Multi-sensing node position deployment method and system based on zero sum game

Abstract

The invention discloses a multi-sensing-node position deployment method and system based on zero-sum game, a strategy pool of multiple sensing nodes and jammers is constructed, game characteristics of both parties are analyzed based on the strategy pool, a double-layer game modeling framework is constructed, an inner layer adopts a cooperative game form, cooperative anti-interference among multiple nodes is realized, and multi-sensing-node position deployment is realized. The optimal response of a sensing node and a jammer to a strategy of an opposite side is calculated respectively to maximize the overall joint detection efficiency and the game behavior between an outer layer and a simulated sensing system and the jammer, a meta-strategy is updated and solved to obtain a mixed strategy Nash equilibrium, the robust decision-making ability of the system facing an uncertain interference strategy is enhanced, and the robustness of the system is improved. Effective detection of the sensing system in a complex environment is ensured, and the anti-interference stability is better.

Description

Technical Field

[0001] This invention belongs to the field of multi-sensor node location deployment technology, and relates to a multi-sensor node location deployment method and system based on zero-sum game theory. Background Technology

[0002] In multi-UAV collaborative detection scenarios, multi-node cooperation and interaction involve multiple dimensions such as detection performance, deployment strategies, and behavioral coordination, requiring the design of targeted anti-interference strategies to address interference sources in the environment. The design of collaborative detection models needs to comprehensively consider the observation space, policy space, and game objectives, and introduce environmental uncertainties to construct a sound policy evaluation mechanism and utility function system, thereby improving the applicability and stability of the model in practical anti-interference scenarios.

[0003] Game theory, as an important method for solving group decision-making problems, has demonstrated significant advantages in resource optimization and strategy decision-making. Research on finding optimal strategies in cooperative games not only has important theoretical value but also has practical significance for improving the combat effectiveness of systems. Faced with diverse forms of interference such as frequency jamming and power disturbances, systems need to possess the ability to adapt to the environment and adjust strategies. Constructing a robust optimization framework and a dynamic strategy generation mechanism helps to improve the system's anti-interference stability in complex environments.

[0004] The main shortcomings of existing technologies are reflected in the following two aspects: (1) Multi-node location resource optimization: Under the condition of information asymmetry, the networking system needs to reasonably allocate resources and adjust the deployment location to ensure detection performance. The current method is mainly based on the location deployment of multiple nodes under a certain task, and lacks the game element for the search area.

[0005] (2) Anti-complex interference strategy: In complex dynamic environment, the system needs to have the ability to adapt to the environment and adjust the strategy. Constructing a game model and realizing robust optimization and dynamic strategy calculation will help improve the anti-interference stability of the system in complex environment.

[0006] In summary, constructing a perception model with game theory decision-making and multi-node collaboration is a key support for improving the network detection efficiency. Summary of the Invention

[0007] The purpose of this invention is to solve the problems of lack of environmental adaptability and strategy adjustment capability in the face of various interference forms such as frequency interference and power disturbance, and poor anti-interference stability of the system in complex environments in the prior art. It provides a multi-sensor node location deployment method and system based on zero-sum game theory.

[0008] To achieve the above objectives, the present invention employs the following technical solution: A multi-sensor node location deployment method based on zero-sum game theory includes the following steps: Obtain the movement positions of the sensing nodes and jammers, and initialize the policy pools of the multiple sensing nodes and jammers respectively based on their movement positions. Calculate the joint detection efficiency of multiple radar nodes against the jammer, define the payoffs of both sides of the game based on the joint detection efficiency, and construct a payoff matrix based on the payoffs of both sides of the game. Extract a portion of the policies from the policy pools of the multi-sensor node and the jammer respectively to obtain the meta-policies of the sensor node and the jammer. Based on the meta-policies of the sensing nodes and jammers, calculate the optimal response of the sensing nodes and jammers to each other's policies, and update the policy pools of the multi-sensing nodes and jammers based on the optimal responses. Based on the updated policy pools of the multi-sensor nodes and the jammer, update the payoff matrix, and solve for the updated meta-policies of the sensor nodes and the jammer based on the updated payoff matrix. Repeatedly iterate and update. When the preset conditions are met, stop updating, solve the meta-policy for updating the current sensing node and the jammer, and obtain the sensing node location deployment policy.

