CN112533221A - Unmanned aerial vehicle anti-interference method combining trajectory planning and frequency spectrum decision - Google Patents

Unmanned aerial vehicle anti-interference method combining trajectory planning and frequency spectrum decision Download PDF

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CN112533221A
CN112533221A CN202011290216.8A CN202011290216A CN112533221A CN 112533221 A CN112533221 A CN 112533221A CN 202011290216 A CN202011290216 A CN 202011290216A CN 112533221 A CN112533221 A CN 112533221A
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刘钢
徐子默
黄赞奇
王梅
刘一甲
李兆智
戚楠
吴启晖
王可为
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Nanjing University of Aeronautics and Astronautics
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W16/00Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
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    • H04W16/20Network planning tools for indoor coverage or short range network deployment
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04KSECRET COMMUNICATION; JAMMING OF COMMUNICATION
    • H04K3/00Jamming of communication; Counter-measures
    • H04K3/80Jamming or countermeasure characterized by its function
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W16/00Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/22Traffic simulation tools or models
    • H04W16/225Traffic simulation tools or models for indoor or short range network
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    • H04WWIRELESS COMMUNICATION NETWORKS
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    • H04W84/02Hierarchically pre-organised networks, e.g. paging networks, cellular networks, WLAN [Wireless Local Area Network] or WLL [Wireless Local Loop]
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
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Abstract

本发明公开了一种联合轨迹规划与频谱决策的无人机抗干扰方法,包括:S1,针对实际通信场景对无人机用户的损失和优化问题进行建模;S2,将优化问题分为两个方面:轨迹规划和频谱决策;首先利用凸优化的求解方法进行无人机用户的轨迹规划,再将频谱决策问题建模为一个Stackelberg博弈,通过分层学习进行均衡求解,最终实现轨迹与频谱的联合优化。本发明能够联合优化上述轨迹优化和用频决策两个维度,实现了无人机用户的抗干扰目标,进一步提高了无人机通信效益,使得无人机用户在飞行能耗有限的情况下高效完成目标通信任务。

Figure 202011290216

The invention discloses an anti-jamming method for unmanned aerial vehicles with joint trajectory planning and spectrum decision-making. Aspects: Trajectory planning and spectrum decision-making; first use the solution method of convex optimization to plan the trajectory of the UAV user, then model the spectrum decision-making problem as a Stackelberg game, and solve the equilibrium solution through hierarchical learning, and finally realize the trajectory and spectrum. joint optimization. The invention can jointly optimize the above two dimensions of trajectory optimization and frequency decision-making, realize the anti-jamming goal of the UAV user, further improve the communication benefit of the UAV, and make the UAV user efficient in the case of limited flight energy consumption Complete the target communication task.

Figure 202011290216

Description

一种联合轨迹规划与频谱决策的无人机抗干扰方法A UAV anti-jamming method based on joint trajectory planning and spectrum decision making

技术领域technical field

本发明涉及军事通信对抗技术领域,具体而言涉及一种联合轨迹规划与频谱决策的无人机抗干扰方法。The invention relates to the technical field of military communication countermeasures, in particular to an unmanned aerial vehicle anti-jamming method for joint trajectory planning and spectrum decision-making.

背景技术Background technique

在当代无人机集群化作战的背景下,无人机得到了迅猛发展,被广泛应用于通信、侦查、信息收集等领域,其主要特点是体积小、移动性强、成本低廉,并且能够按照人为设定的任务需求进行移动,从而满足特定场景下的通信需求。In the context of contemporary UAV cluster operations, UAVs have developed rapidly and are widely used in communication, reconnaissance, information collection and other fields. The human-set task needs to move, so as to meet the communication needs in specific scenarios.

同时,无人机也存在一定的缺陷。单架无人机在执行任务时由于载重负荷有限,导致其飞行能力较差,携带的数据处理装备不足。因此在通常情况下需要一群无人机共同行动来完成任务,并根据实际需求分为主机与僚机,主机运行时必须将其探测得到的数据传输给僚机,来协助整理分析信息数据。因此,我方需要实现无人机通信对之间的互相通信,从而高效完成无人机任务。At the same time, drones also have certain shortcomings. Due to the limited load and load of a single UAV, its flight ability is poor and the data processing equipment it carries is insufficient. Therefore, under normal circumstances, a group of UAVs are required to act together to complete the task, and they are divided into host and wingman according to actual needs. When the host is running, it must transmit the data detected by it to the wingman to assist in sorting and analyzing the information data. Therefore, we need to realize the mutual communication between the UAV communication pairs, so as to efficiently complete the UAV mission.

对于外部恶意干扰下的无人机集群抗干扰问题,在已有研究中均是基于单一的用频规划角度,而我方考虑到无人机飞行轨迹对干扰的影响,联合空间轨迹和用频两个维度对无人机抗干扰问题进行最优化求解。我方无人机的目标是在固定时间内,实现多无人机同时飞行时能够以较小的飞行能量代价来获取较大的信息传输量。在考虑轨迹优化实现抗干扰时,主要涉及以下几个方面,一方面我方无人机需尽量远离干扰源,另一方面避免使用相同频段的我方无人机距离过近,从而造成同频干扰,最后考虑到飞行距离带来的能耗对于无人机飞行有较大的影响,飞行能耗同样需要计算在轨迹优化问题之内。对于轨迹优化问题,此前已有相关研究,但仍然存在一定的问题:(1)距离太近导致的无人机内部干扰问题;(2)地面强干扰机的用频变换导致轨迹优化必须分段进行;(3)无人机飞行任务执行时间有限,必须在有限的时间内从起点到终点,因此各段的轨迹设计不可独立,要考虑后续无人机能否在有限时间飞行到终点的问题。For the anti-jamming problem of UAV swarms under external malicious interference, the existing research is based on a single frequency planning perspective. The optimal solution to the UAV anti-jamming problem is carried out in two dimensions. The goal of our UAV is to achieve a large amount of information transmission at a small cost of flight energy when multiple UAVs are flying at the same time in a fixed time. When considering trajectory optimization to achieve anti-jamming, it mainly involves the following aspects. On the one hand, our UAVs need to stay away from the interference source as much as possible, and on the other hand, we should avoid using the same frequency band of our UAVs too close, resulting in the same frequency. Finally, considering that the energy consumption caused by the flight distance has a greater impact on the UAV flight, the flight energy consumption also needs to be calculated in the trajectory optimization problem. For the trajectory optimization problem, there have been related researches before, but there are still some problems: (1) the internal interference problem of the UAV caused by the distance is too close; (2) the frequency conversion of the strong ground jammer causes the trajectory optimization to be segmented (3) The execution time of the UAV flight mission is limited, and it must go from the starting point to the end point within a limited time. Therefore, the trajectory design of each segment cannot be independent, and it is necessary to consider whether the follow-up UAV can fly to the end point in a limited time.

在无人机用户频谱选择方面,考虑到外部恶意干扰以及用户间互扰两个层面的竞争,需要将无人机用户的用频决策问题建模为一个Stackelberg博弈。在给定干扰策略情况下,其下层子博弈是一个精确势能博弈,并且至少存在一个纳什均衡,据此可以对上述博弈模型进行均衡求解。并基于随机学习理论,在下层子博弈中提出一种基于SLA的抗干扰信道选择算法,从而实现无人机用户自主用频决策躲避干扰的目标。In terms of spectrum selection of UAV users, considering the competition between external malicious interference and mutual interference between users, the frequency decision problem of UAV users needs to be modeled as a Stackelberg game. Given the interference strategy, the underlying sub-game is an exact potential game, and there is at least one Nash equilibrium, according to which the above game model can be solved. And based on stochastic learning theory, an anti-jamming channel selection algorithm based on SLA is proposed in the lower sub-game, so as to achieve the goal of autonomous frequency decision-making by UAV users to avoid interference.

而目前尚无任何现有文献揭示如何联合轨迹规划和频谱决策两种方案对无人机进行抗干扰优化,前述两种方案的抗干扰原理又完全不同,如何实现两者的有效联合是目前亟需解决的问题。However, there is no existing literature that discloses how to combine the two schemes of trajectory planning and spectrum decision-making to optimize the anti-jamming of UAVs. The anti-jamming principles of the two schemes are completely different. How to realize the effective combination of the two is currently an urgent task. problem to be solved.

发明内容SUMMARY OF THE INVENTION

本发明针对现有技术中的不足,提供一种联合轨迹规划与频谱决策的无人机抗干扰方法,联合优化上述轨迹优化和用频决策两个维度,实现了无人机用户的抗干扰目标,进一步提高了无人机通信效益,使得无人机用户在飞行能耗有限的情况下高效完成目标通信任务。Aiming at the deficiencies in the prior art, the present invention provides an anti-jamming method for unmanned aerial vehicles that combines trajectory planning and spectrum decision-making, and jointly optimizes the above two dimensions of trajectory optimization and frequency decision-making, so as to achieve the anti-jamming goal of unmanned aerial vehicle users. , which further improves the communication benefits of UAVs, enabling UAV users to efficiently complete target communication tasks with limited flight energy consumption.

