance each UAV flies at the maximum flight speed V in each time period, q M0 represents the starting point of the base station drone, q MF represents the end point of the base station drone, q J0 represents the starting point of the jamming drone, q JF Indicates the end point of the jamming drone, H min is the minimum altitude of the drone, H max It is the maximum altitude at which the drone can fly;

[0028] Assume that the no-fly zone is represented by a sphere in the air with center C and radius r, which should satisfy the following constraints:

[0029] q J [n]-C||≥r,n=1,…,N,

[0030] q M [n]-C||≥r,n=1,…,N,

[0031] The channel from the base station drone M to the ground node is affected by the line-of-sight path. In time period n, the channel power gain from the base station drone M to the ground user k satisfies the free space path loss model, expressed as:

[0032]

[0033] Among them, d Mk represents the distance between the base station drone M and the ground user k in time period n, ρ0 represents the channel power gain at the reference distance d0 meters, l k represents the horizontal position of the kth user;

[0034] The channel power gain from the base station drone M to the ground target to be detected is:

[0035]

[0036] Among them, d Mp represents the distance between the UAV M and the ground target to be detected in the time period n, and p1 represents the horizontal position of the target to be sensed;

[0037] The communication rate of the base station drone M in each time period is:

[0038]

[0039] Among them, P M [n] represents the transmission power of the base station drone at time period n, P J [n] represents the transmission power of the interfering UAV at time period n, and σ represents the noise power at the user or eavesdropper;

[0040] The coverage rate is used to measure the size of the perception capability, whether the base station drone M covers the perception target in each time period:

[0041]

[0042] Among them, q M [n] represents the position of the base station drone in time period n, p1 represents the horizontal position of the target to be sensed, γ represents the radius of the sensing range, is the indicator function. When the base station drone is within the coverage radius of the sensing target in time period n, otherwise,

[0043] Further, in step S3, the channel power gain from the jamming drone J to the eavesdropper j on the ground is:

[0044]

[0045] e j represents the horizontal position of the jth eavesdropper;

[0046] The interference rate of the jamming drone J to the eavesdropper j in each time period is:

[0047]

[0048] The collision avoidance constraints between the jammer UAV J and the base station UAV M are:

[0049] ||q M [n]-q J [n]|| 2 ≥d 2 min ,n=1,…,N,

[0050] d min Indicates the minimum distance between the base station drone and the jammer drone.

[0051] Further, in step S4, the objective function established is:

[0052]

[0053] The constraints are as follows:

[0054] ||q M [n + 1] - q M [n]|| 2 ≤D 2 , n = 1, …, N - 1,

[0055] ||q M [1] - q M0 || 2 ≤D 2 , q M [N] = q MF ,

[0056] ||q J [n + 1] - q J [n]|| 2 ≤D 2 , n = 1, …, N - 1,

[0057] ||q J [1] - q J0 || 2 ≤D 2 , q J [N] = q JF ,

[0058] ||q M [n] - q J [n]|| 2 ≥d 2 min , n = 1, …, N,

[0059] H min ≤z M [n] ≤ H max ,

[0060] H min ≤z J [n] ≤ H max ,

[0061] ||q J [n] - C|| ≥ r, n = 1, …, N,

[0062] ||q M [n] - C|| ≥ r, n = 1, …, N,

[0063] ||v[n]|| ≤ v max , n = 1, …, N,

[0064] ||v[n]|| ≥ v min , n = 1, …, N,

[0065] ||a[n]||≤a max ,n=1,…,N,

[0066]

[0067] v[n]=v[n-1]+a[n]δ t ,n=2,…,N,

[0068] C p ≥C min

[0069] Among them, C min is the threshold of minimum coverage, and a[n] is the acceleration of the drone.

[0070] Further, in step S5, the optimization problem is decomposed into two sub-problems by block coordinate descent and continuous convex approximation technology, wherein the decomposed sub-problem P1 is:

[0071]

[0072] The decomposed subproblem P2 is:

[0073]

[0074] In steps S6 to S8, the two sub-problems P1 and P2 are iteratively solved.