[0009] A further improvement of the present invention is that: The process of acquiring the movement positions of the sensing nodes and jammers, and initializing the policy pools for the multiple sensing nodes and jammers based on their movement positions, includes: Define the radar's position strategy as follows Define the jammer's position strategy as follows: ; Based on the radar's position strategy Randomly initialize the policy pool of the sensing nodes ; The jammer's policy pool is randomly initialized based on the jammer's location strategy. .

[0010] The calculation of the joint detection efficiency of multiple radar nodes against the jammer, the definition of the payoffs for both sides of the game based on the joint detection efficiency, and the construction of a payoff matrix based on the payoffs of both sides include: Calculate the signal-to-interference-plus-noise ratio (SINR); The probability of a single sensing node detecting a target is calculated based on the signal-to-interference-plus-noise ratio (SINR). ; Based on the detection probability of a target by a single sensing node Calculate the joint detection probability ; Joint detection probability Benefits as a sensing node The benefits of the jammer Defined as joint detection probability The opposite number; Construct a payment matrix based on the revenue of the sensing node and the revenue of the jamming machine.

[0011] The calculation of the signal-to-interference-plus-noise ratio (SINR) includes: When an interference source exists and the interference source is located within the beam of the sensing node:

[0012] When there is no interference source or the interference source is not within the sensing node beam:

[0013] in, Indicates echo signal power, Indicates the power of the interference signal and Indicates noise power.

[0014] The joint detection probability ,include:

[0015] in, To detect the number of nodes. For the first The detection probability of each sensing node.

[0016] The step of calculating the optimal response of the sensing node and the jammer to each other's policies based on their meta-policies, and updating the policy pools of the multi-sensing node and the jammer based on the optimal responses, includes: Calculate the optimal response of the sensing node to the jammer:

[0017] The optimal response of the computational jammer to the sensing node:

[0018] in, The strategy for representing the sensing node. This represents the jammer's meta-policy; This represents the benefit of the sensing node. This indicates the benefits of the jammer; The meta-policy representing the sensing node; The best response of the sensing node Add to the policy pool of the perception node The best response of the jammer Add the jammer's policy pool Complete the policy pool update.

[0019] The step of updating the payment matrix based on the updated policy pools of the multi-sensor nodes and the jammer, and updating the meta-policies of the sensor nodes and the jammer based on the updated payment matrix, includes: All newly added strategies are pitted against existing strategies, and the payoff matrix is ​​filled based on the results of the pitfalls to obtain the updated payoff matrix. Based on the updated payoff matrix, solve for the Nash equilibrium and update the meta-policy:

[0020] in, This represents the jammer's meta-policy; The meta-policy of the sensing node.

[0021] A multi-sensor node location deployment system based on zero-sum game theory includes the following steps: The strategy set construction module is used to obtain the movement positions of the sensing nodes and jammers, and initialize the strategy pools of the multiple sensing nodes and jammers respectively based on the movement positions of the sensing nodes and jammers. The payment matrix construction module is used to calculate the joint detection efficiency of multiple radar nodes against the jammer, define the payoffs of both sides of the game based on the joint detection efficiency, and construct the payment matrix based on the payoffs of both sides of the game. The meta-policy construction module is used to extract partial policies from the policy pools of the multi-sensor nodes and the jammer respectively to obtain the meta-policies of the sensor nodes and the jammer. The policy pool update module is used to calculate the best response of the sensing node and the jammer to each other's policies based on the meta-policies of the sensing node and the jammer, and update the policy pool of the multi-sensing node and the jammer based on the best response. The meta-policy update module is used to update the payoff matrix based on the updated policy pools of the multi-sensor nodes and the jammer, and to solve for the updated meta-policies of the sensor nodes and the jammer based on the updated payoff matrix. The iterative update module is used for repeated iterative updates. When a preset condition is met, the update stops. It solves the meta-policy for updating the current sensing node and the jammer, and obtains the deployment strategy for the sensing node location.