为实现上述目的,本发明采用以下技术方案:To achieve the above object, the present invention adopts the following technical solutions:

一种联合轨迹规划与频谱决策的无人机抗干扰方法,所述无人机抗干扰方法用于在智能干扰环境下,多个无人机通信对从起始地出发以不同飞行高度前往目的地执行任务,联合优化所有无人机通信对的用频策略和飞行轨迹,追求最大化无人机通信对的通信速率;所述抗干扰方法包括以下步骤:A UAV anti-jamming method for joint trajectory planning and spectrum decision-making, the UAV anti-jamming method is used for a plurality of UAV communication pairs starting from a starting point and heading to a destination at different flight heights in an intelligent jamming environment to perform the task on the fly, jointly optimize the frequency strategy and flight trajectory of all UAV communication pairs, and pursue to maximize the communication rate of the UAV communication pair; the anti-jamming method includes the following steps:

S1,针对实际通信场景对无人机用户的损失和优化问题进行建模;S1, model the loss and optimization problems of UAV users for actual communication scenarios;

S2,将优化问题分为两个方面:轨迹规划和频谱决策;首先利用凸优化的求解方法进行无人机用户的轨迹规划,再将频谱决策问题建模为一个Stackelberg博弈,通过分层学习进行均衡求解,最终实现轨迹与频谱的联合优化。S2, the optimization problem is divided into two aspects: trajectory planning and spectrum decision-making; first, the solution method of convex optimization is used to plan the trajectory of the UAV user, and then the spectrum decision-making problem is modeled as a Stackelberg game, which is carried out through hierarchical learning. Equilibrium solution, and finally realize the joint optimization of trajectory and spectrum.

为优化上述技术方案,采取的具体措施还包括:In order to optimize the above technical solutions, the specific measures taken also include:

进一步地,步骤S1中,所述针对实际通信场景对无人机用户的损失和优化问题进行建模的过程包括以下步骤:Further, in step S1, the process of modeling the loss of the UAV user and the optimization problem for the actual communication scenario includes the following steps:

S11,设系统包含N个无人机通信对用户和一个外部恶意干扰,无人机用户对集定义为Un(n=1,2,...N),可用信道集定义为

Figure BDA0002782048100000022
cM表示无人机用户对的可用信道,M为无人机通信对可用信道数,干扰信道集定义为c={c1,c2,…,cJ},cJ为干扰可用信道,J为干扰可用信道数;S11, suppose the system includes N UAV communication pair users and one external malicious interference, the UAV user pair set is defined as Un ( n =1, 2,...N), and the available channel set is defined as
Figure BDA0002782048100000022
c M represents the available channels of the UAV user pair, M is the number of available channels for the UAV communication pair, the interference channel set is defined as c={c 1 , c 2 , ..., c J }, c J is the available channel for interference, J is the number of available channels for interference;

S12,将无人机通信对从起点到终点分为Z段,求解每一段的坐标(xn,zyn,z),xn,z表示无人机n在第z段的横坐标,yn,z表示无人机在第z段的纵坐标,从而形成无人机通信对n的飞行轨迹的坐标集合,即:{(xn,0,yn,0),(xn,1,yn,1),(xn,2,yn,2),...,(xn,z,yn,z),...,(xn,Z,yn,Z)},z=1,2,...,Z,其中(xn,0,yn,0),(xn,z,yn,z),(xn,Z,yn,Z)分别表示无人机通信对的起始坐标、第z段的坐标以及终点坐标;记所有用户在z段时的横坐标构成的向量为X,则X=[x1,z,x1,z,…xn,z],记所有用户在z段时的纵坐标构成的向量为Y,则Y=[y1,z,y1,z,...yn,z];S12, divide the UAV communication pair into Z segments from the starting point to the end point, and solve the coordinates of each segment (x n, z , yn, z ), x n, z represent the abscissa of the UAV n in the z-th segment, y n, z represents the ordinate of the UAV in the z-th segment, thereby forming the coordinate set of the flight trajectory of the UAV communication pair n, namely: {(x n, 0 , y n, 0 ), (x n, 1 , yn , 1 ), (x n, 2 , yn , 2 ), ..., (x n, z , yn , z ), ..., (x n, Z , yn , Z )}, z=1,2,...,Z, where (xn ,0 ,yn ,0 ), (xn ,z ,yn ,z ), (xn ,Z ,yn ,Z ) respectively represent the starting coordinates of the UAV communication pair, the coordinates of the z-th segment and the end-point coordinates; remember that the vector formed by the abscissas of all users in the z segment is X, then X=[x 1, z , x 1, z ,...xn ,z ], remember that the vector formed by the ordinates of all users in the z segment is Y, then Y=[y1 ,z ,y1 ,z ,...yn ,z ];

S13,假设所有用户的信道选择策略组合为a={a1,a2,…,aN},a-n={a0,a1,…,an-1,an+1,…,aN}表示除用户n以外的所有用户的信道选择策略组合;S13, it is assumed that the combination of channel selection strategies of all users is a={a 1 , a 2 , ..., a N }, a -n ={a 0 , a 1 , ..., a n-1 , a n+1 , ... , a N } represents the channel selection strategy combination of all users except user n;

则无人机用户在第z段的损失描述为:Then the loss of the drone user in paragraph z is described as:

Figure BDA0002782048100000021
Figure BDA0002782048100000021

其中,pn表示用户n的发射功率,pj′表示干扰机j的发射功率,

Figure BDA0002782048100000031
为用户n在z段遭受的期望加权和干扰,dj,n,z为第z段无人机通信对用户n与干扰机j之间的距离,
Figure BDA0002782048100000032
dk,n,z为无人机通信对用户n与无人机通信对用户k之间的距离,
Figure BDA0002782048100000033
Figure BDA0002782048100000034
为示性函数,an,z为用户n选择在第z段选择的信道,cj,z为干扰机选择在第z段选的信道,dn,z,z-1=((xn,z-xn,z-1)2+(yn,z-yn,z-1)2)1/2为用户n第z段的飞行距离,C0为单位距离的飞行能耗,C1为干扰水平和飞行能耗平衡因子;where p n represents the transmit power of user n, p j ′ represents the transmit power of jammer j,
Figure BDA0002782048100000031
is the expected weighted sum interference suffered by user n in segment z, d j, n, z is the distance between user n and jammer j in the z-th segment of UAV communication,
Figure BDA0002782048100000032
d k, n, z are the distances between the UAV communication pair user n and the UAV communication pair user k,
Figure BDA0002782048100000033
Figure BDA0002782048100000034
is an illustrative function, an n, z is the channel selected by user n in the zth segment, c j, z is the channel selected by the jammer in the zth segment, d n, z, z-1 = ((x n , z -x n, z-1 ) 2 +(y n, z -y n, z-1 ) 2 ) 1/2 is the flight distance of the z-th segment of user n, C 0 is the flight energy consumption per unit distance, C 1 is the balance factor of interference level and flight energy consumption;

S14,通过优化用户的横纵坐标以及用频策略,以期最小化每段上的损失,从而降低整个过程的损失,优化问题被描述为:S14, by optimizing the user's horizontal and vertical coordinates and the frequency use strategy, in order to minimize the loss on each segment, thereby reducing the loss of the entire process, the optimization problem is described as:

Figure BDA0002782048100000035
Figure BDA0002782048100000035

其中,x为用户的横坐标的构成的向量,Y为用户的纵坐标构成的向量,o为所有用户在第z段的用频策略。Among them, x is the vector formed by the abscissa of the user, Y is the vector formed by the ordinate of the user, and o is the frequency usage policy of all users in the zth segment.

进一步地,步骤S2中,所述利用凸优化的求解方法进行无人机用户的轨迹规划的过程包括以下步骤:Further, in step S2, the process of using the convex optimization solution method to plan the trajectory of the UAV user includes the following steps:

S211,将用户n的损耗建模变换为:S211, transform the loss modeling of user n into:

Figure BDA0002782048100000036
Figure BDA0002782048100000036

其中,Hn、Hk为用户n,k的飞行高度,xi,z为用户i在第z段的横坐标,yi,z为用户i在第z段的纵坐标,xj和yj分别为干扰机的横坐标和纵轴坐标;Among them, H n and H k are the flying heights of users n and k, x i, z are the abscissas of user i in the zth segment, y i, z are the ordinates of user i in the zth segment, x j and y j are the horizontal and vertical coordinates of the jammer, respectively;

S212,设置约束条件如下:S212, set the constraints as follows:

(1)前行约束(1) Forward constraint

为了保证无人机能够飞行到目的地,做如下约束:In order to ensure that the drone can fly to the destination, the following constraints are made:

Figure BDA0002782048100000041
Figure BDA0002782048100000041

其中,dz为无人机在第z段时距离目标位置的距离,dmax=Vmax*T0为无人机每段的最大飞行距离,Vmax为无人机最大飞行速度,T0为每段的飞行时间;Among them, d z is the distance of the drone from the target position in the zth segment, d max =V max *T 0 is the maximum flying distance of the drone in each segment, V max is the maximum flying speed of the drone, and T 0 for the flight time of each segment;

(2)速度约束(2) Speed constraint

约束无人机每段飞行的最大距离为:The maximum distance that constrains the UAV for each segment of flight is:

Figure BDA0002782048100000042
Figure BDA0002782048100000042

S213,将无人机的轨迹规划问题描述为:S213, describe the trajectory planning problem of the UAV as:

Figure BDA0002782048100000043
Figure BDA0002782048100000043

S214,利用连续凸近似的方法对问题P1进行求解。S214 , using the method of continuous convex approximation to solve the problem P1.

