Radar anti-interference game solving method and device, electronic equipment and storage medium

Abstract

The embodiment of the invention relates to the technical field of radar anti-interference, and provides a radar anti-interference game solving method and device, electronic equipment and a storage medium, and the method comprises the steps: generating a plurality of strategy populations for each agent; the intelligent agent comprises a radar array and a jammer; determining a Nash equilibrium strategy of each strategy population based on the dominant function corresponding to each strategy in the strategy population; wherein the strategy represents the optimal reaction of the intelligent agent to other intelligent agents; and for each agent, selecting an optimal strategy from all Nash equilibrium strategies corresponding to the agent. According to the embodiment of the invention, the dominant function is used as a new target function, the strategy obtained by taking the dominant function as a target can definitely reduce the availability of the population, the problem of Nash equilibrium solving in the large-scale game problem in the anti-interference field of radar is effectively solved, and the method has a wide application prospect.

Description

Technical Field

[0001] The present disclosure relates to the field of radar anti-interference technology, and in particular to a radar anti-interference game solving method and device, electronic equipment, and storage medium. Background Art

[0002] Game theory is a theory that is widely used in different disciplines and fields. In the field of radar countermeasures, the interactions between agents, including radar arrays and jammers, are essentially in the form of games. For a specific radar countermeasures game model, its goal is usually to solve its Nash equilibrium. Nash equilibrium is a strategy combination of all agents, representing the stable state when all agents in the current environment adopt the most rational strategy. However, although the existence of Nash equilibrium has been proven, the complexity of its solution is usually considered to be exponential.

[0003] At present, all algorithms for solving Nash equilibrium are some kind of approximate algorithms, which provide specific fast approximate solutions for different environments. The problem of solving Nash equilibrium for large-scale games is still a challenging problem, because the dimensionality disaster of the strategy space makes it very difficult to approach Nash equilibrium. In the prior art, the existing algorithms are basically implemented by the Policy Space Response Oracle (PSRO) algorithm. PSRO constructs a strategy population for each agent, and only solves the sub-game corresponding to the population in each iteration, thereby reducing the complexity of the solution. In order to make the equilibrium of the sub-game close to the Nash equilibrium, it is necessary to continuously generate new strategies and add them to the population to ensure that it is close to the Nash equilibrium. However, in the prior art, most of the methods used in the process of generating new strategies are based on optimal response. Although this can theoretically prove that it can eventually converge to the Nash equilibrium, it cannot guarantee that each iteration can deterministically approach the Nash equilibrium. Even if diversity is introduced as a goal when generating new strategies, it cannot guarantee that the availability will decrease deterministically. Therefore, the above-mentioned prior art is not effective enough in terms of convergence efficiency. Summary of the invention

[0004] The present disclosure aims to solve at least one of the problems existing in the prior art and provides a radar anti-interference game solving method and device, electronic equipment, and storage medium.

[0005] In one aspect of the present disclosure, a radar anti-interference game solving method is provided, the game solving method comprising:

[0006] For each intelligent agent, a plurality of strategy populations are generated respectively; wherein the intelligent agent includes a radar array and a jammer;

[0007] Based on the advantage function corresponding to each strategy in the strategy population, determine the Nash equilibrium strategy of each strategy population respectively; wherein the strategy represents the optimal response of the intelligent agent to other intelligent agents;

[0008] For each of the intelligent agents, the optimal strategy is selected from all the corresponding Nash equilibrium strategies.

[0009] Optionally, the determining of the Nash equilibrium strategy of each strategy population based on the advantage function corresponding to each strategy in the strategy population includes:

[0010] Calculate the Nash equilibrium solution of each strategy population respectively, and obtain the current equilibrium strategy corresponding to each strategy population respectively;

[0011] Based on the current equilibrium strategy and the advantage function, respectively generate a new strategy for each of the strategy populations;

[0012] Adding each new strategy of the strategy population to the corresponding strategy population respectively;

[0013] Repeat the above process until the number of new strategies added to each strategy population meets the preset requirement;

[0014] The Nash equilibrium solutions corresponding to each of the current strategy populations are calculated to obtain the Nash equilibrium strategies corresponding to each of the strategy populations.

