Satellite communication interference confrontation method and system based on game theory

Abstract

The invention discloses a satellite communication interference confrontation method and system based on the game theory, and the method combines a motion model and a communication interference model of a satellite, solves a Nash equilibrium point, optimizes the operation power and electromagnetic interference confrontation strategies of attackers and defenders, and improves the performance of the satellite communication interference confrontation when constructing a performance index. An attacker performance index and a defender performance index of each satellite are respectively established, and the operation power of a physical layer and the channel capacity of a network layer are considered, so that an attacker can reduce the communication capacity of a communication party to the greatest extent while keeping low-power operation, and the purpose of efficient interference is achieved; the channel capacity is related to the relative distance between the satellites, so that the interference satellites can utilize interference signals with lower power to achieve the attack purpose through control, the energy consumption of the satellites can be reduced, and the adaptability can be improved; and the communication party can increase the own communication capacity to the greatest extent while keeping low-power operation, so that the anti-interference purpose is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite anti-interference countermeasure, and relates to a satellite communication interference countermeasure method and system based on game theory. Background Art

[0002] With the continuous development and widespread application of satellite communication technology, satellite communication plays a vital role in the fields of military, aerospace, navigation, remote sensing, etc. As the international space competition continues to intensify, space security has gradually attracted the attention of various countries. In order to deal with space threats, space attack and defense technology has become a research hotspot in the international aerospace field.

[0003] Satellite communication systems face various interferences and threats in practical applications. Especially in the military field, by effectively interfering with enemy satellite communications, the enemy's communication capabilities can be significantly weakened and strategic advantages can be gained. Therefore, it is very necessary to study the corresponding satellite interference countermeasures.

[0004] However, traditional jamming methods mainly rely on high-power jamming signals and complex electronic warfare technologies, but these methods often face problems such as high energy consumption, easy detection and poor adaptability, and most studies only focus on electromagnetic attacks at the network layer without considering the control issues at the physical layer. Therefore, it is very necessary to study the operating power consumption of the satellite physical layer and the electromagnetic interference attack and defense issues at the network layer. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that most of the studies in the prior art only focus on electromagnetic attacks at the network layer without considering the control problem of the physical layer, resulting in the fact that the operating power consumption of the satellite physical layer and the electromagnetic interference attack and defense problems at the network layer cannot be solved. A satellite communication interference countermeasure method and system based on game theory is provided.

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

[0007] A satellite communication interference countermeasure method based on game theory comprises the following steps:

[0008] Construct satellite motion and communication models;

[0009] Based on the motion model and communication model, the attacker performance index and defender performance index of each satellite are established respectively, and the existence of Nash equilibrium is proved according to the attacker performance index and defender performance index.

[0010] Solve the proven Nash equilibrium, obtain the Nash equilibrium control rate, and obtain the anti-interference strategy.

[0011] A further improvement of the present invention is:

[0012] The motion model of the satellite includes:

[0013] In the reference frame coordinates, the motion equations are used to describe the motion of each spacecraft:

[0014]

[0015] in, μ represents the gravitational constant, a0 represents the reference orbit radius, x represents the position of the spacecraft on the x-axis; y represents the position of the spacecraft on the y-axis; z represents the position of the spacecraft on the z-axis; u x Indicates the control amount on the x-axis; u y Indicates the control amount on the y-axis; u z Indicates the control amount on the z-axis;

[0016] definition u=[u x u y u z ] T Then we have:

[0017]

[0018] in:

[0019]

[0020] The communication model building includes:

[0021]

[0022] In the formula, represents the interference power emitted by the attacker, and Respectively represent the communication power of the two satellites of the defender; σ 2 Indicates the ambient noise level; P D1 Indicates the position of defender 1; P D2 Indicates the position of defender 2; P A Indicates the attacker's position.