进一步地,步骤S214中,所述利用连续凸近似的方法对问题P1进行求解的过程包括以下步骤:Further, in step S214, the process of solving the problem P1 by using the continuous convex approximation method includes the following steps:

S2141,记:S2141, note:

Sk,n,z=((xk,z-xn,z)2+(yk,z-yn,z)2+(Hn-Hk)2)-1 Sk,n,z =(( xk,z -xn ,z )2+(yk ,z -yn ,z ) 2+( Hn - Hk )2 ) -1

Figure BDA0002782048100000045
Figure BDA0002782048100000045

Sn,z=((xn,z-xn,z-1)2+(yn,z-yn,z-1)2)1/2 Sn , z = ((x n, z - x n, z-1 ) 2 +(y n, z -y n, z-1 ) 2 ) 1/2

将问题P1转化为:Transform problem P1 into:

Figure BDA0002782048100000044
Figure BDA0002782048100000044

S2142,对Sn,z、Sn,j,z、Sk,n,z进行如下缩放:S2142, scaling Sn,z , Sn ,j,z , Sk,n,z as follows:

Sn,z≥((xn,z-xn,z-1)2+(yn,z-yn,z-1)2)1/2 S n, z ≥ ((x n, z -x n, z-1 ) 2 +(y n, z -y n, z-1 ) 2 ) 1/2

Figure BDA00027820481000000513
Figure BDA00027820481000000513

Sk,n,z≥((xk,z-xn,z)2+(yk,z-yn,z)2+(Hn-Hk)2)-1S k,n,z ≥((x k,z -x n,z ) 2 +(y k,z -y n,z ) 2 +(H n -H k ) 2 ) -1 ;

将P2转变为:Transform P2 into:

Figure BDA0002782048100000051
Figure BDA0002782048100000051

S2143,利用连续凸近似进行近似,得到:S2143, using continuous convex approximation to approximate, get:

Figure BDA0002782048100000052
Figure BDA0002782048100000052

Figure BDA0002782048100000053
Figure BDA0002782048100000053

Figure BDA0002782048100000054
Figure BDA0002782048100000054

其中

Figure BDA0002782048100000055
Figure BDA0002782048100000056
分别为xk,z、xn,z、yk,z、yn,z和Sn,z对应的一阶泰勒展开点,n,k=1,2,…,N;n≠k;in
Figure BDA0002782048100000055
and
Figure BDA0002782048100000056
are the first-order Taylor expansion points corresponding to x k,z , x n,z , y k,z , yn ,z and Sn ,z respectively, n,k=1,2,...,N; n≠k;

S2144,最后通过给出最初的泰勒展开点,对问题P4进行迭代求解,并将每次迭代求出的解作为新的泰勒展开点,经过多次迭代得到原问题P1的解。S2144, finally, by giving the initial Taylor expansion point, the problem P4 is iteratively solved, and the solution obtained by each iteration is used as a new Taylor expansion point, and the solution of the original problem P1 is obtained after multiple iterations.

进一步地,步骤S2中,所述将频谱决策问题建模为一个Stackelberg博弈,通过分层学习进行均衡求解,最终实现轨迹与频谱的联合优化的过程包括以下步骤:Further, in step S2, the spectrum decision problem is modeled as a Stackelberg game, and the equilibrium solution is carried out through hierarchical learning, and the process of finally realizing the joint optimization of the trajectory and the spectrum includes the following steps:

S221,将步骤S1中的频谱决策问题建模为一个Stackelberg博弈,表示为

Figure BDA0002782048100000057
其中,
Figure BDA00027820481000000514
表示无人机用户对集,
Figure BDA0002782048100000058
表示外部恶意干扰,
Figure BDA0002782048100000059
Figure BDA00027820481000000510
分别表示网内用户和干扰的策略集,
Figure BDA00027820481000000511
为无人机用户对的轨迹横坐标所采取的策略,
Figure BDA00027820481000000512
为无人机用户对的轨迹纵坐标所采取的策略,un和uj分别表示无人机用户对n和干扰的效用函数;S221, the spectrum decision problem in step S1 is modeled as a Stackelberg game, expressed as
Figure BDA0002782048100000057
in,
Figure BDA00027820481000000514
represents the drone user pair set,
Figure BDA0002782048100000058
Indicates external malicious interference,
Figure BDA0002782048100000059
and
Figure BDA00027820481000000510
are the policy sets of users and interferences in the network, respectively,
Figure BDA00027820481000000511
The strategy adopted for the abscissa of the trajectory of the drone user pair,
Figure BDA00027820481000000512
is the strategy adopted for the trajectory ordinate of the UAV user pair, u n and u j represent the utility function of the UAV user pair n and interference, respectively;

S222,假设干扰为领导者,无人机用户对为跟随者,将网内用户和干扰都建模为博弈参与者,构建博弈模型;对于无人机用户对n来说,它希望实现损失最小化,因而,在第z段其效用函数被定义为:S222, assuming that the interference is the leader and the drone user pair is the follower, model both the users in the network and the interference as game participants, and build a game model; for the drone user pair n, it hopes to achieve the least loss , thus, its utility function is defined as:

un,z(an,z,a-n,z,cj,z,X,Y)=W-En,z u n, z (an , z , a -n, z , c j, z , X, Y) = WE n, z

其中W为预先定义的正常数,其取值由环境中的用户功率而定,用户对n的优化问题被表示为:where W is a predefined constant, and its value is determined by the user power in the environment, and the user's optimization problem for n is expressed as:

Figure BDA0002782048100000061
Figure BDA0002782048100000061

下层用户子博弈定义为:The lower-level user subgame is defined as:

Figure BDA0002782048100000062
Figure BDA0002782048100000062

对于干扰来说,它的目标是实现干扰效用函数的最大化,其效用函数被定义为:

Figure BDA0002782048100000063
干扰的优化问题被表示为cj=arg max uj(a,cj);For interference, its goal is to maximize the interference utility function, which is defined as:
Figure BDA0002782048100000063
The optimization problem of interference is expressed as c j =arg max u j (a, c j );

上层干扰子博弈被定义为:The upper-level disturbance subgame is defined as:

Figure BDA0002782048100000064
Figure BDA0002782048100000064

其中,策略集为干扰信道集c;Among them, the strategy set is the interference channel set c;

S223,下层博弈

Figure BDA0002782048100000065
的策略空间由离散的用频策略和连续的轨迹构成,将下层
Figure BDA0002782048100000066
子博弈分为两个子问题进行求解,以给出分层均衡。S223, lower game
Figure BDA0002782048100000065
The policy space of is composed of discrete frequency-use policies and continuous trajectories.
Figure BDA0002782048100000066
The subgame is solved in two subproblems to give a stratified equilibrium.

进一步地,步骤S223中,所述将下层

Figure BDA0002782048100000067
子博弈分为两个子问题进行求解,以给出分层均衡的过程包括:Further, in step S223, the lower layer
Figure BDA0002782048100000067
The subgame is divided into two subproblems to be solved to give a stratified equilibrium process including:

无人机通信对用户进行轨迹和用频策略两方面的调整,用户位置固定时在给定干扰策略cj下,下层无人机用户对构成博弈

Figure BDA0002782048100000068
Figure BDA0002782048100000069
是一个精确势能博弈并且该博弈存在至少一个纳什均衡;同时在求得
Figure BDA00027820481000000610
的均衡解的情况下,将轨迹规划转化为凸问题,利用连续凸近似的方法进行求解;通过用频均衡点与轨迹优化不断的迭代,最终给出下层子博弈的策略;在博弈模型
Figure BDA00027820481000000611
中,在求解完成用户的策略后,干扰确定自己的干扰策略从而构成一个分层均衡。UAV communication adjusts the user's trajectory and frequency strategy. When the user's position is fixed, under the given interference strategy c j , the lower-level UAV users constitute a game.
Figure BDA0002782048100000068
Figure BDA0002782048100000069
is an exact potential energy game and there is at least one Nash equilibrium in the game;
Figure BDA00027820481000000610
In the case of the equilibrium solution of , the trajectory planning is transformed into a convex problem, and the solution is solved by the method of continuous convex approximation; through the constant iteration of frequency equilibrium point and trajectory optimization, the strategy of the lower sub-game is finally given; in the game model
Figure BDA00027820481000000611
In , after solving the user's strategy, the interference determines its own interference strategy to form a hierarchical equilibrium.

进一步地,所述在博弈模型

Figure BDA00027820481000000612
中,在求解完成用户的策略后,干扰确定自己的干扰策略从而构成一个分层均衡的过程包括:Further, the in-game model
Figure BDA00027820481000000612
, after solving the user's strategy, the process of determining its own interference strategy to form a hierarchical equilibrium includes:

给定干扰策略θ0,博弈

Figure BDA00027820481000000613
在轨迹调整完成后转变为至少存在一个纯策略纳什均衡的精确势能博弈
Figure BDA00027820481000000614
在博弈
Figure BDA00027820481000000615
中总存在NE(θ0),计算得到干扰的平稳策略
Figure BDA00027820481000000616
Figure BDA0002782048100000071
Figure BDA0002782048100000072
构成一个平稳意义上的分层均衡。Given an interference strategy θ 0 , the game
Figure BDA00027820481000000613
After the trajectory adjustment is completed, it is transformed into an exact potential energy game with at least one pure-strategy Nash equilibrium.
Figure BDA00027820481000000614
in the game
Figure BDA00027820481000000615
There is always NE(θ 0 ) in the
Figure BDA00027820481000000616
Figure BDA0002782048100000071
Will
Figure BDA0002782048100000072
It constitutes a stratified equilibrium in a stationary sense.

本发明的有益效果是:The beneficial effects of the present invention are:

本发明通过联合优化无人机用户的轨迹和用频,可以通过自适应调整轨迹规避干扰机并通过用频变化躲避干扰频段,从而实现无人机抗干扰的目的,相较于此前的单一用频优化,联合优化能够进一步提高无人机用户的通信效益,减少外部恶意干扰带来的损失。By jointly optimizing the trajectory and frequency of the UAV user, the present invention can adjust the trajectory adaptively to avoid the jammer and avoid the interference frequency band by changing the frequency, so as to achieve the purpose of anti-jamming of the UAV. Frequency optimization and joint optimization can further improve the communication efficiency of UAV users and reduce the losses caused by external malicious interference.