[0022] A terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the steps of any of the methods described in this invention.

[0023] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the methods described in this invention.

[0024] Compared with the prior art, the present invention has the following beneficial effects: This invention discloses a multi-sensor node location deployment method based on zero-sum game theory. It constructs a policy pool for multiple sensing nodes and an interfering machine, analyzes the game characteristics of both sides based on the policy pool, and builds a two-layer game modeling framework. The inner layer adopts a cooperative game approach to achieve collaborative anti-interference among multiple nodes, maximizing the overall joint detection efficiency. The outer layer simulates the game behavior between the sensing system and the interfering party, calculates the optimal responses of the sensing nodes and the interfering machine to each other's policies, updates the meta-policies, and obtains a hybrid policy Nash equilibrium. This enhances the system's robust decision-making ability in the face of uncertain interfering policies, ensuring effective detection in complex environments and exhibiting superior anti-interference stability. Attached Figure Description

[0025] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram illustrating the movement of the sensing node position according to an embodiment of the present invention; Figure 2 This is a diagram of the PSRO dual-loop optimization framework according to an embodiment of the present invention; Figure 3 This is a flowchart of the PSRO-based sensing node decision-making method according to an embodiment of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0028] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0029] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0030] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0031] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0032] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0033] The present invention will now be described in further detail with reference to the accompanying drawings: See Figures 1 to 3 This invention discloses a multi-sensor node location deployment method based on zero-sum game theory. The method designs the strategy space of nodes and noise interference based on radar equations, analyzes the game characteristics of both parties, and determines the state and strategy space.

[0034] First, the model assumes that the perception system, i.e., multiple radar nodes and noise interference sources, can observe each other's positions through direction finding and ranging; and that the nodes and noise interference sources have limited maneuverability (e.g., position changes are constrained by radius). Secondly, there is the strategic space of both sides, including radar positioning strategies. The perception system allows each node to choose a position (heading angle maneuver range ±45°), achieving discretized maneuvers through equal division. The policy space for interference sources is set as follows: The jammer can choose the location. To quantify the behavioral characteristics of heterogeneous nodes in a game environment, a quantitative representation method for game characteristics needs to be constructed for the utility function: by defining the node utility function, the node payoffs (such as the information-to-interference ratio, target detection probability, and joint detection probability) are modeled; the evolution of strategies and the game process between nodes are characterized.

[0035] Specifically, the steps include the following: First, the detection probability of a target by a single sensing node. The following empirical formula can be used for approximate calculation:

[0036] in, is a given false alarm probability, representing the probability that a sensing node will falsely alarm in the absence of a target. The signal-to-interference-plus-noise ratio (SNR) is defined as:

[0037] Furthermore, regarding the target echo signal power Interference signal power and noise power Perform the calculation: (1) Target echo signal power : According to the detection equation, the target echo signal power is calculated as follows:

[0038] in, To sense the transmission power of the node, , For transmit and receive antenna gain, To sense the operating wavelength of the node, The distance to the target. The target's radar cross section (RCS). To handle gain or pulse compression ratio, For signal bandwidth, The repetition frequency.

[0039] (2) Interference signal power : For each interference source, the interference signal power is calculated as follows:

[0040] in, For the first The transmission power of each interference source, For sensing nodes and the first The distance between the interference sources.

[0041] The total interference power is the sum of the power of all interference sources:

[0042] (3) Noise power : The noise power is calculated as follows:

[0043] in, Boltzmann's constant is equal to Joules per Kelvin This refers to the system noise temperature, typically 290 Kelvin. This is the receiver noise figure (linear value).