[0023] The establishment of the performance index of the attacker of each satellite includes the following steps:

[0024] The attacker's goals are defined as:

[0025]

[0026] Among them, w A represents the operating power weight factor, which represents the attacker's preference for controlling the operating power, Y Arepresents the communication interference weight factor, which represents the attacker's preference for controlling communication interference; P M represents the attacker's operating power; C t represents capacity; dt represents integration of time;

[0027] The attacker's optimal control problem is described as:

[0028]

[0029] The establishment of defender performance indicators for each satellite includes the following steps:

[0030] The defender's goal is defined as:

[0031]

[0032] Among them, w D1 and w D2 Both represent the operating power weight factor, representing the defender's preference for controlling operating power. and Represents the operating power of Defender 1 and 2 respectively.

[0033] The solution to the proven Nash equilibrium includes the following steps:

[0034] The problem is solved by using the minimum principle, and the necessary conditions that the optimal control sequence of each intelligent agent in the discrete system should satisfy are obtained. The motion model is discretized using the first-order difference method.

[0035] Based on the necessary conditions obtained, the gradient method is used to solve the optimal control.

[0036] The problem of using the minimum principle to solve the problem includes:

[0037] The Hamiltonian function is defined as:

[0038] H=L+λ T f

[0039] Solve the following HJI equations:

[0040]

[0041]

[0042] Discretize the constructed motion model:

[0043]

[0044] In the formula, δ represents the step size or sampling period;

[0045] Get the discrete optimal control sequence u* (k) Necessary conditions that should be satisfied include equation of state, co-equation of state, extreme value conditions, initial conditions and transversality conditions.

[0046] The method of using the gradient method to solve the optimal control comprises the following steps:

[0047] Preset allowable error, given control quantity u 0 (k), and put it into the discretized state equation to obtain the state sequence x under the initial condition x(0) = x0 0 (k), the state sequence x 0 Substitute (k) into the adjoint equation, and under the final value condition λ(k f ) is calculated in the reverse direction of the lower edge time to obtain the covariate variable sequence λ 0 (k);

[0048] x 0 (k) and u 0 (k), λ 0 (k) Substitute into the gradient equation and calculate u 0 (k) make amendments;

[0049] When making corrections, the modification amount Δu 0 (k) Select the gradient The negative direction of Where K>0, K is the step size parameter, and the new approximate value u of the control variable is obtained 1 (k) = u 0 (k)+Δu 0 (k), start a new iteration;

[0050] When the difference between the performance index J of two iterations is less than ε, that is, J j+1 -J j <ε, stop the iteration, and the corresponding control u j+1 This is the final control strategy.

[0051] A satellite communication interference countermeasure system based on game theory, comprising:

[0052] Model building module, used to build the satellite's motion model and communication model;

[0053] The performance index building module is used to build the attacker performance index and defender performance index of each satellite based on the motion model and the communication model, and prove the existence of Nash equilibrium based on the attacker performance index and the defender performance index;

[0054] The anti-interference strategy acquisition module is used to solve the proven Nash equilibrium, obtain the Nash equilibrium control rate, and obtain the anti-interference strategy.

[0055] A terminal device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the steps of any method described in the present invention when executing the computer program.

[0056] A computer-readable storage medium stores a computer program, wherein the computer program, when executed by a processor, implements the steps of any method described in the present invention.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] The invention discloses a satellite communication interference countermeasure method based on game theory. The method combines the motion model and communication interference model of the satellite, optimizes the operating power and electromagnetic interference countermeasure strategy of the attacking and defending parties by solving the Nash equilibrium point, and respectively establishes the attacker performance index and the defender performance index of each satellite when constructing the performance index, taking into account both the operating power of the physical layer and the channel capacity of the network layer, so that the attacking party can reduce the communication capacity of the communicating party to the maximum extent while maintaining low-power operation, thereby achieving the purpose of efficient interference, and because the channel capacity is related to the relative distance between satellites, the interfering satellite can be controlled to use a lower-power interference signal to achieve the purpose of attack, thereby reducing the energy consumption of the satellite and improving the adaptability; the communicating party can increase its own communication capacity to the maximum extent while maintaining low-power operation, thereby achieving the purpose of anti-interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0060] Figure 1 It is a schematic diagram of the process of the present invention;