附图说明Description of drawings

图1是本发明所设计的无人机与干扰机通信对抗场景示意图。FIG. 1 is a schematic diagram of a communication confrontation scenario between a UAV and a jammer designed by the present invention.

图2所示为无人机飞行轨迹分成4段时的示意图。Figure 2 shows a schematic diagram when the UAV flight trajectory is divided into 4 segments.

图3是干扰机位置不同时的无人机飞行轨迹示意图。Figure 3 is a schematic diagram of the UAV flight trajectory when the jammer positions are different.

图4是对应图2情况下的无人机用频情况示意图。FIG. 4 is a schematic diagram corresponding to the frequency situation of the UAV under the situation of FIG. 2 .

图5分别是选取图2和图3中段编号为47-48所得的无人机用频和轨迹示意图。Fig. 5 is a schematic diagram of the frequency and trajectory of the UAV obtained by selecting the middle sections of Fig. 2 and Fig. 3 numbered 47-48, respectively.

图6是干扰机功率不同时的无人机飞行轨迹示意图。Figure 6 is a schematic diagram of the UAV flight trajectory when the jammer power is different.

图7是干扰机位置不同时平均每段的无人机消耗比较。Figure 7 is a comparison of the average UAV consumption per segment when the jammer positions are different.

图8是不同分段下无人机的平均消耗比较。Figure 8 is a comparison of the average consumption of UAVs under different segments.

图9是无人机在不同的最大飞行速度下的消耗比较。Figure 9 is a comparison of the consumption of UAVs at different maximum flight speeds.

图10是所提出的优化问题的收敛曲线。Figure 10 is the convergence curve of the proposed optimization problem.

图11是本发明的联合轨迹规划与频谱决策的无人机抗干扰方法流程图。11 is a flowchart of the UAV anti-jamming method for joint trajectory planning and spectrum decision-making according to the present invention.

具体实施方式Detailed ways

现在结合附图对本发明作进一步详细的说明。The present invention will now be described in further detail with reference to the accompanying drawings.

需要注意的是,发明中所引用的如“上”、“下”、“左”、“右”、“前”、“后”等的用语,亦仅为便于叙述的明了,而非用以限定本发明可实施的范围,其相对关系的改变或调整,在无实质变更技术内容下,当亦视为本发明可实施的范畴。It should be noted that the terms such as "up", "down", "left", "right", "front", "rear", etc. quoted in the invention are only for the convenience of description and clarity, and are not used for Limiting the applicable scope of the present invention, the change or adjustment of the relative relationship shall be regarded as the applicable scope of the present invention without substantially changing the technical content.

为了清晰说明本发明所提出的无人机抗干扰方法,首先对下述实施例中涉及到的部分符号和其对应的取值示例进行说明。表1是本发明所有符号的含义汇总表,表2是部分符号的取值示例表。In order to clearly illustrate the anti-jamming method for unmanned aerial vehicles proposed by the present invention, some symbols involved in the following embodiments and their corresponding value examples are first described. Table 1 is a summary table of the meanings of all symbols in the present invention, and Table 2 is an example table of values of some symbols.

表1符号表Table 1 Symbol table

Figure BDA0002782048100000073
Figure BDA0002782048100000073

Figure BDA0002782048100000081
Figure BDA0002782048100000081

表2部分字符的取值表Table 2 The value table of some characters

Figure BDA0002782048100000082
Figure BDA0002782048100000082

Figure BDA0002782048100000091
Figure BDA0002782048100000091

结合图11,本发明提及一种联合轨迹规划与频谱决策的无人机抗干扰方法,所述无人机抗干扰方法用于在智能干扰环境下,多个无人机通信对从起始地出发以不同飞行高度前往目的地执行任务,联合优化所有无人机通信对的用频策略和飞行轨迹,追求最大化无人机通信对的通信速率;所述抗干扰方法包括以下步骤:With reference to FIG. 11 , the present invention refers to a UAV anti-jamming method for joint trajectory planning and spectrum decision-making. The UAV anti-jamming method is used for multiple UAV communication pairs from the Departure from the ground to the destination at different flight heights to perform tasks, jointly optimize the frequency strategy and flight trajectory of all UAV communication pairs, and pursue maximizing the communication rate of the UAV communication pairs; the anti-jamming method includes the following steps:

S1,针对实际通信场景对无人机用户的损失和优化问题进行建模。S1, the loss and optimization problem of UAV users are modeled for actual communication scenarios.

S2,将优化问题分为两个方面:轨迹规划和频谱决策;首先利用凸优化的求解方法进行无人机用户的轨迹规划,再将频谱决策问题建模为一个Stackelberg博弈,通过分层学习进行均衡求解,最终实现轨迹与频谱的联合优化。S2, the optimization problem is divided into two aspects: trajectory planning and spectrum decision-making; first, the solution method of convex optimization is used to plan the trajectory of the UAV user, and then the spectrum decision-making problem is modeled as a Stackelberg game, which is carried out through hierarchical learning. Equilibrium solution, and finally realize the joint optimization of trajectory and spectrum.

多个无人机通信对在智能干扰环境下,从起始地出发以不同飞行高度前往目的地执行任务。目标为联合优化所有无人机通信对的用频策略和飞行轨迹,追求最大化无人机通信对的通信速率。In an intelligent jamming environment, multiple UAV communication pairs start from the origin and travel to the destination at different flight altitudes to perform tasks. The goal is to jointly optimize the frequency strategy and flight trajectories of all UAV communication pairs, and pursue to maximize the communication rate of UAV communication pairs.

系统包含N个无人机通信对用户和一个外部恶意干扰。无人机通信对用户在从起点飞行至终点的过程中需要实时进行数据传输以完成目标通信任务。无人机用户对集定义为Un(n=1,2,...N),可用信道集定义为M={c1,c2,…,cM},cM表示无人机用户对的可用信道,M无人机通信对可用信道数,干扰信道集定义为,c={c1,c2,…,cJ),cJ为干扰可用信道,J为干扰可用信道数。在该系统中,干扰可以感知用户的信道,它可以根据用户的策略和环境信息调整其干扰策略,并追求最大化干扰效用。另一方面,用户也具有智能性,它们采用灵活的信道选择策略以减小用户间互扰和外部恶意干扰造成的影响。同时,无人机用户对可以灵活的改变飞行轨迹,以减少用户间互扰和外部干扰造成的影响。图1为本发明系统模型图,包含N个无人机通信对用户和一个外部恶意干扰体现了无人机通信对用户从起点飞行至终点的过程。The system contains N drones communicating to users and one external malicious jammer. UAV communication requires real-time data transmission for users to complete the target communication task during the flight from the starting point to the end point. The pair set of UAV users is defined as Un ( n =1, 2,...N), and the available channel set is defined as M={c 1 , c 2 ,..., c M }, where c M represents UAV users Pair of available channels, the number of available channels for M UAV communication pairs, and the set of interference channels is defined as, c={c 1 , c 2 , ..., c J ), c J is the available channel for interference, and J is the number of available channels for interference. In this system, the interference can sense the user's channel, it can adjust its interference strategy according to the user's strategy and environmental information, and pursues to maximize the interference utility. On the other hand, users are also intelligent, and they adopt flexible channel selection strategies to reduce the influence of mutual interference among users and external malicious interference. At the same time, UAV users can flexibly change the flight trajectory to reduce the impact of mutual interference and external interference between users. FIG. 1 is a system model diagram of the present invention, which includes N drone communication pairs for users and one external malicious interference, which reflects the process of drone communication for users flying from the starting point to the end point.

将无人机通信对从起点到终点分为Z段,求解每一段的坐标(xn,z,yk,z),xn,z表示无人机n在第z段的横坐标,yn,z表示无人机在第z段的纵坐标。从而形成无人机通信对n的飞行轨迹的坐标集合,即:{(xn,0,yn,0),(xn,1,yn,1),(xn,2,yn,2),...,(xn,z,yn,z),...,(xn,Z,yn,Z)},(z=1,2,...,Z),其中(xn,0,yn,0),(xn,z,yn,z),(xn,Z,yn,Z)分别表示无人机通信对的起始坐标、第z段的坐标以及终点坐标。记所有用户在z段时的横坐标构成的向量为X,则X=[x1,z,x1,z,...xn,z],记所有用户在z段时的纵坐标构成的向量为Y,则Y=[y1,z,y1,z,…yn,z]。Divide the UAV communication pair into Z segments from the starting point to the end point, and solve the coordinates of each segment (x n, z , y k, z ), x n, z represent the abscissa of UAV n in the z-th segment, y n, z represent the ordinate of the UAV in the z-th segment. Thus, the coordinate set of the flight trajectory of the UAV communication pair n is formed, namely: {(x n, 0 , y n, 0 ), (x n, 1 , yn , 1 ), (x n, 2 , y n ,2 ),...,(xn ,z ,yn ,z ),...,(xn ,Z ,yn ,Z )},(z=1,2,...,Z) , where (x n, 0 , y n, 0 ), (x n, z , y n, z ), (x n, Z , yn , Z ) represent the starting coordinates of the UAV communication pair, the first The coordinates of the z segment and the coordinates of the end point. Note that the vector composed of the abscissas of all users in the z segment is X, then X=[x 1, z , x 1, z ,...x n, z ], and the ordinates of all users in the z segment are composed. The vector of is Y, then Y=[y 1, z , y 1, z , ... y n, z ].