[0075] Further, in step S6, for sub-problem P1, let:

[0076]

[0077] in,

[0078] A continuous function is used to approximate the trajectory Q of the jamming drone. J :

[0079]

[0080] Then, by introducing the slack variable T = {t[n] = || (x M [n],y M [n])-l k || 2 +z M [n] 2} and U={u[n]=||(x M [n],y M [n])-e j || 2 +z M [n]2}Optimize subproblem P1:

[0081]

[0082] By applying the continuous convex approximation technique, Replace it with its convex lower bound and replace -||(x M [n],y M [n])-e j || 2 Replace it with a concave upper bound at a given initial point;

[0083] definition is the trajectory of the base station drone in the k0th iteration, then the following inequality can be obtained:

[0084]

[0085] Therefore, subproblem P1 can be approximated as follows:

[0086]

[0087] The non-convex constraint ||v[n]||≥v in the above constraints min ,n=1,…,N,||q M [n]-C||≥r,n=1,…,N, Use SCA to convert to convex constraints:

[0088]

[0089] ||q M0 [n]-C|| 2 +2(q M0 [n]-C) T (q M [n]-q M0 [n])≥r 2

[0090]

[0091] Among them, v0[n] and q M0 [n] indicates a reference point;

[0092] Use the solving tool to optimally solve the transformed sub-problems.

[0093] Further, in step S7, for subproblem P2, by introducing slack variables:

[0094]

[0095] Subproblem P2 is transformed into:

[0096]

[0097] in, make represents the flight trajectory of the interfering UAV in the k0th iteration, then the term and -||(x J [n],y J [n])-l k || 2 The upper bounds of are expressed as:

[0098]

[0099] Among them, F k0 [n]=||(x k0 J [n],y k0 J [n])|| 2 -2[((x k0 J [n],y k0 J [n])-l k )] T (x J [n],y J [n])-||l k || 2 , m k0 [n]=||(x k0 J [n],y ko J [n])-e j || 2 .

[0100] Therefore, the trajectory optimization problem P2 of the jamming UAV J is approximately as follows:

[0101]

[0102] Among them, the non-convex constraint ||v[n]||≥v min ,n=1,…,N,||q M [n]-q J [n]|| 2 ≥d 2 min ,n=1,…,N,||q J [n]-C||≥r,n=1,…,N is transformed into a convex constraint using SCA:

[0103]

[0104] ||q J0 [n]-C|| 2 +2(q J0 [n]-C) T (q J [n]-q J0 [n])≥r 2

[0105]

[0106] Among them, v0[n] and q J0 [n] indicates the reference point;

[0107] Subproblem P2 after optimization by the solver.

[0108] Further, in step S8, the trajectories of the two UAVs are continuously optimized alternately, and the number of iterations is updated by k0=k0+1 until the relative increment of the objective function is less than a small threshold Γ0.

[0109] The beneficial effects of the present invention are:

[0110] The present invention constructs a dual-UAV cooperative communication and jamming system model and uses an optimization algorithm to jointly optimize the trajectories of the base station UAV and the jamming UAV. On the basis of ensuring the communication rate and perception coverage, the present invention effectively suppresses the eavesdropping effect while strictly abiding by multiple constraints such as no-fly zone avoidance and safe distance. The method of the present invention significantly ensures the communication and jamming coordination capabilities of the multi-UAV system in a complex environment, and has important theoretical value and practical application prospects.

[0111] The present invention adopts the multi-user communication rate in the communication process as the communication performance indicator, and the perception coverage rate as the perception performance indicator, so as to design the optimization problem in order to maximize the communication rate, the perception coverage performance and minimize the effect of eavesdropping by the eavesdropper. The optimization problem is solved by block coordinate descent and continuous convex approximation, which ensures the performance of communication and perception and reduces the possibility of eavesdropping, thereby effectively enhancing the physical layer security of the system.

[0112] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0113] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0114] Figure 1 A flowchart of a method for optimizing the trajectory of a drone for information security according to the present invention;

[0115] Figure 2 This is a system architecture diagram of a drone trajectory optimization method for information security according to the present invention. DETAILED DESCRIPTION

[0116] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and the features in the embodiments can be combined with each other without conflict.