[0015] Optionally, generating a new strategy for each strategy population based on the current equilibrium strategy and the advantage function includes:

[0016] Based on the current equilibrium strategy, determining the alternative strategy intervals corresponding to each strategy population respectively;

[0017] For each of the strategy populations, a plurality of candidate strategies are randomly sampled from the corresponding candidate strategy interval, and based on the advantage function, the advantage function values ​​corresponding to the candidate strategies are respectively determined;

[0018] The candidate strategy with the largest advantage function value is taken as the new strategy of the corresponding strategy population.

[0019] Optionally, the advantage function is expressed as:

[0020]

[0021] Among them, π i represents the detection strategy of the i-th radar node; Represents π i The corresponding advantage function; BR(π i ) represents thei The jamming strategy with the best jamming effect; U i Denotes the detection strategy π i The corresponding utility function.

[0022] Optionally, the advantage function has the following properties:

[0023]

[0024] Among them, δ represents the entire space of detection strategies; d represents the exploration range of the current detection strategy; θ i represents the current balancing strategy of the i-th radar node, and θ′ i represents the equilibrium strategy corresponding to the i-th radar node, θ′ j represents the balancing strategy corresponding to the jth jammer, Denote θ′ i The corresponding advantage function is represents all equilibrium strategies, represents the entire strategy space corresponding to the i-th radar node and the j-th jammer, represents the equilibrium strategy solved according to the preset equilibrium solution process; Δπ i Represents the update direction of the detection strategy of the i-th radar node; represents the advantage function; V(θ i ) represents θ i The corresponding advantage function.

[0025] Optionally, the new strategy of the strategy population is expressed as:

[0026]

[0027] in, Represents the strategy population Detection strategy at iteration t+1; Δπ represents the update direction of the radar node’s detection strategy, represents the action space, and t represents the number of strategy iterations.

[0028] Optionally, the Nash equilibrium strategy is expressed as:

[0029]

[0030] in, represents the optimal detection strategy for the jammer's jammer strategy at the tth iteration; represents the average value of the jamming strategy of the jth jammer from the 1st to the tth iteration and represents the kth interference strategy corresponding to the jth jammer.

[0031] Another aspect of the present disclosure provides a radar anti-interference game solving device, the game solving device comprising:

[0032] A generation module, used for generating a plurality of strategy populations for each intelligent agent, wherein the intelligent agent includes a radar array and a jammer;

[0033] A determination module, used to determine the Nash equilibrium strategy of each strategy population based on the advantage function corresponding to each strategy in the strategy population; wherein the strategy represents the optimal response of the agent to other agents;

[0034] The selection module is used to select the optimal strategy from all the corresponding Nash equilibrium strategies for each intelligent agent.

[0035] Another aspect of the present disclosure provides an electronic device, including:

[0036] at least one processor; and,

[0037] a memory communicatively connected to at least one processor; wherein,

[0038] The memory stores instructions that can be executed by at least one processor, and the instructions are executed by at least one processor so that the at least one processor can execute the radar counter-interference game solving method recorded above.

[0039] Another aspect of the present disclosure provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the radar countermeasure interference game solving method described above.

[0040] Compared with the prior art, the present invention proposes an advantage function as a new objective function in the radar countermeasure interference game by analyzing the game transfer structure and the loop structure. The advantage function is directly related to the geometric structure of the game and has an equivalent relationship with the Nash equilibrium, thereby ensuring that the strategy obtained by taking the advantage function as the target can deterministically reduce the population availability, effectively solving the Nash equilibrium solution problem in the large-scale game problem in the field of radar countermeasure interference, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] One or more embodiments are exemplarily described by pictures in the corresponding drawings, and these exemplifications do not constitute limitations on the embodiments. Elements with the same reference numerals in the drawings represent similar elements, and unless otherwise stated, the figures in the drawings do not constitute proportional limitations.