假设所有用户的信道选择策略组合为a={a1,a2,…,aN}。a-n={a0,a1,…,an-1,an+1,...,aN}表示除用户n以外的所有用户的信道选择策略组合。对用户来说,如果两个或更多的用户选择相同的信道,则将产生互扰。对于干扰来说,它选择1个信道cj进行干扰。假设可用信道经历自由空间衰减,干扰可用信道与用户可用信道集相同,每个用户在一个时隙内选择一个信道进行信息传输。It is assumed that the combination of channel selection strategies of all users is a={a 1 , a 2 , . . . , a N }. a -n ={a 0 , a 1 , . . . , a n-1 , a n+1 , . . . , a N } represents the combination of channel selection strategies for all users except user n. For users, if two or more users select the same channel, mutual interference will occur. For interference, it selects 1 channel c j for interference. Assuming that the available channels experience free space fading, the available channels for interference are the same as the set of available channels for users, and each user selects a channel for information transmission in a time slot.

在每一阶段z,假设用户n和干扰选择的信道分别为an∈M和cj∈c。用户对n可获得速率可以表示为At each stage z, it is assumed that the channels chosen by user n and the interferer are an ∈ M and c j ∈ c, respectively . The available rate of users for n can be expressed as

Figure BDA0002782048100000101
Figure BDA0002782048100000101

其中,pn表示用户n的发射功率,

Figure BDA0002782048100000102
表示在第z段(段编号从z-1到z)的用户间互扰,
Figure BDA0002782048100000103
表示外部干扰,B表示信道带宽,N0表示噪声功率谱密度,
Figure BDA0002782048100000104
表示用户对n的自由空间衰减。where p n represents the transmit power of user n,
Figure BDA0002782048100000102
represents the mutual interference between users in segment z (segment numbers from z-1 to z),
Figure BDA0002782048100000103
represents external interference, B represents the channel bandwidth, N 0 represents the noise power spectral density,
Figure BDA0002782048100000104
represents the user's free-space decay for n.

在本场景下,实现高效的抗干扰面临如下挑战:(1)考虑因用频冲突而产生的同频干扰问题;(2)考虑外部恶意干扰问题;(3)考虑航迹以减轻同频干扰和恶意干扰。In this scenario, achieving efficient anti-jamming faces the following challenges: (1) Consider co-channel interference caused by frequency conflict; (2) Consider external malicious interference; (3) Consider flight paths to mitigate co-channel interference and malicious interference.

用户n在z段遭受的期望加权和干扰可以表示为:The expected weighted sum interference suffered by user n in segment z can be expressed as:

Figure BDA0002782048100000105
Figure BDA0002782048100000105

其中,in,

Figure BDA0002782048100000106
Figure BDA0002782048100000106

dj,n,z为第z段无人机通信对用户n与干扰机j之间的距离。d j, n, z are the distances between user n and jammer j in the zth segment of UAV communication.

Figure BDA0002782048100000107
Figure BDA0002782048100000107

dk,n,z为无人机通信对用户n与无人机通信对用户k之间的距离。d k, n, z are the distances between the UAV communication pair user n and the UAV communication pair user k.

Figure BDA0002782048100000108
Figure BDA0002782048100000108

f(x,y)为示性函数,an,z为用户n选择在第z段选择的信道,cj,z为干扰机选择在第z段选的信道。f(x, y) is an indicative function, an n, z are the channel selected by user n in the z-th segment, and c j, z are the channel selected by the jammer in the z-th segment.

由于无人机用户飞行能量一定,导致其飞行距离十分有限,因此飞行能耗对无人机用户的影响不可忽视,需将其计入用户损失的计算中。Due to the certain flight energy of UAV users, their flight distance is very limited, so the impact of flight energy consumption on UAV users cannot be ignored, and it needs to be included in the calculation of user losses.

在期望加权和干扰的基础上,并考虑飞行代价,设无人机用户在第z段的损失描述为:On the basis of expected weighting and interference, and considering the flight cost, let the UAV user's loss in the z-th segment be described as:

Figure BDA0002782048100000111
Figure BDA0002782048100000111

dn,z,z-1=((xn,z-xn,z-1)2+(yn,z-yn,z-1)2)1/2 (7)d n, z, z-1 = ((x n, z - x n, z-1 ) 2 +(y n, z - y n, z-1 ) 2 ) 1/2 (7)

其中,dn,z,z-1为用户n第z段的飞行距离,C0为单位距离的飞行能耗,C1为干扰水平和飞行能耗平衡因子。Among them, d n, z, z-1 is the flight distance of the zth segment of user n, C 0 is the flight energy consumption per unit distance, and C 1 is the balance factor of the interference level and the flight energy consumption.

通过优化用户的横纵坐标以及用频策略,以期最小化每段上的损失,从而降低整个过程的损失,问题可以描述为:By optimizing the user's horizontal and vertical coordinates and frequency use strategy, in order to minimize the loss on each segment, thereby reducing the loss of the entire process, the problem can be described as:

Figure BDA0002782048100000112
Figure BDA0002782048100000112

其中,x为用户的横坐标的构成的向量,Y为用户的纵坐标构成的向量,o为所有用户在第z段的用频策略。Among them, x is the vector formed by the abscissa of the user, Y is the vector formed by the ordinate of the user, and o is the frequency usage policy of all users in the zth segment.

通过以下步骤进行我方无人机用户的问题求解:Solve the problem of our drone users through the following steps:

步骤一:上述问题可以建模为一个Stackelberg博弈。数学上,它可表示为

Figure BDA0002782048100000113
其中,
Figure BDA0002782048100000114
表示无人机用户对集,
Figure BDA0002782048100000115
表示外部恶意干扰,
Figure BDA0002782048100000116
Figure BDA0002782048100000117
分别表示网内用户和干扰的策略集,
Figure BDA0002782048100000118
为无人机用户对的轨迹横坐标所采取的策略,
Figure BDA0002782048100000119
为无人机用户对的轨迹纵坐标所采取的策略,un和uj分别表示无人机用户对n和干扰的效用函数。该模型中,无人机用户对为了有效应对抗干扰需要进行干扰检测,并假设干扰为领导者,无人机用户对为跟随者。将网内用户和干扰都建模为博弈参与者,构建博弈模型。对于无人机用户对n来说,它希望实现损失最小化。因而,在第z段其效用函数可定义为:Step 1: The above problem can be modeled as a Stackelberg game. Mathematically, it can be expressed as
Figure BDA0002782048100000113
in,
Figure BDA0002782048100000114
represents the drone user pair set,
Figure BDA0002782048100000115
Indicates external malicious interference,
Figure BDA0002782048100000116
and
Figure BDA0002782048100000117
are the policy sets of users and interferences in the network, respectively,
Figure BDA0002782048100000118
The strategy adopted for the abscissa of the trajectory of the drone user pair,
Figure BDA0002782048100000119
The strategy adopted for the trajectory ordinate of the UAV user pair, u n and u j represent the utility function of the UAV user pair n and interference, respectively. In this model, the UAV user pair needs to perform interference detection in order to effectively deal with the anti-jamming, and it is assumed that the interference is the leader and the UAV user pair is the follower. Both users and disturbances in the network are modeled as game participants, and a game model is constructed. For the drone user pair n, it wants to achieve loss minimization. Therefore, its utility function can be defined as:

un,z(an,z,a-n,z,cj,z,X,Y)=W-En,z (9)u n, z (an , z , a -n, z , c j, z , X, Y) = WE n, z (9)

其中W为预先定义的正常数,其取值由环境中的用户功率而定,可以自由调整。用户对n的优化问题可表示为:Wherein W is a predefined constant, and its value is determined by the user power in the environment and can be adjusted freely. The user's optimization problem for n can be expressed as:

Figure BDA00027820481000001110
Figure BDA00027820481000001110

下层用户子博弈定义为:The lower-level user subgame is defined as:

Figure BDA00027820481000001111
Figure BDA00027820481000001111

对于干扰来说,它的目标是实现干扰效用函数的最大化,其效用函数可定义为:For interference, its goal is to maximize the interference utility function, which can be defined as:

Figure BDA0002782048100000121
Figure BDA0002782048100000121

干扰的优化问题可表示为:The optimization problem of interference can be expressed as:

cj=arg max uj(a,cj)。 (13)c j =arg max u j (a, c j ). (13)

上层干扰子博弈可定义为The upper-level disturbance subgame can be defined as

Figure BDA0002782048100000122
Figure BDA0002782048100000122

其中,策略集为干扰信道集

Figure BDA0002782048100000123
Among them, the strategy set is the interference channel set
Figure BDA0002782048100000123

下层博弈

Figure BDA0002782048100000124
的策略空间由离散的用频策略和连续的轨迹构成,并且由式(6)(7)可知用户的轨迹与其他用户具有很强的耦合性,将下层
Figure BDA0002782048100000125
子博弈分为两个子问题进行求解,以给出分层均衡。lower game
Figure BDA0002782048100000124
The strategy space is composed of discrete frequency strategies and continuous trajectories, and it can be seen from equations (6) and (7) that the user's trajectory has a strong coupling with other users, and the lower layer
Figure BDA0002782048100000125
The subgame is solved in two subproblems to give a stratified equilibrium.