[0117] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0118] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0119] See also Figure 1-2 , which is a UAV trajectory optimization method for information security.

[0120] Example

[0121] This embodiment provides an overall implementation process of a UAV trajectory optimization method for information security. Figure 1 As shown, the method comprises the following steps:

[0122] S1: Establish a system framework based on a network scenario that includes multiple communication users, a base station drone, a jamming drone, a no-fly zone, multiple eavesdroppers, and detection targets;

[0123] In the embodiment of the present invention, Figure 2 As shown in the figure, in the dual-UAV assisted interaceptive integrated system, the base station UAV provides services for K single-antenna users, senses targets in the environment at the same time, and the jammer UAV transmits jamming signals to confuse eavesdroppers, thereby protecting the communication security of the base station UAV within the flight time T.

[0124] S2: Under the system framework of step S1, establish the mobility model and no-fly zone of the two drones, establish a multi-user channel model according to the mission requirements of the base station drone, and define performance indicators such as communication rate and coverage rate to measure the size of perception capability;

[0125] In the embodiment of the present invention, for the convenience of analysis, the flight time T is divided into N time periods of equal length, that is, T=Nδ t , where δ t Choose a sufficiently small value so that the position of the UAV can be considered unchanged in each time period. The trajectory of the base station UAV and the jammer UAV in the T time period is expressed as: q M [n] = [x M [n],y M [n],z M [n]] T and q J [n] = [x J [n],y J [n],z J [n]] T ,in The following mobility constraints are met:

[0126] ||q M [n+1]-q M [n]|| 2 ≤D 2 ,n=1,…,N-1,

[0127] ||q M [1]-q M0 || 2 ≤D 2 ,q M [N] = q MF ,

[0128] ||q J [n+1]-q J [n]|| 2 ≤D 2 ,n=1,…,N-1,

[0129] ||q J [1]-q J0 || 2 ≤D 2 ,q J [N] = q JF ,

[0130] H min ≤z M [n]≤H max ,

[0131] H min ≤z J [n]≤H max ,

[0132] Where D = Vδ t represents the maximum distance each drone can fly at the maximum flight speed V in each time period, q M0 represents the starting point of the base station drone, q MF represents the end point of the base station drone, q J0 represents the starting point of the jamming drone, q JF Indicates the end point of the jamming drone, H min is the minimum altitude that the drone is required to fly. max It is the maximum altitude at which the drone is required to fly.

[0133] Sometimes due to specific environments or regulations, drones cannot enter certain areas, which are usually called "no-fly zones". Assume that the no-fly zone is represented by a sphere in the air with a center of C and a radius of r, which should satisfy the following constraints:

[0134] ||q J [n]-C||≥r,n=1,…,N,

[0135] ||q M [n]-C||≥r,n=1,…,N,

[0136] The channel from the base station drone (M) to the ground node is mainly affected by the line-of-sight (LOS) path. In time period n, the channel power gain from the base station drone (M) to the ground user k satisfies the free space path loss model, expressed as:

[0137]

[0138] Among them, d Mk represents the distance between UAV M and ground user k in time period n, ρ0 represents the channel power gain at the reference distance d0 = 1 meter, l k represents the horizontal position of the kth user.

[0139] By the same token, the channel power gain from the base station drone (M) to the ground target to be detected is:

[0140]

[0141] Among them, d Mp represents the distance between the UAV M and the ground target to be detected in the time period n, and p1 represents the horizontal position of the target to be sensed;

[0142] The communication rate of the base station drone in each time period is:

[0143]

[0144] Among them, P M [n] represents the transmission power of the base station drone at time period n, P J [n] represents the transmission power of the interfering UAV at time period n, and σ represents the noise power at the user or eavesdropper;

[0145] The coverage rate is used to measure the size of the perception capability, whether the base station drone covers the perception target in each time period:

[0146]

[0147] Among them, q M [n] represents the position of the base station drone in time period n, p1 represents the horizontal position of the perceived target, γ represents the radius of the perception range, is the indicator function. When the base station drone is within the coverage radius of the sensing target in time period n, otherwise,

[0148] S3: Based on the location and channel characteristics of the eavesdropper, a jamming model for the jamming drone is established to reduce the effect of the eavesdropper's eavesdropping, while ensuring a safe distance between the jamming drone and the base station drone;