[0042] Figure 1 A flowchart of a radar anti-interference game solving method provided in one embodiment of the present disclosure;

[0043] Figure 2 A schematic diagram of the structure of a radar anti-interference game solving device provided in another embodiment of the present disclosure;

[0044] Figure 3 A schematic structural diagram of an electronic device provided in another embodiment of the present disclosure. DETAILED DESCRIPTION

[0045] In the radar countermeasures game, by analyzing the geometric structure of the game, it can be found that the key to approaching Nash equilibrium is to improve the transfer dimension of the game. Therefore, the embodiment of the present disclosure designs an advantage function as a new strategy evaluation indicator. The advantage function has a certain equivalence relationship with the Nash equilibrium. Using the advantage function as the target, the Nash equilibrium can be deterministically approached in each iteration. On this basis, the embodiment of the present disclosure designs a strategy space response algorithm A-PSRO based on the advantage function as a radar countermeasures game solution method. The algorithm can effectively solve the Nash equilibrium solution problem in the large-scale game problem of radar countermeasures, and has broad application prospects.

[0046] First, consider a static game environment containing multiple radars and multiple jammers, which can be modeled by a normal-form game. Generally speaking, a normal-form game is usually represented by (N, A, U). Among them, N represents all agents, including radar arrays and jammers. A represents the action space of the agent, including the movement, angle, power, etc. of the radar at each moment. U represents the utility function, which is generally represented by the detection area of ​​the current radar for the entire space. In this environment, the radar needs to adopt a specific detection strategy, and the jammer will also adopt a corresponding interference strategy. The strategies adopted by both parties at the same time will constitute a Nash equilibrium, which represents the stable state when both parties adopt the strongest strategy. Since Nash equilibrium usually exists in the form of mixed strategies, the agent actually adopts strategy π rather than action a. Among them, p = (p 1 ,…,p |A| ) is a linear convex combination of actions. A Nash equilibrium is a special combination of all agents (π 1 ,…,π n ), where each agent’s strategy is the best response to other agents. Among them, π -irepresents the strategies of all agents except agent i. In order to measure the distance between a strategy combination and the Nash equilibrium, that is, whether the current radar strategy is robust enough to face the interference of the opponent, the availability is usually used for measurement. The availability is usually expressed as

[0047] Since the complexity of solving Nash equilibrium is exponential, existing technologies usually use approximate learning algorithms to solve it. The classic paper "Consistency and cautious fictitious play" gives a fictitious game as an equilibrium solver, which realizes strategy update through the optimal response in each cycle: The above formula indicates that during each update, the radar will select the optimal strategy for the current interference, and then change it as the interference changes.

[0048] In the prior art, the concept of strategy space response was first proposed in A unified game-theoretic approach to multiagent reinforcement learning for solving large-scale game problems. The strategy space response algorithm first randomly generates a strategy population for each radar and jammer. That is to say, first limit all radar and jamming strategies to a very small limited range, such as the angle can only be adjusted within 5°. In each iteration, only the empirical game matrix corresponding to the population is considered. That is, the equilibrium result when all individuals adopt strategies within this limited range. By solving the matrix using virtual game and other techniques, the above equilibrium can be obtained, which is also called meta-strategy equilibrium. Then, by applying the optimal response to generate new strategies and adding them to the population, the sub-game equilibrium can be continuously approached to the Nash equilibrium.

[0049] In the prior art, "Aunified diversity measure for multiagent reinforcement learning" also proposed a user-defined function (UDF) algorithm. This algorithm is also improved on the basis of PSRO, and introduces diversity as a goal when generating new strategies. Due to the existence of cyclic dimensions in the game, diversity is conducive to improving the probability of discovering better strategies. When calculating diversity, the classic EC metric can be used: in, In addition, when calculating diversity, BD metric, RD metric, etc. can also be used.

