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

Abstract

The embodiment of the present disclosure relates to the technical field of radar countermeasure jamming, and provides a radar countermeasure jamming game solving method and device, electronic equipment and storage medium, the method comprising: generating a plurality of strategy populations for each agent respectively; the agent comprises a radar array and a jammer; Nash equilibrium strategies of each strategy population are determined 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; for each agent, the optimal strategy is selected from all the Nash equilibrium strategies corresponding thereto. The embodiment of the present disclosure proposes the advantage function as a new objective function, which ensures that the strategy obtained by taking the advantage function as the target can deterministically reduce the population availability, effectively solves the Nash equilibrium solving problem in the large-scale game problem in the field of radar countermeasure jamming, and has a wide application prospect.

Description

Technical Field

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

[0002] Game theory is widely applied across various disciplines and fields. In the field of radar countermeasures, the interactions between intelligent agents, including radar arrays and jammers, are essentially games. For a specific radar countermeasures game model, the goal is typically to find its Nash equilibrium. A Nash equilibrium is a combination of strategies for all agents in the environment, representing the stable state when all agents adopt the most rational strategy. However, while the existence of a Nash equilibrium has been proven, its solution is generally considered exponentially complex.

[0003] Currently, all algorithms for solving Nash equilibrium are approximate algorithms, each providing a specific, fast, approximate solution for a specific environment. Solving Nash equilibrium for large-scale games remains a challenging problem, as the curse of dimensionality in the policy space makes approaching a Nash equilibrium extremely difficult. Existing algorithms in the prior art are generally implemented using the Policy Space Response Oracle (PSRO) algorithm. PSRO constructs a population of strategies for each agent and solves only the subgame corresponding to that population in each iteration, thereby reducing solution complexity. To ensure that the equilibrium of the subgame approaches a Nash equilibrium, new strategies must be continuously generated and added to the population to ensure proximity. However, in the prior art, the methods used to generate new strategies are mostly based on optimal response. While this approach theoretically demonstrates that convergence to a Nash equilibrium is ultimately achieved, it cannot guarantee that each iteration will deterministically approach a Nash equilibrium. Even when diversity is incorporated into the generation of new strategies, there is no guarantee that availability will decrease deterministically. Therefore, these prior art techniques are not effective 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 counter-interference game solving method and device, electronic equipment, and storage medium.

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

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

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

[0010] Calculating the Nash equilibrium solution of each of the strategy populations respectively to obtain the current equilibrium strategy corresponding to each of the strategy populations;

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

[0012] Adding the new strategy of each 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 requirements;

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

[0017] For each of the strategy populations, randomly sampling multiple alternative strategies from the corresponding alternative strategy interval, and determining the advantage function value corresponding to each of the alternative strategies based on the advantage function;

[0018] The alternative strategy with the largest advantage function value is used 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 the relationship between πi The interference strategy with the best interference 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 j-th jammer, Represents 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 policy iterations.

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

[0029]

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

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

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

[0033] a determination module, configured 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 the at least one processor so that the at least one processor can execute the radar countermeasure interference game solving method described 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 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 target can deterministically reduce the population availability, effectively solving the Nash equilibrium problem in large-scale game problems in the field of radar countermeasure interference, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] One or more embodiments are exemplarily illustrated 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 countermeasures interference game solution method provided in one embodiment of the present disclosure;

[0043] Figure 2 A schematic structural diagram of a radar countermeasure interference game solving device provided by 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 radar countermeasures, an analysis of the game's geometry reveals that the key to approaching a Nash equilibrium lies in improving the game's transfer dimension. Therefore, the disclosed embodiments design an advantage function as a new strategy evaluation metric. This advantage function has a certain equivalence relationship with the Nash equilibrium. Using the advantage function as a target, a Nash equilibrium can be deterministically approached in each iteration. Based on this, the disclosed embodiments design a strategy space response algorithm (A-PSRO) based on the advantage function as a method for solving radar countermeasures. This algorithm can effectively solve the Nash equilibrium problem in large-scale 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=(p1,…,p |A| ) is a linear convex combination of actions. A Nash equilibrium is a special combination of all agents (π1,…,π n ), where each agent’s strategy is the best response to other agents, i.e. Among them, π -iIndicates the strategies of all agents except agent i. In order to measure the distance between a strategy combination and Nash equilibrium, that is, whether the current radar strategy is robust enough to withstand the interference of the opponent, the availability is usually used for measurement. The availability is usually expressed as