[0061] Figure 2 A diagram of a satellite communication interference scenario in an embodiment of the present invention;

[0062] Figure 3 : is a communication interference simulation result diagram in an embodiment of the present invention (wherein, a represents the trajectory diagram of the attacker, defender No. 1, and defender No. 2; b represents the control curve diagram of defender No. 1; c represents the control curve diagram of defender No. 2; d represents the control curve diagram of the attacker);

[0063] Figure 4 Schematic diagram of the influence of the attacker interference weight on the simulation in the embodiment of the present invention (where a represents YA =5, the trajectory of the attacker, defender 1, and defender 2; b represents Y A =10: Attacker, Defender 1, Defender 2 trajectory diagram);

[0064] Figure 5 Schematic diagram of the effect of the attacker's interference power on the simulation in the embodiment of the present invention (where a represents At the time of attack, defender 1, defender 2 trajectory diagram; b represents Attacker, Defender 1, and Defender 2 trajectory diagram). DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0066] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0068] In the description of the embodiments of the present invention, it should be noted that if the terms "upper", "lower", "horizontal", "inner", etc. indicate an orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the product of the invention is usually placed when in use, it is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0069] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", which does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0070] In the description of the embodiments of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "set", "install", "connect", and "connect" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal connection of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0071] The present invention is further described in detail below in conjunction with the accompanying drawings:

[0072] See also Figure 1 This embodiment discloses a satellite communication interference countermeasure method based on game theory, which can provide a Nash equilibrium solution of the game problem in the scenario of satellite communication interference countermeasure, and provide simulation results under different interference powers and different weights. This method combines the satellite motion model and the communication interference model, and optimizes the operating power and electromagnetic interference countermeasure strategy of both the attacker and the defender by solving the Nash equilibrium point. Different from the existing research methods that only consider the electromagnetic interference countermeasure of the network layer, through the present invention, the attacker can minimize the communication capacity of the communicator while maintaining low power operation, thereby achieving the purpose of efficient interference; the communicator can maximize its own communication capacity while maintaining low power operation, thereby achieving the purpose of anti-interference.

[0073] Example 1

[0074] This embodiment discloses a satellite communication interference countermeasure method based on game theory, comprising the following steps:

[0075] Step 1: Construct the satellite motion model and communication model;

[0076] Step 1.1: Constructing the satellite motion model includes:

[0077] A virtual spacecraft (primary star) O that is independently orbiting in a circular orbit is selected near the participant as the origin to establish the LVLH reference coordinate system. The OX axis points radially from the center of mass of the earth to the primary star, OY is perpendicular to OX in the reference orbital plane and points to the flight direction of the spacecraft, and OZ is perpendicular to the orbital plane and forms a right-handed rectangular coordinate system with OX and OY.

[0078] Then, the CW equation is used to describe the motion of each spacecraft in this reference coordinate system:

[0079]

[0080] in, μ represents the gravitational constant, a0 represents the reference orbit radius;

[0081] definition u=[u x u y u z ] T Then we have:

[0082]

[0083] in:

[0084]

[0085] Step 1.2: Build the satellite communication model

[0086] Assume that the distance between the transmitter and the receiver is d, and the transmitter emits a power of P. T Transmit, then the received signal power P R for:

[0087] P R =P T d -α (2)

[0088] Pick is the interference power emitted by the attacker, is the communication power of the two satellites of the defender;

[0089] The signal-to-noise ratio (SINR) is given by:

[0090]

[0091] Among them, P I is the electromagnetic interference imposed by other participants received by the receiver, σ 2 is the ambient noise level.