[0050] In order to make the purpose, technical scheme and advantages of the embodiments of the present disclosure clearer, the embodiments of the present disclosure will be described in detail below in conjunction with the accompanying drawings. However, it can be understood by those skilled in the art that in each embodiment of the present disclosure, many technical details are proposed in order to enable readers to better understand the present disclosure. However, even without these technical details and various changes and modifications based on the following embodiments, the technical scheme claimed for protection in the present disclosure can also be implemented. The division of the following embodiments is for the convenience of description and should not constitute any limitation on the specific implementation of the present disclosure. The various embodiments can be combined and referenced with each other without contradiction.

[0051] One embodiment of the present disclosure relates to a radar anti-interference game solving method, the process of which is as follows: Figure 1 As shown, including:

[0052] Step S110, generating a plurality of strategy populations for each intelligent agent respectively; wherein the intelligent agent includes a radar array and a jammer.

[0053] Specifically, the radar array includes multiple radar nodes. Taking the radar node as an example, step S110 can randomly generate a series of strategies such as π for each radar node. 1 , …, π n , where π 1 ,…,π n Represent different strategies, such as moving the radar along a certain angle. A series of strategies corresponding to each radar node constitutes a population. in, represents the strategy population corresponding to the i-th radar node, Represent the strategy population The 1st,…,tth detection strategies in are the 1st,…,tth detection strategies corresponding to the ith radar node respectively.

[0054] Step S120, based on the advantage function corresponding to each strategy in the strategy population, determine the Nash equilibrium strategy of each strategy population respectively; wherein the strategy represents the optimal response of an intelligent agent to other intelligent agents.

[0055] Specifically, this embodiment proposes the concept of advantage function for zero-sum game: Among them, π i represents the detection strategy of the i-th radar node. Denotes the detection strategy π i The corresponding advantage function. BR(π i ) represents the i The jamming strategy with the best jamming effect. i Denotes the detection strategy π i The corresponding utility function.

[0056] The concept of advantage function can be understood as follows: assuming that the radar adopts a detection strategy of sub-band broadcasting π i , then among the many jamming strategies of the jammer, BR(π i ) is the best interference strategy for this detection strategy. The detection efficiency under this best interference strategy can be called its advantage.

[0057] The larger the advantage function of a strategy, the higher its distance from the Nash equilibrium, i.e., its absolute strength. In addition, the advantage function has the convexity and Lipschitz continuity of the function, which provides rationality for setting it as the optimization target of the strategy.

[0058] For the strategy space response algorithm that takes the population as the optimization object, for the current population Always That is, the equilibrium has a higher advantage than any other strategy. Here, Indicates all the interference strategies currently being recorded. represents the kth detection strategy of the ith radar node. express The advantage function of θ i Represents the strategy population The current equilibrium strategy of , that is, the current equilibrium strategy of the i-th radar node. Represents the strategy population The equilibrium strategy θ i The advantage function of Indicates that the recorded detection strategies gradually cover the strategy population All available detection strategies.

[0059] Therefore, step S120 can first calculate the current Nash equilibrium solution of each strategy population to obtain the current equilibrium strategy corresponding to each strategy population, and then continuously generate new strategies for each strategy population based on the current equilibrium strategy and advantage function, and add the new strategies to the corresponding strategy population. When the added new strategies meet the quantity requirement, such as reaching N, the Nash equilibrium solution of each strategy population is calculated at this time, and the strategy corresponding to the Nash equilibrium solution is used as the final Nash equilibrium strategy of the corresponding population.