无人机通信对用户进行轨迹和用频策略两方面的调整,用户位置固定时在给定干扰策略cj下,下层无人机用户对构成博弈

Figure BDA0002782048100000126
Figure BDA0002782048100000127
是一个精确势能博弈并且该博弈存在至少一个纳什均衡。同时在求得
Figure BDA0002782048100000128
的均衡解的情况下,将轨迹规划转化为凸问题,利用连续凸近似的方法进行求解。通过用频均衡点与轨迹优化不断的迭代,最终给出下层子博弈的策略。在博弈模型
Figure BDA0002782048100000129
中,在求解完成用户的策略后,干扰确定自己的干扰策略从而构成一个分层均衡。UAV communication adjusts the user's trajectory and frequency strategy. When the user's position is fixed, under the given interference strategy c j , the lower-level UAV users constitute a game.
Figure BDA0002782048100000126
Figure BDA0002782048100000127
is an exact potential energy game and the game has at least one Nash equilibrium. while seeking
Figure BDA0002782048100000128
In the case of the equilibrium solution of , the trajectory planning is transformed into a convex problem, and the continuous convex approximation method is used to solve it. Through the constant iteration of frequency equilibrium point and trajectory optimization, the strategy of the lower sub-game is finally given. in game model
Figure BDA0002782048100000129
In , after solving the user's strategy, the interference determines its own interference strategy to form a hierarchical equilibrium.

步骤二:Step 2:

如前所述,用户n的损耗建模为:As mentioned before, the loss for user n is modeled as:

Figure BDA00027820481000001210
Figure BDA00027820481000001210

其中,Hn、Hk为用户n,k的飞行高度,xi,z为用户i在第z段的横坐标,yi,z为用户i在第z段的纵坐标,xj和yj分别为干扰机的横坐标和纵轴坐标。Among them, H n and H k are the flying heights of users n and k, x i, z are the abscissas of user i in the zth segment, y i, z are the ordinates of user i in the zth segment, x j and y j are the abscissa and ordinate coordinates of the jammer, respectively.

约束条件如下:The constraints are as follows:

(1)前行约束(1) Forward constraint

为了保证无人机能够飞行到目的地,做如下约束:In order to ensure that the drone can fly to the destination, the following constraints are made:

Figure BDA0002782048100000131
Figure BDA0002782048100000131

其中,dz为无人机在第z段时距离目标位置的距离,dmax=Vmax*T0为无人机每段的最大飞行距离,Vmax为无人机最大飞行速度,T0为每段的飞行时间。图2所示为无人机飞行轨迹分成4段时的示意图,将无人机轨迹分成4段,0·T0=0秒开始飞行,到1·T0=T0秒(即第一段飞行间隔结束)时,无人机距离终点的距离应小于3*dmax,如此才能在剩余的3T0时间内飞行到目的地;1·T0=T0秒开始飞行,到2.T0=2T0秒(即第二段飞行间隔结束)时,无人机距离终点的位置应小于2*dmaxAmong them, d z is the distance of the drone from the target position in the zth segment, d max =V max *T 0 is the maximum flying distance of the drone in each segment, V max is the maximum flying speed of the drone, and T 0 for the flight time of each segment. Figure 2 shows a schematic diagram of the UAV flight trajectory divided into 4 segments, the UAV trajectory is divided into 4 segments, 0·T 0 =0 seconds to start flying, to 1·T 0 =T 0 seconds (that is, the first segment When the flight interval ends), the distance from the UAV to the end point should be less than 3*d max , so that it can fly to the destination within the remaining 3T 0 time; 1·T 0 =T 0 seconds to start flying, to 2.T 0 = 2T 0 seconds (ie, the end of the second flight interval), the position of the UAV from the end point should be less than 2*d max .

(2)速度约束(2) Speed constraint

由于无人机飞行速度不可能无限大,所以约束无人机每段飞行的最大距离:Since the flying speed of the drone cannot be infinite, the maximum distance of each flight of the drone is constrained:

Figure BDA0002782048100000132
Figure BDA0002782048100000132

因此,无人机的轨迹规划问题可描述为:Therefore, the trajectory planning problem of UAV can be described as:

Figure BDA0002782048100000133
Figure BDA0002782048100000133

通过对P1进行二次求导并分析可知问题P1为非凸问题。By taking the second derivative of P1 and analyzing it, we can see that the problem P1 is a non-convex problem.

记:Sk,n,z=((xk,z-xn,z)2+(yk,z-yn,z)2+(Hn-Hk)2)-1 (19)Note: Sk,n,z =(( xk,z -xn ,z )2+(yk ,z -yn ,z ) 2+( Hn - Hk )2 ) -1 (19)

Figure BDA0002782048100000134
Figure BDA0002782048100000134

Sn,z=((xn,z-xn,z-1)2+(yn,z-yn,z-1)2)1/2 (21)Sn , z = ((x n, z - x n, z-1 ) 2 +(y n, z -y n, z-1 ) 2 ) 1/2 (21)

则有:Then there are:

Figure BDA0002782048100000135
Figure BDA0002782048100000135

对Sn,z、Sn,j,z、Sk,n,z进行如下缩放:Scaling Sn,z , Sn ,j,z , Sk,n,z as follows:

Sn,z≥((xn,z-xn,z-1)2+(yn,z-yn,z-1)2)1/2 (23)S n, z ≥ ((x n, z - x n, z-1 ) 2 +(y n, z -y n, z-1 ) 2 ) 1/2 (23)

Figure BDA0002782048100000141
Figure BDA0002782048100000141

Sk,n,z≥((xk,z-xn,z)2+(yk,z-yn,z)2+(Hn-Hk)2)-1 (25)S k, n , z ≥ ((x k, z - x n, z ) 2 +(y k, z -y n, z ) 2 +(H n -H k ) 2 ) -1 (25)

由(19)、(20)、(21)可知,当(23)、(24)、(25)取等号时,进行的缩放为等效松弛,即P2逼近目标最小值。那么P2将转变为:It can be seen from (19), (20), (21) that when (23), (24), and (25) take equal signs, the scaling performed is equivalent relaxation, that is, P2 approaches the target minimum value. Then P2 will be transformed into:

Figure BDA0002782048100000142
Figure BDA0002782048100000142

分析(23)、(24)、(25)发现它们为非凸不等式,所以P3依然为非凸问题,不能直接求解。因此利用连续凸近似进行近似,可得:Analysis of (23), (24), (25) shows that they are non-convex inequalities, so P3 is still a non-convex problem and cannot be solved directly. Therefore, using continuous convex approximation to approximate, we can get:

Figure BDA0002782048100000143
Figure BDA0002782048100000143

Figure BDA0002782048100000144
Figure BDA0002782048100000144

Figure BDA0002782048100000145
Figure BDA0002782048100000145

Figure BDA0002782048100000146
Figure BDA0002782048100000146

其中

Figure BDA0002782048100000147
分别为xk,z,xn,z,yk,z,yn,z,Sn,z对应的一阶泰勒展开点。in
Figure BDA0002782048100000147
are the first-order Taylor expansion points corresponding to x k, z , x n, z , y k, z , y n, z , Sn , z respectively.

最后通过给出最初的泰勒展开点,对P4进行迭代求解,并将每次迭代求出的解作为新的泰勒展开点,经过多次迭代可以得到原问题P1的解。Finally, by giving the initial Taylor expansion point, iteratively solve P4, and take the solution obtained by each iteration as a new Taylor expansion point, and the solution of the original problem P1 can be obtained after several iterations.

步骤三:Step 3:

给定一个干扰策略cj,下层子博弈

Figure BDA0002782048100000148
是一个精确势能博弈,并且该博弈
Figure BDA0002782048100000149
至少存在一个纳什均衡。因此给定一个干扰策略cj,下层子博弈的势能函数可以构造为:Given an interference strategy c j , the lower subgame
Figure BDA0002782048100000148
is an exact potential energy game, and the game
Figure BDA0002782048100000149
At least one Nash equilibrium exists. Therefore, given an interference strategy c j , the potential energy function of the lower subgame can be constructed as:

Figure BDA0002782048100000151
Figure BDA0002782048100000151

其中,in,

Figure BDA0002782048100000152
Figure BDA0002782048100000152

考虑用户对间的干扰对称性。利用对称性

Figure BDA0002782048100000153
Figure BDA0002782048100000154
可得:Consider interference symmetry between user pairs. Take advantage of symmetry
Figure BDA0002782048100000153
and
Figure BDA0002782048100000154
Available:

Figure BDA0002782048100000155
Figure BDA0002782048100000155

综上,Φ1(an,a-n,cj)可以重新表述为:In summary, Φ 1 (a n , a -n , c j ) can be reformulated as:

Figure BDA0002782048100000156
Figure BDA0002782048100000156

其中,

Figure BDA0002782048100000157
与an,z无关。in,
Figure BDA0002782048100000157
Has nothing to do with an , z .

此外,also,

Figure BDA0002782048100000158
Figure BDA0002782048100000158

其中,

Figure BDA0002782048100000159
与an,z无关。in,
Figure BDA0002782048100000159
Has nothing to do with an , z .

注意到Φ3(dn,z,z-1)为距离的函数,与an无关。因此,可以得到Note that Φ 3 (d n , z, z-1 ) is a function of distance, independent of an. Therefore, it can be obtained

Figure BDA0002782048100000161
Figure BDA0002782048100000161

上述分析可知,任意用户单方面改变策略而造成的用户效用函数的变化和势能函数的变化相同,下层子博弈

Figure BDA0002782048100000162
是一个精确势能博弈。The above analysis shows that the change of the user's utility function caused by the unilateral change of the strategy by any user is the same as the change of the potential energy function.
Figure BDA0002782048100000162
It is an exact potential energy game.

在所提的抗干扰博弈中,存在一个干扰的平稳策略和用户的NE策略,组成一个分层均衡。In the proposed anti-jamming game, there is a stationary strategy for interference and a user's NE strategy to form a hierarchical equilibrium.