[0092] Furthermore, the channel capacity C t Given by:

[0093]

[0094] Then we have:

[0095]

[0096] Step 2: Based on the motion model and communication model, establish the attacker performance index and defender performance index of each satellite respectively, and prove the existence of Nash equilibrium according to the attacker performance index and defender performance index;

[0097] Step 2.1: Establish attacker performance indicators for each satellite including:

[0098] According to Newton's laws of motion, we have F(t) = ma(t), where F(t) is the force generated by the engine and m is the mass of the participant. Therefore, the average power required over a period of time (t, t+dt) can be approximately expressed as:

[0099]

[0100] From the CW equation, we know that:

[0101] a=A 21 p+A 22 v+u (7)

[0102] Substituting equation (7) into equation (6), we obtain:

[0103]

[0104] Approximate operating power P M for:

[0105]

[0106] Pick is the operating power of the attacker, is the operating power of the defender’s two satellites;

[0107] Step 2.2: Establish attacker performance indicators for each satellite including:

[0108] For the attacker, the goal is to minimize its own operating power while maximizing the interference to the enemy's communication (that is, to minimize the enemy's communication capacity). Therefore, the attacker's goal can be defined as:

[0109]

[0110] Among them, w A is the operating power weight factor, representing the attacker’s preference for controlling the operating power, τ A is the communication interference weight factor, which represents the attacker’s preference for controlling communication interference.

[0111] The attacker’s optimal control problem can be described as:

[0112]

[0113] For the defender, the goal is to minimize its own operating power while maximizing its own communication capacity. Therefore, the defender's goal can be defined as:

[0114]

[0115] w D1 、wD2 is the operating power weight factor, which represents the defender’s preference for controlling the operating power.

[0116] Therefore, the optimal control problem of the defender can be described as:

[0117]

[0118] Step 2.3: Prove the existence of Nash equilibrium based on the attacker's performance indicators and the defender's performance indicators, including:

[0119] Proof: According to the above definition, {u A} and {u D1 ,u D2} are all compact metric spaces, and the objective function J A and J D is continuous and bounded, we can find:

[0120]

[0121] At the same time, we can obtain:

[0122]

[0123] From formulas (14)-(16), we can see that j A For u A is convex, j D For u D1 and u D2 is convex; therefore, for the above differential game, there exists a pure strategy Nash equilibrium.

[0124] Step 3: Solve the proven Nash equilibrium, obtain the Nash equilibrium control rate, and obtain the anti-interference strategy

[0125] The problem is solved using the minimum principle, and the Hamiltonian function is defined as:

[0126] H=L+λ T f (17)

[0127] Solve the following HJI equations:

[0128]

[0129] In the above problem, due to the problems of too many dimensions and complex objective functions, it is impossible to directly obtain an analytical solution. When using a computer to solve the problem, the original system is first discretized. This embodiment uses the first-order difference method to approximate the first-order differential, that is:

[0130]

[0131] Where δ is the step size or sampling period.

[0132] Get the discrete optimal control sequence u * (k) The necessary conditions to be met are:

[0133] Equation of state:

[0134] x * (k+1)=x * (k)+δf[x * (k),u * (k),k] (22)

[0135] Co-state equation:

[0136]

[0137] Extreme value conditions:

[0138]

[0139] Initial conditions:

[0140] x * (k0) = x0 (25)

[0141] Transversal conditions:

[0142] λ(k f )=0 (26)

[0143] By using the above formula to discretize the original system, we can obtain the necessary conditions that each agent should satisfy for the optimal control sequence in the discrete system.

[0144] Furthermore, the gradient method is used to solve the optimal control:

[0145] According to the minimum principle, the optimal control u * The Hamiltonian function H should be minimized. In the iterative process, this paper will use the gradient descent method to continuously adjust the control variables to minimize the performance index. In each iteration, the update rule will adjust the control variables in the direction of reducing the performance index.