[0149] In the embodiment of the present invention, the channel power gain from the jamming drone (J) to the eavesdropper j on the ground is:

[0150]

[0151] e j represents the horizontal position of the jth eavesdropper;

[0152] The interference rate of the jamming drone on the eavesdropper in each time period is:

[0153]

[0154] The interference drone and the base station drone must be prevented from colliding with each other. The constraints are:

[0155] ||q M [n]-q J [n]|| 2 ≥d 2 min ,n=1,…,N,

[0156] S4: According to the communication model and the perception model, an optimization problem is established with the objective function of maximizing the achievable communication rate and the coverage of the perception target and minimizing the eavesdropper's eavesdropping effect;

[0157] In the embodiment of the present invention, the established objective function is as follows:

[0158]

[0159] The constraints are:

[0160] ||q M [n+1]-q M [n]|| 2 ≤D 2 ,n=1,…,N-1,

[0161] ||q M [1]-q M0 || 2 ≤D 2 ,q M [N]=q MF ,

[0162] ||q J [n+1]-q J [n]|| 2 ≤D 2 ,n=1,…,N-1,

[0163] ||q J [1]-q J0 || 2 ≤D 2 ,q J [N] = q JF ,

[0164] ||q M [n]-q J [n]|| 2 ≥d 2 min ,n=1,…,N,

[0165] H min ≤z M [n]≤H max ,

[0166] H min ≤z J [n]≤H max ,

[0167] ||q J [n]-C||≥r,n=1,…,N,

[0168] ||q M [n]-C||≥r,n=1,…,N,

[0169] ||v[n]||≤v max ,n=1,…,N,

[0170] ||v[n]||≥v min ,n=1,…,N,

[0171] ||a[n]||≤a max ,n=1,…,N,

[0172]

[0173] v[n]=v[n-1]+a[n]δ t ,n=2,…,N,

[0174] C p ≥C min

[0175] Among them, C min is the threshold of the minimum coverage, and a[n] is the acceleration of the drone. By observation, the optimization problem is non-convex and difficult to solve.

[0176] S5: The optimization problem is implemented by block coordinate descent (BCD) and continuous convex approximation (SCA) technology, and iteratively solved in steps S6 to S8;

[0177] In the embodiment of the present invention, the optimization problem is decomposed into two sub-problems through block coordinate descent.

[0178] Sub-problem 1 is:

[0179]

[0180] Sub-problem 2 is:

[0181]

[0182] S6: Under the condition of fixed interference drone trajectory, optimize the trajectory Q of the base station drone with the goal of maximizing communication rate and perception coverage M ;

[0183] In the embodiment of the present invention, for sub-problem 1, by observing the above objective function, let in,

[0184] For a given jammer UAV trajectory Q J In order to solve the discontinuity of the indicator function, a continuous function is used to approximate it, namely: Then, by introducing the slack variable T = {t[n] = || (x M [n],y M [n])-l k || 2 +z M [n] 2} and U={u[n]=||(x M [n],y M [n])-e j || 2 +z M [n] 2 The above optimization problem can be restated as:

[0185]

[0186] By observing that the optimization problem is still non-convex, it is difficult to directly find the optimal solution. By applying the continuous convex approximation technique, the term Replace it with its convex lower bound and replace -||(x M [n],y M [n])-e j || 2 is replaced by a concave upper bound at the given initial point. Definition is the trajectory of the base station drone in the k0th iteration, then the following inequality can be obtained:

[0187]

[0188] Therefore, subproblem 1 can be approximated as follows:

[0189]

[0190] The non-convex constraint ||v[n]||≥v in the above constraints min ,n=1,…,N,||q M [n]-C||≥r,n=1,…,N, It can also be converted into a convex constraint using SCA:

[0191]

[0192] ||q M0 [n]-C||2 +2(q M0 [n]-C) T (q M [n]-q M0 [n])≥r 2

[0193]

[0194] Among them, v0[n] and q M0 [n] indicates the reference point.

[0195] After the above processing, the objective function of the optimization problem is concave and its feasible domain is convex, so the solving tool can be used to find the optimal solution.