由于给定干扰策略,博弈

Figure BDA0002782048100000163
在轨迹调整完成后转变为精确势能博弈
Figure BDA0002782048100000164
由于精确势能博弈至少存在一个纯策略纳什均衡。因此,在给定干扰策略θ0,在博弈
Figure BDA0002782048100000165
中总存NE(θ0)。干扰的平稳策略可以表示为Given the interference strategy, the game
Figure BDA0002782048100000163
After the trajectory adjustment is completed, it is transformed into a precise potential energy game
Figure BDA0002782048100000164
Since there is at least one pure-strategy Nash equilibrium in exact potential games. Therefore, given the interference strategy θ 0 , in the game
Figure BDA0002782048100000165
NE(θ 0 ) is always stored in . The stationary policy of disturbance can be expressed as

Figure BDA0002782048100000166
Figure BDA0002782048100000166

每个有限策略博弈有一个混合策略均衡,因此

Figure BDA0002782048100000167
构成一个平稳意义上的分层均衡。Every finite strategy game has a mixed strategy equilibrium, so
Figure BDA0002782048100000167
It constitutes a stratified equilibrium in a stationary sense.

图3为6个用户3个可用频段干扰功率相同下的无人机用户轨迹,可以清楚地发现当无人机用户飞行到干扰附近时,为了保持通信畅通所有的无人机用户都远离干扰。与此同时,由于无人机存在互扰,无人机之间的位置也在进行不断的调整。例如图3中a子图X轴坐标80-400m这一段,无人机用户2和无人机用户3在80-200m时相距很近,200-400m后相距很远。出现这一现象的原因主要是为了降低用户之间的互扰。Figure 3 shows the trajectories of UAV users with the same interference power in 3 available frequency bands of 6 users. It can be clearly found that when UAV users fly to the vicinity of interference, all UAV users are kept away from interference in order to maintain smooth communication. At the same time, due to the mutual interference of drones, the positions of drones are constantly being adjusted. For example, in the section of X-axis coordinate 80-400m of sub-graph a in Figure 3, UAV user 2 and UAV user 3 are very close at 80-200m, and far apart after 200-400m. The reason for this phenomenon is mainly to reduce mutual interference between users.

图4为每一段上的用频情况,可以发现当无人机与干扰机位置较近时,干扰机能干扰到较多的用户。子图a对应干扰位置(800,130),10-18段时,干扰机每次都能干扰到最多的用户,并且有可用信道未使用。子图b对应干扰位置(200,30),2-7段时干扰机每次都能干扰到最多的用户,并且有可用信道未使用。子图c对应干扰位置(1600,275),22-29段时,干扰机每次都能干扰到最多的用户,并且有可用信道未使用。这一现象是因为此时用户距离干扰机较近,用户先决策干扰后决策。干扰离用户近,为了避免干扰的强干扰,用户放弃了被干扰的信道。干扰具有智能性,在用户决策后,干扰为了使自己的效用最大,就具有最多用户的信道进行干扰。Figure 4 shows the frequency usage of each segment. It can be found that when the UAV and the jammer are located close to each other, the jammer can interfere with more users. Sub-picture a corresponds to the interference position (800, 130). In segments 10-18, the jammer can interfere with the most users every time, and there are available channels that are not used. Sub-picture b corresponds to the interference position (200, 30). In segments 2-7, the jammer can interfere with the most users every time, and there are available channels that are not used. The sub-picture c corresponds to the interference position (1600, 275). In segments 22-29, the jammer can interfere with the most users every time, and there are available channels that are not used. This phenomenon is because the user is closer to the jammer at this time, and the user first decides to jam and then decides. The interference is close to the user. In order to avoid the strong interference of the interference, the user abandons the interfered channel. Interference is intelligent. After the user makes a decision, in order to maximize its utility, the interference will interfere with the channel with the most users.

图5选取了图3和图4中段编号为47-48所得用户的用频和轨迹,以此具体分析所提算法在减弱用户间互扰方面的作用。观察子图a.1和子图a.2可以发现,在段编号为47时用户1和用户5之间的距离近,但是它们使用的信道不同。用户2、用户5和用户6用频相同因此相距较远。这一现象在子图b.1和子图b.2以及子图c.1和子图c.2同样存在。产生这一现象的原因为使用信道相同时,距离越远互扰越小,距离越近互扰越大。Figure 5 selects the frequency and trajectories of users numbered 47-48 in Figure 3 and Figure 4, so as to analyze the effect of the proposed algorithm in reducing mutual interference between users. Observing subgraphs a.1 and a.2, it can be found that the distance between user 1 and user 5 is close when the segment number is 47, but they use different channels. User 2, User 5, and User 6 use the same frequency and are therefore far apart. This phenomenon also exists in subgraphs b.1 and b.2 as well as in subgraphs c.1 and c.2. The reason for this phenomenon is that when using the same channel, the farther the distance is, the smaller the mutual interference, and the closer the distance is, the greater the mutual interference.

图6为不同干扰功率下的用户轨迹,子图a、b和分别对应干扰功率100w,50w,25w。可以发现,干扰越大用户距离干扰越远。Figure 6 shows the user trajectories under different interference powers, and the subgraphs a and b correspond to the interference powers of 100w, 50w, and 25w, respectively. It can be found that the greater the interference, the farther the user is from the interference.

图7中locl、loc2、loc3和loc4分别对应干扰位置为(800,130)、(200,30)、(1600,275)和(1000,130)。可以发现无论干扰位于何处,干扰功率越大平局消耗越大,这是因为为了对比干扰,无人机将飞行的更远。In FIG. 7 , the corresponding interference positions of loc1, loc2, loc3 and loc4 are (800, 130), (200, 30), (1600, 275) and (1000, 130), respectively. It can be found that no matter where the jamming is located, the larger the jamming power, the greater the draw consumption, because in order to compare the jamming, the UAV will fly farther.

由图8可以看到,当最大飞行速度越大,无人机的损耗越小,这是因为最大飞行速度越大,无人机轨迹可调整的自由度越大。换句话说也就是可以降低无人机之间的同频互扰。It can be seen from Figure 8 that when the maximum flight speed is greater, the loss of the UAV is smaller, because the greater the maximum flight speed, the greater the degree of freedom that the UAV trajectory can be adjusted. In other words, it can reduce the co-frequency mutual interference between UAVs.

图9为不同干扰功率下设计的算法与其他算法的对比。用频随机轨迹均匀与用频优化轨迹均匀的比可以发现,用频优化的损失更少;用频优化轨迹均匀与联合求解相比,联合求解损失更小。综合来看,所提算法有最少的损失,也即其性能最好。Figure 9 shows the comparison between the algorithm designed under different interference power and other algorithms. The ratio of using frequency random trajectory uniformity to using frequency optimization trajectory uniformity shows that the loss of using frequency optimization is less; compared with the joint solution, the joint solution loss is smaller when using frequency optimization trajectory uniformity. On the whole, the proposed algorithm has the least loss, that is, its performance is the best.

图10中提供了所提出的优化问题的收敛曲线。如果满足预设目标函数公差或迭代次数达到最大值,则迭代停止。具体来说,用频求解时要求用频概率>1-0.001,并且最大迭代次数为1000,轨迹规划时要求前后两次相对变化小于10-4并且最大迭代次数为100次。从图中可知,本专利所设计算法收敛时间少于200次,表明了所设计算法的有效性。Convergence curves for the proposed optimization problem are provided in Figure 10. The iteration stops if the preset objective function tolerance is met or the number of iterations reaches the maximum value. Specifically, when solving by frequency, the probability of using frequency is required to be > 1-0.001 , and the maximum number of iterations is 1000. When planning the trajectory, it is required that the relative change between the two times before and after is less than 10-4 and the maximum number of iterations is 100 times. It can be seen from the figure that the convergence time of the algorithm designed in this patent is less than 200 times, which shows the effectiveness of the designed algorithm.

以上仅是本发明的优选实施方式,本发明的保护范围并不仅局限于上述实施例,凡属于本发明思路下的技术方案均属于本发明的保护范围。应当指出,对于本技术领域的普通技术人员来说,在不脱离本发明原理前提下的若干改进和润饰,应视为本发明的保护范围。The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions that belong to the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims (7)