[0060] Exemplarily, step S120 includes: calculating the Nash equilibrium solution of each strategy population respectively to obtain the current equilibrium strategy corresponding to each strategy population; generating a new strategy for each strategy population based on the current equilibrium strategy and the advantage function; adding the new strategy of each strategy population to the corresponding strategy population; repeating the above process until the number of new strategies added to each strategy population meets the preset requirements; calculating the Nash equilibrium solution corresponding to each current strategy population respectively to obtain the Nash equilibrium strategy corresponding to each strategy population respectively.

[0061] Specifically, when calculating the Nash equilibrium solution of the strategy population, a virtual game algorithm can be used, or a similar solver such as a linear complementarity problem (LCP) solver, a replicate dynamic (RD) solver, etc. can be used, and this embodiment does not limit this.

[0062] Regarding the number of new strategies added to each strategy population, the preset requirements can be set according to actual needs. For example, the preset requirements can be set to the number of new strategies added to each strategy population as N. At this time, for each strategy population, the steps of generating new strategies and adding new strategies to the corresponding strategy population are repeated N times, so that N new strategies can be added to each strategy population. After all new strategies are added, the Nash equilibrium solutions corresponding to each current strategy population are calculated, and the Nash equilibrium strategies corresponding to each strategy population can be obtained. At this time, the Nash equilibrium strategy is the strategy closest to the Nash equilibrium.

[0063] In the radar countermeasures interference game, this implementation method generates a new strategy by utilizing the advantage function and adds it to the corresponding strategy population. On this basis, the Nash equilibrium strategy corresponding to each strategy population is calculated. The advantage function can more directly reflect the distance between the strategy and the Nash equilibrium, further effectively improving the convergence and convergence efficiency of the Nash equilibrium solution algorithm in the radar countermeasures interference field game problem.

[0064] Exemplarily, the Nash equilibrium strategy obtained by using the virtual game algorithm can be expressed as: in, Represents the strategy population The detection strategy at the t+1th iteration, that is, the strategy population The corresponding new strategy is compared with the detection strategy at the tth iteration. It represents the optimal detection strategy for the interference strategy of the jth jammer at the tth iteration, which is also the optimal response to the current interference, that is, the optimal detection strategy under the current interference. represents the average value of the jamming strategy of the jth jammer from the 1st to the tth iteration, and t represents the number of policy iterations. represents the kth interference strategy corresponding to the jth jammer, k represents the interference strategy number and the value range of k is 1 to t.

[0065] Exemplarily, in step S120, based on the current equilibrium strategy and the advantage function, a new strategy for each strategy population is generated respectively, including: based on the current equilibrium strategy, respectively determining the alternative strategy interval corresponding to each strategy population; for each strategy population, randomly sampling multiple alternative strategies from its corresponding alternative strategy interval, and based on the advantage function, respectively determining the advantage function value corresponding to each alternative strategy; and taking the alternative strategy with the largest advantage function value as the new strategy of its corresponding strategy population.

[0066] Specifically, the generation of new strategies is the core of the radar anti-interference game solving method provided by this embodiment. In order to make the new strategy deterministically close to the Nash equilibrium, this embodiment aims to improve the advantage of the new strategy during the learning process. The principle of this is that the advantage function has the following properties:

[0067] Among them, δ represents the entire space of detection strategies. For example, taking the detection angle as an example, the entire space of detection strategies includes all detection directions from 0° to 360°. d represents the current detection strategy search range. For example, assuming that the current detection strategy only detects at a detection angle of 10° to 20°, in order to update the detection strategy, it may be necessary to search for a new optimal strategy at a detection angle of 0° to 30°. At this time, the detection angle of 0° to 30° is the current detection strategy search range. θ i Represents the strategy population The current equilibrium strategy is also the current equilibrium strategy of the i-th radar node. For example, for the i-th radar node, if the detection effect is best when the detection angle is 16°, then the current equilibrium strategy of the radar node is the detection strategy with a detection angle of 16°. θ′ i Represents the equilibrium strategy corresponding to the i-th radar node. θ′ j Represents the balancing strategy corresponding to the jth jammer. Denote θ′ i The corresponding advantage function. represents all equilibrium strategies, because, in some cases, the equilibrium strategy is not unique. Represents the entire strategy space corresponding to the i-th radar node and the j-th jammer respectively. It represents the equilibrium strategy solved by the preset equilibrium solution process, that is, the equilibrium strategy solved by a specific equilibrium solution process, including the strategy population corresponding to the i-th radar node And the strategy population corresponding to the jth jammer The corresponding equilibrium strategies. i Indicates the update direction of the detection strategy of the i-th radar node. For example, if the current equilibrium strategy of the i-th radar node is that the detection angle is 16°, and the detection angle is increased by 10° at the next moment, then at this time, Δπ i The value of is the detection angle 10°. represents the advantage function. V(θ i ) represents θ i The corresponding advantage function.