[0146] The basic idea of ​​the gradient method is to first guess a u 0 , find a corresponding H 0 , and then modify u successively to reduce the corresponding H value until it approaches the minimum value; and each modification of u is carried out along the "steepest descent" direction (i.e., the negative gradient direction) of the function H value. Obviously, such a modification should be the most favorable, and the convergence of the successive approximation process should also be the fastest.

[0147] The specific steps include:

[0148] First, choose the allowable error ε and guess a u 0 (k), substituting into the state equation, the state sequence x can be calculated under the initial condition x(0) = x0 0 (k), and then substitute it into the adjoint equation, under the final value condition λ(k f ) is calculated in the reverse direction of the lower edge time to obtain the covariate variable sequence λ 0 (k).

[0149] x 0 (k) and u 0 (k), λ 0 (k) Substitute into the gradient equation, since u 0 (k) is generally not optimal control, so the control equation does not hold at this time, that is, J(u 0 ) is not the smallest, so we must 0 (k) Make amendments.

[0150] During correction, in order to maximize the reduction of performance index J, the modification amount Δu 0 (k) should be selected in the gradient The negative direction of Among them, K>0, K is the step size parameter.

[0151] This gives us a new approximate value u of the control variable: 1 (k) = u 0 (k)+Δu 0 (k), and then start a new iteration process.

[0152] When the difference between the performance index J of the two iterations is less than ε, that is, J j+1 -J j <ε, stop the iteration, and the corresponding control u j+1 This is the desired control strategy.

[0153] The specific calculation methods include the following:

[0154]

[0155] The present invention also discloses a specific embodiment

[0156] In order to verify the correctness and effectiveness of the theory, the present invention considers an actual attack and defense game situation occurring in a satellite system.

[0157] Satellite communication interference scenario diagram Figure 2 .

[0158] The initial altitude of the reference orbit is h = 500 km, and the gravitational acceleration is g = 9.8 × 10 -3 km / s 2, the radius of the earth is R = 6371.393 km. Take α = 3.75, σ = 0.005, m A =m D =10 3 kg, δ = 0.01, K = 0.99, in order to better observe the game situation of each agent under the electromagnetic interference attack and reduce the impact of power consumption on the simulation results, w is selected A =0.1, w D1 =0.05, w D2 =0.05. Select A=1, The initial positions and velocities of each satellite are shown in Table 1.

[0159] Status parameters Attacker Defender 1 Defender 2 x(km) 0 3 -1 y(km) 0 8 8 z(km) 0 0 0 <![CDATA[v x (km·s -1 )]]> 0 0 0 <![CDATA[v y (km·s -1 )]]> 7 7 7 <![CDATA[v z (km·s -1 )]]> 0 0 0

[0160] See also Figure 3 In the early stage of the game, in order to increase the communication interference to the defender, the attacker chooses to get close to the defender's position, so it generates control forces in the positive direction of the x-axis and the positive direction of the y-axis to ensure that it can get close to the defender at a faster speed. As for the defender, in order to enhance the communication quality, the two choose to get close to each other, so defender No. 1 generates a control force in the negative direction of the x-axis, and defender No. 2 generates a force in the positive direction of the x-axis. In addition, both hope to avoid the interference of the attacker as much as possible, so they generate a control amount in the positive direction of the y-axis to ensure that they can better avoid interference. After a period of time, the attacker basically caught up with the defender, and the defender tried to avoid interference, so a force in the positive direction of the x-axis was generated. In order to ensure the quality of their own communication, the defender chose to get close to each other and escape together. Because the attacker accelerated too much when pursuing forward, it exceeded the middle position of the defender. Therefore, in the second half, the attacker generated a deceleration control amount to get as close to the defender as possible, among which, Figure 3 The channel capacity simulation results shown in are: t =72276.776519.