[0044] Based on the above indicators, the calculation of the joint detection probability can be derived as follows: in the case of multi-sensor node collaborative detection, assuming that the detection events of each sensor node are independent of each other, the probability that the target is detected by at least one sensor node (joint detection probability) can be obtained. for:

[0045] in, To detect the number of nodes. For the first The detection probability of each sensing node.

[0046] This formula demonstrates the effectiveness of multi-sensor node collaborative detection in improving target detection probability. By calculating the detection probability of each sensor node at the target's location and using the above formula, the joint detection performance of the overall system can be obtained.

[0047] Furthermore, considering the spatial relationship between the target and the interference, in actual calculations, it is necessary to consider the spatial positional relationship between the target, the sensing node, and the interference source, as well as the 3dB beamwidth of the sensing node beam. It can be approximated as:

[0048] in, Indicates the number of antenna array elements. This indicates the spacing between array elements. For each sensing node, it is necessary to determine whether the interference source is within its beam range. Only when the interference source falls within the beam of the sensing node will it have an interference effect on the sensing node.

[0049] Furthermore, regarding the calculation of SINR, when an interference source is present and located within the sensing node beam:

[0050] When there is no interference source or the interference source is not within the sensing node beam:

[0051] Using the above methods, a complete computational model for the joint detection probability of a multi-node detection system can be established. In a multi-interference source environment, the effects of signal, interference, and noise, as well as the spatial relationships between sensing nodes, targets, and interference sources, are considered. Using the detection equation and signal processing gain, the target echo signal power and interference signal power are calculated, thus obtaining the SINR.

[0052] Based on this, the detection probability of a single sensing node is calculated using an empirical formula. Then, by using the joint detection probability formula and combining the detection capabilities of multiple sensing nodes, the joint detection probability of the overall system is obtained. This series of calculations provides a theoretical basis for evaluating the detection performance of the network detection system under strong interference environments, and also lays the foundation for the evaluation and optimization of subsequent game strategies. Specifically, in the next calculation, the joint detection probability of the entire system is taken as the reward of the sensing node, and the reward of the jammer is the negative of the joint detection probability. The movable positions of the sensing node and the jammer are taken as the strategy set of both parties, thus generating a zero-sum game problem between the sensing node and the jammer.

[0053] Specifically, based on the joint detection probability of the overall system, the payoffs of the two players can be defined, where, The benefit of the sensing node is:

[0054] The benefits of the jammer are:

[0055] Based on this, a zero-sum game between the sensing nodes and the jamming machine was generated.

[0056] This embodiment addresses the zero-sum game problem between the sensing node and the interfering machine using the PSRO algorithm. The PSRO algorithm is suitable for policy learning problems in multi-agent environments, especially when considering the mutual influence between policies. PSRO aims to select diverse interfering factors to increase the policy pool, and then randomly select high-value policies from the pool. The specific modeling and solution processes of the PSRO algorithm are as follows: Step 1: Initialize the policy pool Randomly initialize the policy pool of the sensing nodes and jammer's policy pool .

[0057] Step 2: Construct the payment matrix Define the payoff matrix for the sensing node and the jammer. ,in Indicates the sensing node selection strategy and jammer selection strategy The detection utility at that time (such as joint detection probability).

[0058] Step 3: Initialize the meta-policy Initialize the meta-policy of the sensing nodes and the jammer and The strategies are usually evenly distributed (equally likely to be selected from the initial strategy pool).

[0059] Step 4: Calculate the optimal response and empirical utility In each iteration cycle, the perceptor node and the interfering machine train new policies (oracles) using deep reinforcement learning, each approximating the optimal response to the other's policy, based on the other's meta-policy. Simulations are then used to calculate the expected utility of the newly added policy in combination with all other policies, and the payoff matrix is ​​updated.