[0196] S7: Under the condition of fixed base station drone trajectory, the trajectory Q of the jamming drone is optimized with the goal of minimizing the eavesdropper's eavesdropping effect. J , introduce auxiliary variables, use continuous convex approximation technology to transform non-convex objective functions and constraints into convex optimization problems, and combine solvers to iteratively solve them;

[0197] In the embodiment of the present invention, for sub-problem 2, by introducing the slack variable and The optimization problem can be reformulated as:

[0198]

[0199] in, make represents the flight trajectory of the interfering drone in the k0th iteration. and -||(x J [n],y J [n])-l k || 2 The upper bounds of can be expressed as:

[0200]

[0201] Among them, F k0 [n]=||(x k0 J [n],y k0 J [n])|| 2 -2[((x k0 J [n],y k0 J [n])-l k )] T (x J [n],y J[n])-||l k || 2 , m k0 [n]=||(x k0 J [n],y ko J [n])-e j || 2 .

[0202] Therefore, the trajectory optimization problem of jamming UAV can be approximated as:

[0203]

[0204] Among them, the non-convex constraint ||v[n]||≥v min ,n=1,…,N,||q M [n]-q J [n]|| 2 ≥d 2 min ,n=1,…,N,||q J [n]-C||≥r,n=1,…,N, can be transformed into a convex constraint using SCA:

[0205]

[0206] ||q J0 [n]-C|| 2 +2(q J0 [n]-C) T (q J [n]-q J0 [n])≥r 2

[0207]

[0208] Among them, v0[n] and q J0 [n] indicates the reference point.

[0209] Since the above has been converted into a convex optimization problem, it can be solved efficiently by the solver.

[0210] S8: By alternately optimizing the UAV trajectory between sub-problems and iteratively updating the auxiliary variables and constraints, the optimization algorithm is ensured to converge to the global optimal solution within a limited number of iterations.

[0211] In the embodiment of the present invention, the trajectories of the two UAVs are continuously optimized alternately, and the number of iterations is updated by k0=k0+1 until the relative increment of the objective function is less than a small threshold Γ0.

[0212] Table 1 is an algorithm pseudo code of an information security-oriented UAV trajectory optimization method of the present invention:

[0213] Table 1

[0214]

[0215] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A UAV trajectory optimization method for information security, characterized by: The method comprises the following steps: S1: Establish a system framework based on a network scenario that includes multiple communication users, a base station drone, a jamming drone, a no-fly zone, multiple eavesdroppers, and detection targets; S2: Under the system framework, the mobility model and no-fly zone of the base station drone and the jammer drone are established. According to the mission requirements of the base station drone, a multi-user channel model is established, and the communication rate and coverage rate that measure the size of the perception capability are defined; S3: Based on the location and channel characteristics of the eavesdropper, a jamming model for the jamming drone is established to reduce the effect of the eavesdropper's eavesdropping, while ensuring a safe distance between the jamming drone and the base station drone; S4: According to the communication model and the perception model, an optimization problem is established with the objective function of maximizing the achievable communication rate and the coverage of the perception target and minimizing the eavesdropper's eavesdropping effect; S5: The optimization problem is decomposed into two sub-problems by block coordinate descent technique and solved iteratively by continuous convex approximation technique in subsequent steps; S6: Under the condition of fixed interference drone trajectory, optimize the trajectory Q of the base station drone with the goal of maximizing communication rate and perception coverage M ; S7: Under the condition of fixed base station drone trajectory, the trajectory Q of the jamming drone is optimized with the goal of minimizing the eavesdropper's eavesdropping effect. J , introduce auxiliary variables, use continuous convex approximation technology to transform non-convex objective functions and constraints into convex optimization problems, and combine solvers to iteratively solve them; S8: By alternately optimizing the UAV trajectory between sub-problems and iteratively updating the auxiliary variables and constraints, the optimization algorithm is ensured to converge to the global optimal solution within a limited number of iterations.