[0068] That is, there is always a new strategy that can improve the population advantage near the meta-game equilibrium. Therefore, the new strategy of the strategy population can be expressed as: in, Represents the strategy population The detection strategy at the t+1th iteration. t is the number of strategy iterations.

[0069] Δπ represents the update direction of the detection strategy of the radar node. For example, if the current equilibrium strategy of the radar node is a detection angle of 16°, and the detection angle is increased by 10° at the next moment as the best, then at this time, the value of Δπ is a detection angle of 10°. Represents the action space, taking the detection angle as an example, including increasing the angle or decreasing the angle. represents ((1-d)·θ i +d·Δπ) corresponding to the advantage function.

[0070] The new strategy generated according to the above goal can ensure that the availability is reduced in each iteration. Among them, the generation of new strategies can be used by the forward-looking module and accomplish.

[0071] For example, assuming that the current equilibrium strategy of the current strategy population calculated in step S120 before generating a new strategy is that the radar flies in the direction of 30°, and the corresponding interference flies in the direction of 60°, then when generating a new strategy to be added to the strategy population corresponding to the radar, an interval around the flight in the direction of 30° can be first selected, for example, the flight direction is the interval of [25°, 35°]. Then, in the interval of [25°, 35°], multiple strategies are randomly adopted with flight directions of 27°, 29°, 31°, and 33° respectively. Then, the advantage function values ​​when the flight directions are 27°, 29°, 31°, and 33° are calculated respectively according to the calculation formula of the advantage function. Assuming that the calculated advantage function values ​​are 0.4, 0.45, 0.55, and 0.36 respectively, at this time, the advantage function value corresponding to the strategy with a flight direction of 31° is the largest, indicating that the strategy with a flight direction of 31° is the strongest strategy at this time. The strongest strategy can be added to the current strategy population as the generated new strategy. At this time, the strategy population is expanded.

[0072] Step S130: For each intelligent agent, select the optimal strategy from all corresponding Nash equilibrium strategies.

[0073] Specifically, when each intelligent agent corresponds to multiple strategy populations, for each intelligent agent, the Nash equilibrium strategies finally obtained by the corresponding strategy populations are compared, and the best Nash equilibrium strategy is taken as the optimal strategy corresponding to the intelligent agent.

[0074] In particular, the radar countermeasure game solution method provided by the embodiment of the present disclosure needs to be improved accordingly when applied to more complex general sum games and multi-agent games. In general sum games, the advantage function as a target will induce a non-convex optimization problem. However, there is always a region of non-zero measure in the entire strategy space that can converge to the optimal equilibrium. Therefore, in order to migrate the application of the advantage function, the advantage function can be made to first generate multiple initial points when applied and select the one with better final effect. This ensures that the optimal solution to the target is learned:

[0075]

[0076] For example, in a complex system containing multiple radar nodes and multiple interferences, multiple strategy populations can be initialized for each radar node. For example, a population is randomly generated every 30°, and the above radar anti-interference game solving method is run for each population. The optimal value of all the optimal equilibrium solutions obtained can be taken.