[0161] To illustrate the impact of attacker interference weight on the results, we select A =5, A = 10 to simulate and compare, the simulation results are as follows Figure 4 By comparison Figure 3 a. Figure 4 a and Figure 4 b, and the simulation results of each simulated channel capacity, it can be found that increasing the attacker's interference weight factor can effectively reduce the defender's channel capacity and achieve the purpose of interfering with the defender's communication. Figure 4 The channel capacity simulation result shown in a is: C t =6278.183118; Figure 4 The channel capacity simulation result shown in b is: Ct =1011.014420.

[0162] To illustrate the impact of the attacker’s interference power on the results, we select A =5 Select P T A =1.4W, P T A = 1.8W for simulation and comparison. The simulation results are as follows Figure 5 By comparison Figure 4 a. Figure 5 a. Figure 5 b, and the simulation results of each simulated channel capacity, it can be found that increasing the attacker's interference power can effectively reduce the defender's channel capacity and achieve the purpose of interfering with the defender's communication. And by comparing several figures, it can be found that P T A =1W, the three agents are basically moving side by side, and after increasing the power, the defender increases his avoidance of the attacker. This is because after increasing the interference power, the attacker's interference to the defender is enhanced at the same distance, so the original balance is broken and the defender has more tendency to escape.

[0163] in, Figure 5 The channel capacity simulation result shown in a is: C t =3767.325049; Figure 4 The channel capacity simulation result shown in b is: C t =2765.235083.

[0164] The method disclosed in the present invention utilizes a game theory method, combined with a satellite motion model and a communication interference model, and optimizes the operating power and electromagnetic interference countermeasure strategies of both the attacker and the defender by solving the Nash equilibrium point. Different from the method of only considering electromagnetic interference countermeasures at the network layer in the existing research, the present invention considers both the operating power of the physical layer and the channel capacity of the network layer in the design of performance indicators, which enables the attacker to minimize the communication capacity of the communication party while maintaining low power operation, thereby achieving the purpose of efficient interference, and because the channel capacity is related to the relative distance between satellites, the interference satellite can be controlled to use a lower power interference signal to achieve the purpose of attack, thereby reducing the energy consumption of the satellite and improving adaptability; the communication party can maximize its own communication capacity while maintaining low power operation, thereby achieving the purpose of anti-interference.

[0165] Example 2

[0166] This embodiment also discloses a satellite communication interference countermeasure system based on game theory, including:

[0167] Model building module, used to build the satellite's motion model and communication model;

[0168] The performance index building module is used to build the attacker performance index and defender performance index of each satellite based on the motion model and the communication model, and prove the existence of Nash equilibrium based on the attacker performance index and the defender performance index;

[0169] The anti-interference strategy acquisition module is used to solve the proven Nash equilibrium, obtain the Nash equilibrium control rate, and obtain the anti-interference strategy.

[0170] A schematic diagram of a terminal device provided in an embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps in the above-mentioned method embodiments are implemented. Alternatively, when the processor executes the computer program, the functions of the modules / units in the above-mentioned device embodiments are implemented.

[0171] The computer program may be divided into one or more modules / units, and the one or more modules / units are stored in the memory and executed by the processor to accomplish the present invention.

[0172] The terminal device may be a computing device such as a desktop computer, a notebook, a PDA, a cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0173] The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0174] The memory may be used to store the computer programs and / or modules, and the processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory.

[0175] If the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0176] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A satellite communication interference countermeasure method based on game theory, characterized in that: The following steps are involved: Construct satellite motion and communication models; Based on the motion model and communication model, the attacker performance index and defender performance index of each satellite are established respectively, and the existence of Nash equilibrium is proved according to the attacker performance index and defender performance index. Solve the proven Nash equilibrium, obtain the Nash equilibrium control rate, and obtain the anti-interference strategy.