[0047] Because 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" proposes a fictitious game as an equilibrium solver, which updates the strategy 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” to solve 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, for example, the angle can only be adjusted within 5 degrees. In each iteration, only the experience game matrix corresponding to the population is considered. That is, the equilibrium result when all individuals adopt strategies within this limited range. By solving this matrix using techniques such as virtual games, the above equilibrium can be obtained, which is also called meta-strategy equilibrium. Then, by applying the optimal response to generate a new strategy and adding it 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 proposes a User-Defined Function (UDF) algorithm. This algorithm also improves upon PSRO and incorporates diversity as a goal when generating new strategies. Due to the presence of cyclic dimensions in the game, diversity helps increase the probability of discovering a superior strategy. 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 solutions and advantages of the embodiments of the present disclosure clearer, the embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings. However, it will be understood by those skilled in the art that in each embodiment of the present disclosure, many technical details are provided 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 solutions claimed in the present disclosure can 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 under the premise that there is no contradiction.

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

[0052] Step S110 , generating multiple strategy populations for each intelligent agent respectively; wherein the intelligent agents include radar arrays and jammers.

[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 π1, ..., π n , where π1,…,π n Each radar node corresponds to a series of strategies that constitute a population. in, represents the strategy population corresponding to the i-th radar node, Represents the strategy population The 1st,…,tth detection strategies in are the 1st,…,tth detection strategies corresponding to the i-th 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 relationship between π 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 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, the greater the distance from the Nash equilibrium, i.e., the higher the absolute strength. Furthermore, the advantage function exhibits convexity and Lipschitz continuity, which justifies its use as the optimization objective for the strategy.

[0058] For the strategy space response algorithm with population as the optimization object, for the current population There is always That is, the equilibrium has a higher advantage than any other strategy. Here, Indicates all currently recorded interference strategies. represents the kth detection strategy of the i-th radar node. express 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 the advantage function, and add the new strategies to the corresponding strategy population. When the number of newly added strategies meets the quantity requirement, such as reaching N, the Nash equilibrium solution of each strategy population at this time is calculated, 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 replica dynamic (RD) solver, etc. can be used. This embodiment does not limit this.

[0062] The preset requirement for the number of new strategies added to each strategy population can be set based on actual needs. For example, the preset requirement can be set to N new strategies to be added to each strategy population. In this case, for each strategy population, the loop consisting of the steps of generating new strategies and adding them to the corresponding strategy population is repeated N times, thereby adding N new strategies to each strategy population. After all new strategies have been added, the Nash equilibrium solutions corresponding to each current strategy population are calculated to obtain the Nash equilibrium strategies corresponding to each strategy population. At this point, the Nash equilibrium strategies are the strategies that are closest to the Nash equilibrium.

[0063] In the radar countermeasures interference game, this embodiment uses the advantage function to generate a new strategy 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 game problem.

[0064] For example, 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 compared to the detection strategy at the t-th iteration. It represents the optimal detection strategy for the jammer j at the tth iteration, and is also the optimal response to the current jammer, that is, the optimal detection strategy under the current jammer. 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 is generated for each strategy population, including: based on the current equilibrium strategy, 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, 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 a new strategy is the core of the radar countermeasures game solution method provided in this embodiment. To ensure that the new strategy can deterministically approach a 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] Where 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 detection angles of 10° to 20°, in order to update the detection strategy, it may be necessary to search for a new optimal strategy at detection angles of 0° to 30°. In this case, the detection angle of 0° to 30° is the current detection strategy search range. θ i Represents the strategy population The current balancing strategy is also the current balancing 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 balancing strategy of the radar node is the detection strategy with a detection angle of 16°. θ′ i Represents the balancing strategy corresponding to the i-th radar node. θ′ j Represents the balancing strategy corresponding to the j-th jammer. Represents 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. Represents the equilibrium strategy solved according to 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 j-th 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 a detection angle of 16°, and the detection angle is increased by 10° at the next moment, then Δπ i The value is the detection angle 10°. Denotes 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 iteration t+1. t is the number of strategy iterations.

[0069] Δπ represents the update direction of the radar node's detection strategy. For example, if the current equilibrium strategy of the radar node is a detection angle of 16°, and the optimal detection angle is increased by 10° at the next moment, then 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 the new strategy can be achieved through 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 a direction of 30° and the corresponding interference flies in a 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 direction of 30° can be first selected, for example, the flight direction interval of [25°, 35°]. Then, multiple strategies are randomly adopted in the interval [25°, 35°] with flight directions of 27°, 29°, 31°, and 33°, respectively. Then, the advantage function values ​​for the flight directions of 27°, 29°, 31°, and 33° are calculated according to the advantage function calculation formula. 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. This strongest strategy can be added to the current strategy population as the generated new strategy, and the strategy population is now expanded.