[0077] In view of the problem that in the existing technology, in the process of solving radar countermeasure interference games, only the current population information is considered, and most of them adopt new strategies based on optimal response or diversity as the goal to generate new strategies, and the obtained new strategies cannot theoretically guarantee to be close to the Nash equilibrium, the radar countermeasure interference game solving method provided by the embodiment of the present disclosure proposes an advantage function as a new objective function in the radar countermeasure interference game by analyzing the game transfer structure and the loop structure. The advantage function is directly related to the geometric structure of the game and has an equivalent relationship with the Nash equilibrium, thereby ensuring that the strategy obtained by taking the advantage function as the goal can deterministically reduce the population availability, effectively solving the Nash equilibrium solution problem in large-scale game problems in the field of radar countermeasure interference, and has broad application prospects.

[0078] Another embodiment of the present disclosure relates to a radar anti-interference game solving device, such as Figure 2 As shown, it includes a generating module 210 , a determining module 220 , and a selecting module 230 .

[0079] The generation module 210 is used to generate a plurality of strategy populations for each intelligent agent, wherein the intelligent agent includes a radar array and a jammer.

[0080] The determination module 220 is used to determine the Nash equilibrium strategy of each strategy population based on the advantage function corresponding to each strategy in the strategy population; wherein the strategy represents the optimal response of an intelligent agent to other intelligent agents.

[0081] The selection module 230 is used to select the optimal strategy from all corresponding Nash equilibrium strategies for each intelligent agent.

[0082] The specific implementation method of the radar counter-interference game solving device provided in the embodiment of the present disclosure can be referred to the radar counter-interference game solving method provided in the embodiment of the present disclosure, which will not be repeated here.

[0083] Compared with the prior art, the radar counter-interference game solving device provided in the embodiment of the present disclosure proposes an advantage function as a new objective function in the radar counter-interference game by analyzing the game transfer structure and the loop structure. The advantage function is directly related to the geometric structure of the game and has an equivalent relationship with the Nash equilibrium, thereby ensuring that the strategy obtained by taking the advantage function as the target can deterministically reduce the population availability, effectively solving the Nash equilibrium solution problem in large-scale game problems in the field of radar counter-interference, and has broad application prospects.

[0084] Another embodiment of the present disclosure relates to an electronic device, such as Figure 3 As shown, including:

[0085] at least one processor 301; and,

[0086] A memory 302 is communicatively connected to at least one processor 301; wherein,

[0087] The memory 302 stores instructions that can be executed by at least one processor 301, and the instructions are executed by at least one processor 301, so that the at least one processor 301 can execute the radar counter-interference game solving method described in the above embodiment.

[0088] Among them, the memory and the processor are connected in a bus manner, and the bus may include any number of interconnected buses and bridges, and the bus connects various circuits of one or more processors and memories together. The bus can also connect various other circuits such as peripherals, voltage regulators, and power management circuits, which are well known in the art and are therefore not further described herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be one element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. The data processed by the processor is transmitted on a wireless medium via an antenna, and further, the antenna also receives data and transmits the data to the processor.

[0089] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory can be used to store data used by the processor when performing operations.

[0090] Another embodiment of the present disclosure relates to a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the radar counter-interference game solving method described in the above embodiment.

[0091] That is, those skilled in the art can understand that all or part of the steps in the method described in the above embodiments can be completed by instructing the relevant hardware through a program, and the program is stored in a storage medium, including several instructions for making a device (which can be a single-chip microcomputer, chip, etc.) or a processor (processor) perform all or part of the steps of the method described in each embodiment of the present disclosure. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk and other media that can store program codes.

[0092] Those skilled in the art will appreciate that the above-mentioned embodiments are specific embodiments for implementing the present disclosure, and in actual applications, various changes may be made thereto in form and detail without departing from the spirit and scope of the present disclosure.