2. A satellite communication interference countermeasure method based on game theory according to claim 1, characterized in that: The motion model of the satellite includes: In the reference frame coordinates, the motion equations are used to describe the motion of each spacecraft: in, μ represents the gravitational constant, a0 represents the reference orbit radius, x represents the position of the spacecraft on the x-axis; y represents the position of the spacecraft on the y-axis; z represents the position of the spacecraft on the z-axis; u x Indicates the control amount on the x-axis; u y Indicates the control amount on the y-axis; u z Indicates the control amount on the z-axis; Determined u = [u x u y u z ] T Existing: in:

3. The satellite communication interference countermeasure method based on game theory according to claim 1 is characterized in that: The communication model building includes: In the formula, represents the interference power emitted by the attacker, and Respectively represent the communication power of the two satellites of the defender; σ 2 Indicates the ambient noise level; p D1 Indicates the position of defender 1; p D2 Indicates the position of defender 2; P A Indicates the attacker's position.

4. The satellite communication interference countermeasure method based on game theory according to claim 1, characterized in that: The establishment of the performance index of the attacker of each satellite includes the following steps: The attacker's goals are defined as: Among them, w A represents the operating power weight factor, which represents the attacker’s preference for controlling the operating power, γ A represents the communication interference weight factor, which represents the attacker's preference for controlling communication interference; P M represents the attacker's operating power; C t represents capacity; dt represents integration of time; The attacker's optimal control problem is described as: The establishment of defender performance indicators for each satellite includes the following steps: The defender's goal is defined as: Among them, w D1 and w D2 Both represent the operating power weight factor, representing the defender's preference for controlling operating power. and Represents the operating power of Defender 1 and 2 respectively.

5. The satellite communication interference countermeasure method based on game theory according to claim 1, characterized in that: The solution to the proven Nash equilibrium includes the following steps: The problem is solved by using the minimum principle, and the necessary conditions that the optimal control sequence of each intelligent agent in the discrete system should satisfy are obtained. The motion model is discretized using the first-order difference method. Based on the necessary conditions obtained, the gradient method is used to solve the optimal control.

6. A satellite communication interference countermeasure method based on game theory according to claim 5, characterized in that: The problem of solving the problem by using the minimum principle includes: The Hamiltonian function is defined as: H=L+λ T f Solve the following HJI equations: Discretize the constructed motion model: In the formula, δ represents the step size or sampling period; Get the discrete optimal control sequence u * (k) Necessary conditions that should be satisfied include equation of state, co-equation of state, extreme value conditions, initial conditions and transversality conditions.

7. A satellite communication interference countermeasure method based on game theory according to claim 6, characterized in that: The method of using the gradient method to solve the optimal control comprises the following steps: Preset allowable error, given control quantity u 0 (k), and put it into the discretized state equation to obtain the state sequence x under the initial condition x(0) = x0 0 (k), the state sequence x 0 Substitute (k) into the adjoint equation, and under the final value condition λ(k f ) is calculated in the reverse direction of the lower edge time to obtain the covariate variable sequence λ 0 (k); x 0 (k) and u 0 (k), λ 0 (k) Substitute into the gradient equation and calculate u 0 (k) make amendments; When making corrections, the modification amount Δu 0 (k) Select the gradient The negative direction of Where K>0, K is the step size parameter, and the new approximate value u of the control variable is obtained 1 (k) = u 0 (k)+Δu 0 (k), start a new iteration; When the difference between the performance index J of two iterations is less than ε, that is, J j+1 -J j <ε, stop the iteration, and the corresponding control u j+1 This is the final control strategy.

8. A satellite communication interference countermeasure system based on game theory, characterized in that: include: Model building module, used to build the satellite's motion model and communication model; The performance index building module is used to build the attacker performance index and defender performance index of each satellite based on the motion model and the communication model, and prove the existence of Nash equilibrium based on the attacker performance index and the defender performance index; The anti-interference strategy acquisition module is used to solve the proven Nash equilibrium, obtain the Nash equilibrium control rate, and obtain the anti-interference strategy.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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