2. The information security-oriented UAV trajectory optimization method according to claim 1 is characterized by: In step S1, in the established dual-UAV assisted interaceptive integrated system framework, the base station UAV provides services for K single-antenna users, while sensing targets in the environment, and the jammer UAV transmits jamming signals to confuse eavesdroppers, protecting the communication security of the base station UAV within the flight time T.

3. The information security-oriented UAV trajectory optimization method according to claim 2 is characterized in that: In step S2, the flight time T is divided into N time periods of equal length δ t , that is, T = Nδ t , where it is determined that the drone is in each time period δ t The position remains unchanged, then the trajectories of the base station drone M and the interference drone J in the time period T are expressed as: q M [n]=[x M [n],y M [n],z M [n]] T q J [n]=[x J [n],y J [n],z J [n]] T Among them, x M [n],y M [n],z M [n] represents the three-dimensional coordinates of the base station drone in the nth time period, x J [n],y J [n],z J [n] represents the three-dimensional coordinates of the base station drone in the nth time period, The following mobility constraints are met: ||q M [n+1]-q M [n]|| 2 ≤D 2 ,n=1,…,N-1, ||q M [1]-q M0 || 2 ≤D 2 ,q M [N]=q MF , ||q J [n+1]-q J [n]|| 2 ≤D 2 ,n=1,…,N-1, ||q J [1]-q J0 || 2 ≤D 2 ,q J [N]=q JF , H min ≤z M [n]≤H max , H min ≤z J [n]≤H max , Where D = Vδ t represents the maximum distance each UAV flies at the maximum flight speed V in each time period, q M0 represents the starting point of the base station drone, q MF represents the end point of the base station drone, q J0 represents the starting point of the jamming drone, q JF Indicates the end point of the jamming drone, H min is the minimum altitude of the drone, H max It is the maximum altitude at which the drone can fly; Assume that the no-fly zone is represented by a sphere in the air with center C and radius r, which should satisfy the following constraints: ||q J [n]-C||≥r,n=1,…,N, ||q M [n]-C||≥r,n=1,…,N, The channel from the base station drone M to the ground node is affected by the line-of-sight path. In time period n, the channel power gain from the base station drone M to the ground user k satisfies the free space path loss model, expressed as: Among them, d Mk represents the distance between the base station drone M and the ground user k in time period n, ρ0 represents the channel power gain at the reference distance d0 meters, l k represents the horizontal position of the kth user; The channel power gain from the base station drone M to the ground target to be detected is: Among them, d Mp represents the distance between the drone M and the target to be detected on the ground in time period n; p1 represents the horizontal position of the target to be detected; The communication rate of the base station drone M in each time period is: Among them, P M [n] represents the transmission power of the base station drone at time period n, P J [n] represents the transmission power of the interfering UAV at time period n, and σ represents the noise power at the user or eavesdropper; The coverage rate is used to measure the size of the perception capability, whether the base station drone M covers the perception target in each time period: Among them, q M [n] represents the position of the base station drone in time period n, p1 represents the horizontal position of the target to be sensed, γ represents the radius of the sensing range, is the indicator function. When the base station drone is within the coverage radius of the sensing target in time period n, otherwise, 4. The information security-oriented UAV trajectory optimization method according to claim 3 is characterized by: In step S3, the channel power gain from the jamming drone J to the eavesdropper j on the ground is: e j represents the horizontal position of the jth eavesdropper; The interference rate of the jamming drone J to the eavesdropper j in each time period is: The collision avoidance constraints between the jammer UAV J and the base station UAV M are: ||q M [n]-q J [n]|| 2 ≥d 2 min ,n=1,…,N, d min Indicates the minimum distance between the base station drone and the jammer drone.

5. The information security-oriented UAV trajectory optimization method according to claim 4 is characterized in that: In step S4, the objective function established is: The constraints are: ||q M [n+1]-q M [n]|| 2 ≤D 2 ,n=1,…,N-1, ||q M [1]-q M0 || 2 ≤D 2 ,q M [N]=q MF , ||q J [n+1]-q J [n]|| 2 ≤D 2 ,n=1,…,N-1, ||q J [1]-q J0 || 2 ≤D 2 ,q J [N]=q JF , ||q M [n]-q J [n]|| 2 ≥d 2 min ,n=1,…,N, H min ≤z M [n]≤H max , H min ≤z J [n]≤H max , ||q J [n]-C||≥r,n=1,…,N, ||q M [n]-C||≥r,n=1,…,N, ||v[n]||≤v max ,n=1,…,N, ||v[n]||≥v min ,n=1,…,N, ||a[n]||≤a max ,n=1,…,N, v[n]=v[n-1]+a[n]δ t ,n=2,…,N, C p ≥C min Among them, C min is the threshold of minimum coverage, and a[n] is the acceleration of the drone.