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

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

[0074] In particular, the radar countermeasure game solution method provided by the embodiments of the present disclosure requires corresponding improvements when applied to more complex general sum games and multi-agent games. In general sum games, using the advantage function as an objective induces a non-convex optimization problem. However, there is always a region of non-zero measure in the entire strategy space that converges to the optimal equilibrium. Therefore, in order to migrate the application of the advantage function, the advantage function can be used to first generate multiple initial points and select the one with the best final effect. This ensures that the optimal solution to the objective 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 counter-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 the existing technology only considers the current population information in the process of solving the radar countermeasure interference game, most of them adopt the method of generating new strategies based on optimal response or diversity as the goal, 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 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 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 multiple strategy populations for each intelligent agent, wherein the intelligent agents include radar arrays and jammers.

[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 found in 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 countermeasures game solving device provided in the embodiments of the present disclosure proposes an advantage function as a new objective function in the radar countermeasures game by analyzing the game's transfer structure and loop structure. This advantage function is directly related to the game's geometric structure and has an equivalent relationship with the Nash equilibrium, thereby ensuring that the strategy obtained by using the advantage function as the objective can deterministically reduce the population availability. This effectively solves the problem of solving the Nash equilibrium in large-scale game problems in the field of radar countermeasures, and has broad application prospects.

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

[0085] at least one processor 301; and,

[0086] A memory 302 in communication with at least one processor 301; wherein,

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

[0088] The memory and processor are connected using a bus, which can include any number of interconnected buses and bridges. The bus connects various circuits of one or more processors and memories. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits. These are all well known in the art and are therefore not described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over a wireless medium via an antenna. Furthermore, the antenna receives data and transmits it 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 countermeasure interference game solving method described in the above embodiment.

[0091] That is, those skilled in the art will understand that all or part of the steps in the methods described in the above embodiments can be implemented by instructing related hardware through a program, which is stored in a storage medium and includes a number of instructions for causing a device (which may be a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps in the methods described in the various embodiments of the present disclosure. The aforementioned storage medium includes: a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc., various media that can store program code.

[0092] Those skilled in the art will appreciate that the above-mentioned embodiments are specific embodiments for implementing the present disclosure, and that 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 counter-interference game solving method, characterized in that: The game solving method includes: For each intelligent agent, a plurality of strategy populations are generated respectively; wherein the intelligent agent includes a radar array and a jammer; Determining 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; For each of the intelligent agents, selecting the optimal strategy from all the corresponding Nash equilibrium strategies; 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 relationship between π i The interference strategy with the best interference effect; U i Denotes the detection strategy π i The corresponding utility function; 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 j-th jammer, Represents 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.

2. The game solving method according to claim 1, characterized in that: 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: Calculating the Nash equilibrium solution of each of the strategy populations respectively to obtain the current equilibrium strategy corresponding to each of the strategy populations; Based on the current equilibrium strategy and the advantage function, generating a new strategy for each of the strategy populations; Adding the new strategy of each 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 requirements; The Nash equilibrium solutions corresponding to the current strategy populations are calculated to obtain the Nash equilibrium strategies corresponding to the strategy populations.

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

4. The game solving method according to claim 3, 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 policy iterations.

5. The game solving method according to claim 4, characterized in that: The Nash equilibrium strategy is expressed as: in, represents the optimal detection strategy for the jamming strategy of the j-th jammer at the t-th iteration; represents the average value of the jamming strategy of the jth jammer from the 1st to the tth iteration and represents the kth jammer strategy corresponding to the jth jammer.

6. A radar anti-interference game solving device, characterized in that: The game solving device comprises: A generation module, configured to generate a plurality of strategy populations for each intelligent agent, wherein the intelligent agent includes a radar array and a jammer; a determination module, configured 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; A selection module is used to select the optimal strategy from all the Nash equilibrium strategies corresponding to each intelligent agent; 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 relationship between π i The interference strategy with the best interference effect; U i Denotes the detection strategy π i The corresponding utility function; 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 j-th jammer, Represents 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.

7. 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 to enable the at least one processor to execute the radar countermeasure interference game solving method according to any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the radar countermeasure interference game solving method according to any one of claims 1 to 5 is implemented.

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