Claims

1. A radar anti-interference game solving method, characterized in that: The game solving method comprises: For each intelligent agent, a plurality of strategy populations are generated respectively; wherein the intelligent agent includes a radar array and a jammer; Based on the advantage function corresponding to each strategy in the strategy population, determine the Nash equilibrium strategy of each strategy population respectively; wherein the strategy represents the optimal response of the intelligent agent to other intelligent agents; For each of the intelligent agents, the optimal strategy is selected from all the corresponding Nash equilibrium strategies.

2. The game solving method according to claim 1, characterized in that: The step of determining the Nash equilibrium strategy of each strategy population based on the advantage function corresponding to each strategy in the strategy population comprises: Calculate the Nash equilibrium solution of each strategy population respectively, and obtain the current equilibrium strategy corresponding to each strategy population respectively; Based on the current equilibrium strategy and the advantage function, respectively generate a new strategy for each of the strategy populations; Adding each new strategy of the strategy population to the corresponding strategy population respectively; Repeat the above process until the number of new strategies added to each strategy population meets the preset requirement; The Nash equilibrium solutions corresponding to each of the current strategy populations are calculated to obtain the Nash equilibrium strategies corresponding to each of the strategy populations.

3. The game solving method according to claim 2, characterized in that: The generating of a new strategy for each strategy population based on the current equilibrium strategy and the advantage function comprises: Based on the current equilibrium strategy, determining the alternative strategy intervals corresponding to each strategy population respectively; For each of the strategy populations, randomly sample multiple candidate strategies from the corresponding candidate strategy interval, and determine the advantage function value corresponding to each of the candidate strategies based on the advantage function; The candidate strategy with the largest advantage function value is taken as the new strategy of the corresponding strategy population.

4. The game solving method according to claim 3, characterized in that: The advantage function is expressed as: Among them, π i represents the detection strategy of the i-th radar node; Represents π i The corresponding advantage function; BR(π i ) represents the i The jamming strategy with the best jamming effect; U i Denotes the detection strategy π i The corresponding utility function.

5. The game solving method according to claim 4, characterized in that: The advantage function has the following properties: Among them, δ represents the entire space of detection strategies; d represents the exploration range of the current detection strategy; θ i represents the current balancing strategy of the i-th radar node, and θ′ i represents the equilibrium strategy corresponding to the i-th radar node, θ′ j represents the balancing strategy corresponding to the jth jammer, Denote θ′ i The corresponding advantage function is represents all equilibrium strategies, represents the entire strategy space corresponding to the i-th radar node and the j-th jammer, represents the equilibrium strategy solved according to the preset equilibrium solution process; Δπ i Represents the update direction of the detection strategy of the i-th radar node; represents the advantage function; V(θ i ) represents θ i The corresponding advantage function.

6. The game solving method according to claim 5, characterized in that: The new strategy of the strategy population is expressed as: in, Represents the strategy population Detection strategy at iteration t+1; Δπ represents the update direction of the radar node’s detection strategy, represents the action space, and t represents the number of strategy iterations.

7. The game solving method according to claim 6, characterized in that: The Nash equilibrium strategy is expressed as: in, represents the optimal detection strategy for the jammer's jammer strategy at the tth iteration; represents the average value of the jamming strategy of the jth jammer from the 1st to the tth iteration and represents the kth interference strategy corresponding to the jth jammer.

8. A radar anti-interference game solving device, characterized in that: The game solving device comprises: A generation module, used for generating a plurality of strategy populations for each intelligent agent, wherein the intelligent agent includes a radar array and a jammer; A determination module, used to determine the Nash equilibrium strategy of each strategy population based on the advantage function corresponding to each strategy in the strategy population; wherein the strategy represents the optimal response of the intelligent agent to other intelligent agents; The selection module is used to select the optimal strategy from all the corresponding Nash equilibrium strategies for each intelligent agent.

9. An electronic device, characterized in that: include: at least one processor; as well as, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the radar counter-interference game solving method according to any one of claims 1 to 7.

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

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