6. The information security-oriented UAV trajectory optimization method according to claim 5 is characterized by: In step S5, the optimization problem is decomposed into two sub-problems by block coordinate descent and continuous convex approximation technology, wherein the decomposed sub-problem P1 is: s.t.||q M [n+1]-q M [n]|| 2 ≤D 2 ,n=1,…,N-1, ||q M [1]-q M0 || 2 ≤D 2 ,q M [N]=q MF , ||q M [n]-qJ[n]|| 2 ≥d 2 min ,n=1,...,N, H min ≤z M [n]≤H max , ||q M [n]-C||≥r,n=1,…,N, ||v[n]||≤v max ,n=1,…,N, ||v[n]||≥v min ,n=1,…,N, ||a[n]||≤a max ,n=1,…,N, v[n]=v[n-1]+a[n]δ t ,n=2,…,N, C p ≥C min The decomposed sub-problem P2 is: s.t.||q J [n+1]-q J [n]|| 2 ≤D 2 ,n=1,…,N-1, ||q J [1]-q J0 || 2 ≤D 2 ,q J [N]=q JF , ||q M [n]-qJ[n]|| 2 ≥d 2 min ,n=1,...,N, H min ≤z J [n]≤H max , ||q J [n]-C||≥r,n=1,…,N, ||v[n]||≤v max ,n=1,…,N, ||v[n]||≥v min ,n=1,…,N, ||a[n]||≤a max ,n=1,…,N, v[n]=v[n-1]+a[n]δ t ,n=2,…,N, C p ≥C min In steps S6 to S8, the two sub-problems P1 and P2 are iteratively solved.

7. The information security-oriented UAV trajectory optimization method according to claim 6 is characterized by: In step S6, for sub-problem P1, let: in, A continuous function is used to approximate the trajectory Q of the jamming drone. J : Then, by introducing the slack variable T = {t[n] = || (x M [n],y M [n])-l k || 2 +z M [n] 2 } and U={u[n]=||(x M [n],y M [n])-e j || 2 +z M [n] 2 }Optimize subproblem P1: s.t.||q M [n+1]-q M [n]|| 2 ≤D 2 ,n=1,…,N-1, ||q M [1]-q M0 || 2 ≤D 2 ,q M [N]=q MF , ||q M [n]-q J [n]|| 2 ≥d 2 min ,n=1,…,N, H min ≤z M [n]≤H max , ||q M [n]-C||≥r,n=1,…,N, ||v[n]||≤v max ,n=1,…,N, ||v[n]||≥v min ,n=1,…,N, ||a[n]||≤a max ,n=1,…,N, v[n]=v[n-1]+a[n]δ t ,n=2,…,N, C p ≥C min ||(x M [n],y M [n])-l k || 2 +z M [n] 2 -t[n]≤0, u[n]-||(x M [n],y M [n])-e j || 2 -z M [n] 2 ≤0, u[n]≥0, By applying the continuous convex approximation technique, Replace it with its convex lower bound and replace -||(x M [n],y M [n])-e j || 2 Replace it with a concave upper bound at a given initial point; definition is the trajectory of the base station drone in the k0th iteration, then the following inequality can be obtained: Therefore, subproblem P1 can be approximated as follows: s.t.||q M [n+1]-q M [n]|| 2 ≤D 2 ,n=1,…,N-1, ||q M [1]-q M0 || 2 ≤D 2 ,q M [N]=q MF , ||q M [n]-q J [n]|| 2 ≥d 2 min ,n=1,…,N, H min ≤z M [n]≤H max , ||q M [n]-C||≥r,n=1,…,N, ||v[n]||≤v max ,n=1,…,N, ||v[n]||≥v min ,n=1,…,N, ||a[n]||≤a max ,n=1,…,N, v[n]=v[n-1]+a[n]δ t ,n=2,…,N, C p ≥C min ||(x M [n],y M [n])-l k || 2 +z M [n] 2 -t[n]≤0, u[n]+||(x k0 M [n],y k0 M [n])|| 2 -||e j || 2 -z M [n] 2 −2[(x k0 M [n],y k0 M [n])-e j ] T ((x M [n],y M [n]))≤0, u[n]≥0, The non-convex constraint ||v[n]||≥v in the above constraints min , n=1,…,N,||q M [n]-C||≥r, n=1,…,N, Use SCA to convert to convex constraints: ||q M0 [n]-C|| 2 +2(q M0 [n]-C) T (q M [n]-q M0 [n])≥r 2 Among them, v0[n] and q M0 [n] indicates the reference point; Use the solving tool to optimally solve the transformed sub-problems.