1. An unmanned aerial vehicle anti-interference method combining trajectory planning and frequency spectrum decision is characterized in that the unmanned aerial vehicle anti-interference method is used for executing tasks on a plurality of unmanned aerial vehicle communication pairs starting from a starting place and going to a destination at different flight heights in an intelligent interference environment, jointly optimizing frequency utilization strategies and flight trajectories of all unmanned aerial vehicle communication pairs and pursuing maximization of communication rate of the unmanned aerial vehicle communication pairs; the anti-interference method comprises the following steps:
s1, modeling the loss and optimization problem of the unmanned aerial vehicle user aiming at the actual communication scene;
s2, the optimization problem is divided into two aspects: trajectory planning and spectrum decision making; firstly, a convex optimization solving method is used for planning the track of an unmanned aerial vehicle user, then a frequency spectrum decision problem is modeled into a Stackelberg game, balanced solution is carried out through layered learning, and finally the joint optimization of the track and the frequency spectrum is realized.
2. The unmanned aerial vehicle anti-jamming method based on joint trajectory planning and spectrum decision of claim 1, wherein in step S1, the process of modeling the loss and optimization problem of the unmanned aerial vehicle user for the actual communication scenario includes the following steps:
s11, the system comprises N unmanned aerial vehicle communication pairs and a malicious interference outside, and the unmanned aerial vehicle user pair set is defined as Un(N ═ 1, 2.. N), and the available channel set is defined as
Figure FDA0002782048090000011
cMRepresenting available channels of unmanned aerial vehicle user pairs, M being the number of available channels of unmanned aerial vehicle communication pairs, and the set of interference channels being defined as
Figure FDA0002782048090000012
cJJ is the number of interference available channels;
s12, dividing the unmanned aerial vehicle communication pair into Z sections from the starting point to the end point, and solving the coordinate (x) of each sectionn,z,yn,z),xn,zDenotes the abscissa, y, of drone n in the z-th segmentn,zThe ordinate of the drone in the z-th segment, forming a set of coordinates of the flight trajectory of the drone communication pair n, namely: { (x)n,0,yn,0),(xn,1,yn,1),(xn,2,yn,2),...,(xn,z,yn,z),...,(xn,Z,yn,Z) 1,2, Z, wherein (x)n,0,yn,0),(xn,z,yn,z),(xn,Z,yn,Z) Respectively representing the initial coordinate, the z-th segment coordinate and the end point coordinate of the unmanned aerial vehicle communication pair; note that the vector formed by the abscissa of all users in the z segment is X, and X ═ X1,z,x1,z,...xn,z]If the vector formed by the vertical coordinates of all users in the z segment is Y, Y ═ Y1,z,y1,z,...yn,z];
S13, assuming that the combination of the channel selection policies of all users is a ═ a1,a2,…,aN},a-n={a0,a1,…,an-1,an+1,…,aNRepresents the channel selection strategy combination of all users except the user n;
the loss of the drone user in the z-th segment is described as:
Figure FDA0002782048090000013
wherein p isnRepresenting the transmission power, p, of user nj' denotes the transmit power of the jammer j,
Figure FDA0002782048090000014
for the expectation that user n suffers in section zWeight and interference, dj,n,zFor the distance between user n and jammer j for the z-th drone communication pair,
Figure FDA0002782048090000021
dk,n,zfor the distance between drone communication pair user n and drone communication pair user k,
Figure FDA0002782048090000022
Figure FDA0002782048090000023
as an indicative function, an,zSelecting the channel selected in the z-th segment for user n, cj,zSelecting the channel selected in the z-th segment for the jammer, dn,z,z-1=((xn,z-xn,z-1)2+(yn,z-yn,z-1)2)1/2For the flight distance of the nth segment of the user, C0Energy consumption per unit distance, C1Interference level and flight energy consumption balance factors;
s14, the optimization problem is described as follows, by optimizing the horizontal and vertical coordinates of the user and the frequency strategy to minimize the loss on each segment, thereby reducing the loss of the whole process:
Figure FDA0002782048090000024
wherein, X is a vector formed by the abscissa of the user, Y is a vector formed by the ordinate of the user, and O is a frequency utilization strategy of all users in the z-th section.
3. The unmanned aerial vehicle anti-jamming method based on joint trajectory planning and spectrum decision of claim 2, wherein in step S2, the process of planning the trajectory of the unmanned aerial vehicle user by using the convex optimization solution method includes the following steps:
s211, modeling and transforming the loss of user n into:
Figure FDA0002782048090000025
wherein Hn、HkIs the flight height, x, of the user n, ki,zFor user i on the abscissa, y, of segment zi,zFor user i in the z-th segment, xjAnd yjRespectively an abscissa and an ordinate of the jammer;
s212, setting the constraint conditions as follows:
(1) forward motion restraint
In order to ensure that the unmanned aerial vehicle can fly to the destination, the following constraints are made:
Figure FDA0002782048090000026
wherein d iszFor the distance of the unmanned plane from the target position in the z-th segment, dmax=Vmax*T0For maximum flight distance, V, of each segment of the dronemaxFor maximum flight speed, T, of the unmanned aerial vehicle0Is the time of flight of each segment;
(2) speed constraint
The maximum distance for restricting each flight of the unmanned aerial vehicle is as follows:
Figure FDA0002782048090000031
s213, describing the trajectory planning problem of the unmanned aerial vehicle as follows:
Figure FDA0002782048090000032
s214, the problem P1 is solved by using the continuous convex approximation method.
4. The unmanned aerial vehicle anti-jamming method based on joint trajectory planning and spectrum decision of claim 3, wherein in step S214, the process of solving the problem P1 by using the continuous convex approximation method includes the following steps:
s2141, note:
Sk,n,z=((xk,z-xn,z)2+(yk,z-yn,z)2+(Hn-Hk)2)-1
Figure FDA0002782048090000033
Sn,z=((xn,z-xn,z-1)2+(yn,z-yn,z-1)2)1/2
problem P1 was converted into:
Figure FDA0002782048090000034
s2142, to Sn,z、Sn,j,z、Sk,n,zThe following scaling was performed:
Sn,z≥((xn,z-xn,z-1)2+(yn,z-yn,z-1)2)1/2
Figure FDA0002782048090000035
Sk,n,z≥((xk,z-xn,z)2+(yk,z-yn,z)2+(Hn-Hk)2)-1
converting P2 to:
Figure FDA0002782048090000041
s2143, approximation is performed by using continuous convex approximation, and the following is obtained:
Figure FDA0002782048090000042
Figure FDA0002782048090000043
Figure FDA0002782048090000044
Figure FDA0002782048090000045
wherein
Figure FDA0002782048090000046
And
Figure FDA0002782048090000047
are respectively xk,z、xn,z、yk,z、yn,zAnd Sn,zA corresponding first-order taylor expansion point, N, k being 1, 2. n is not equal to k;
s2144, the problem P4 is solved iteratively by giving out an initial Taylor expansion point, the solution obtained by each iteration is used as a new Taylor expansion point, and the solution of the original problem P1 is obtained through multiple iterations.
5. The unmanned aerial vehicle anti-interference method combining trajectory planning and spectrum decision making according to claim 2, wherein in step S2, the spectrum decision problem is modeled as a Stackelberg game, equilibrium solution is performed through layered learning, and finally, the process of achieving joint optimization of trajectory and spectrum comprises the following steps:
s221, modeling the spectrum decision problem in the step S1 into a Stackelberg game, which is expressed as
Figure FDA0002782048090000048
Wherein,
Figure FDA0002782048090000049
representing a set of pairs of drone users,
Figure FDA00027820480900000410
indicating an external malicious disturbance that may be present,
Figure FDA00027820480900000411
and
Figure FDA00027820480900000412
respectively representing the set of policies for in-network users and interference,
Figure FDA00027820480900000413
the strategy adopted for the trajectory abscissa of the drone user pair,
Figure FDA00027820480900000414
strategy adopted for the trajectory ordinate of the unmanned aerial vehicle user pair, unAnd ujRespectively representing utility functions of the unmanned aerial vehicle user on n and interference;
s222, assuming that the interference is a leader and the unmanned aerial vehicle user pair is a follower, modeling both users and the interference in the network as game participants, and constructing a game model; for drone user pair n, it wants to achieve loss minimization, and thus its utility function is defined in segment z as:
un,z(an,z,a-n,z,cj,z,X,Y)=W-En,z
where W is a predefined normal number whose value depends on the user power in the environment, and the user's optimization problem for n is expressed as:
Figure FDA0002782048090000051
the lower level user sub-game is defined as:
Figure FDA0002782048090000052
for interference, its goal is to achieve a maximization of the interference utility function, which is defined as:
Figure FDA0002782048090000053
the optimization problem of the interference is denoted cj=argmaxuj(a,cj);
The upper level disturbing sub-game is defined as:
Figure FDA0002782048090000054
wherein the strategy set is an interference channel set
Figure FDA0002782048090000055
S223, lower layer game
Figure FDA0002782048090000056
The strategy space of (A) is composed of discrete frequency strategy and continuous track, and the lower layer is
Figure FDA0002782048090000057
The sub-game is divided into two sub-problems to solve to give hierarchical equilibrium.
6. The unmanned aerial vehicle anti-jamming method based on joint trajectory planning and spectrum decision of claim 5, wherein in step S223, the lower layer is processed
Figure FDA0002782048090000058
The sub game is divided into two sub problems to be solved, and the process of giving hierarchical equilibrium comprises the following steps:
the unmanned aerial vehicle communication adjusts the user in two aspects of track and frequency strategy, and the user position is fixed under the given interference strategy cjLower, lower-layer unmanned aerial vehicle user pair composition game
Figure FDA0002782048090000059
Figure FDA00027820480900000510
Is an accurate potential energy game and the game has at least one nash equilibrium; at the same time obtain
Figure FDA00027820480900000511
Under the condition of the equilibrium solution, converting the trajectory planning into a convex problem, and solving by using a continuous convex approximation method; through continuous iteration of frequency balance points and track optimization, a strategy of a lower-layer sub game is finally given; game playing model
Figure FDA00027820480900000512
After the strategy of the user is solved, the interference determines the own interference strategy so as to form layered balance.
7. The unmanned aerial vehicle anti-jamming method based on joint trajectory planning and spectrum decision of claim 6, wherein the game model is
Figure FDA00027820480900000513
After the strategy of the user is solved, the process of interference determining the own interference strategy so as to form hierarchical equilibrium comprises the following steps:
given interference strategy θ0Game of chance
Figure FDA00027820480900000514
After the track adjustment is completed, the method is changed into the method that at least one pure object existsStrategic Nash balanced accurate potential energy gaming
Figure FDA00027820480900000515
On game
Figure FDA00027820480900000516
In the presence of NE (theta)0) Calculating a stationary strategy for interference
Figure FDA00027820480900000517
Figure FDA0002782048090000061
Will be provided with
Figure FDA0002782048090000062
A hierarchical equalization in the sense of stationarity is formed.
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