8. The information security-oriented UAV trajectory optimization method according to claim 7 is characterized by: In step S7, for subproblem P2, by introducing the slack variable and Subproblem P2 is transformed into: s.t.||q J [n+1]-q J [n]|| 2 ≤D 2 ,n=1,…,N-1, ||q J [1]-q J0 || 2 ≤D 2 ,q J [N]=q JF , ||q M [n]-q J [n]|| 2 ≥d 2 min ,n=1,…,N, H min ≤z J [n]≤H max , ||q J [n]-C||≥r,n=1,…,N, ||v[n]||≤v max ,n=1,…,N, ||v[n]||≥v min ,n=1,…,N, ||a[n]||≤a max ,n=1,…,N, v[n]=v[n-1]+a[n]δ t ,n=2,…,N, C p ≥C min , l[n]−||(x J [n],y J [n])-l k || 2 -z J [n] 2 ≤0, l[n]≥0， ||(x J [n],y J [n])-e j || 2 +z J [n] 2 -m[n]≤0, in, make represents the flight trajectory of the interfering UAV in the k0th iteration, then the term and -||(x J [n],y J [n])-l k || 2 The upper bounds of are expressed as: -||(x J [n],y J [n])-l k || 2 ≤F k0 [n] where, F k0 [n] = ||(x k0 J [n], y k0 J [n])|| 2 - 2[((x k0 J [n], y k0 J [n]) - l k )] T (x J [n], y J [n]) - ||l k || 2 , m k0 [n] = ||(x k0 J[n], y ko J[n]) - e j || 2 ; Therefore, the trajectory optimization problem P2 of the jamming UAV J is approximately as follows: s.t.||q J [n+1]-q J [n]|| 2 ≤D 2 ,n=1,…,N-1, ||q J [1]-q J0 || 2 ≤D 2 ,q J [N]=q JF , ||q M [n]-q J [n]|| 2 ≥d 2 min ,n=1,…,N, H min ≤z J [n]≤H max , ||q J [n]-C||≥r,n=1,…,N, ||v[n]||≤v max ,n=1,…,N, ||v[n]||≥v min ,n=1,…,N, ||a[n]||≤a max ,n=1,…,N, v[n]=v[n-1]+a[n]δ t ,n=2,…,N, C p ≥C min , l[n]+F k0 [n]-z J [n] 2 ≤0, l[n]≥0， ||(x J [n],y J [n])-e j || 2 +z J [n] 2 -m[n]≤0, Among them, the non-convex constraint ||v[n]||≥v min , n=1,…,N,||q M [n]-q J [n]|| 2 ≥d 2 min , n=1,…,N,||q J [n]-C||≥r, n=1,…,N is transformed into a convex constraint using SCA: ||q J0 [n]-C|| 2 +2(q J0 [n]-C) T (q J [n]-q J0 [n])≥r 2 Among them, v0[n] and q J0 [n] indicates a reference point; Subproblem P2 after optimization by the solver.

9. The information security-oriented UAV trajectory optimization method according to claim 8, characterized in that: In step S8, the trajectories of the two UAVs are continuously optimized alternately, and the number of iterations is updated by k0=k0+1 until the relative increment of the objective function is less than a small threshold Γ0.

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