[0060] Step 5: Meta-policy update Using empirical game theory analysis methods (such as regret matching, Hedge, or projected replicator dynamics), the meta-policies of the sensing node and the interfering machine are computed.

[0061] Step 6: Termination Condition Check Check if the algorithm meets the termination conditions (such as the performance improvement of the best response being less than a threshold, or reaching the maximum number of iterations). If the conditions are met, the algorithm terminates; otherwise, return to step 4.

[0062] Table 1 Pseudocode of PSRO Algorithm

[0063] This embodiment proposes an innovative two-layer game-theoretic modeling framework for multi-node networked radar sensing systems in future high-dynamic environments, and conducts a systematic study on model construction, strategy evaluation, algorithm optimization, and practical verification. In terms of model design, the inner layer adopts a cooperative game approach to achieve collaborative anti-interference among multiple nodes, thereby maximizing the overall detection probability. The outer layer constructs a zero-sum adversarial game model to simulate the game behavior between the perception system and the interfering party. The PSRO algorithm is introduced to solve the mixed strategy Nash equilibrium, thereby enhancing the system's robust decision-making ability when facing uncertain interference strategies.

[0064] Specifically, in terms of strategy evaluation, this embodiment constructs a multi-dimensional utility function system, which includes the target detection probability. False alarm rate Coverage area Key indicators are incorporated into the strategy effectiveness evaluation to form a quantitative assessment closed loop. The joint detection probability is calculated comprehensively using the following expression:

[0065] Furthermore, in terms of algorithm engineering, the PSRO (Policy Space Response Optimization) algorithm was used to effectively address the equilibrium problem brought about by high-dimensional policy spaces, and to support game reasoning in scenarios where the interference policies are unknown, thereby enhancing the feasibility of the model's engineering deployment and providing the possibility for embedding the game model into a real-time combat system.

[0066] In summary, this embodiment constructs a game theory model with collaborative and dynamic adaptability under complex conditions, and provides solid theoretical support and technical foundation for future intelligent networked multi-node sensing systems through theoretical design and experimental verification. It has broad application prospects and promotional value.

[0067] This embodiment discloses a multi-sensor node location deployment method based on zero-sum game theory, including the following steps: The strategy set construction module is used to obtain the movement positions of the sensing nodes and jammers, and initialize the strategy pools of the multiple sensing nodes and jammers respectively based on the movement positions of the sensing nodes and jammers. The payment matrix construction module is used to calculate the joint detection efficiency of multiple radar nodes against the jammer, define the payoffs of both sides of the game based on the joint detection efficiency, and construct the payment matrix based on the payoffs of both sides of the game. The meta-policy construction module is used to extract partial policies from the policy pools of the multi-sensor nodes and the jammer respectively to obtain the meta-policies of the sensor nodes and the jammer. The policy pool update module is used to calculate the best response of the sensing node and the jammer to each other's policies based on the meta-policies of the sensing node and the jammer, and update the policy pool of the multi-sensing node and the jammer based on the best response. The meta-policy update module is used to update the payoff matrix based on the updated policy pools of the multi-sensor nodes and the jammer, and to solve for the updated meta-policies of the sensor nodes and the jammer based on the updated payoff matrix. The iterative update module is used for repeated iterative updates. When a preset condition is met, the update stops, and the meta-policy for updating the current sensing node and jammer is solved to obtain the sensing node location deployment strategy. The invention protected by this patent is to construct a game model and strategy evaluation method for multi-node collaborative detection. Based on the radar equation, the strategy space of sensing nodes and noise interference sources is designed, the game characteristics of both parties are analyzed, the state and strategy space are determined, and a multi-sensor node location deployment method and system based on zero-sum game is proposed.

[0068] This invention establishes a game model between multiple sensing nodes and noise interference sources, evaluates the payoffs of both parties' strategies based on radar equations, designs the location deployment strategy space for both parties, further improves and constructs the game model between the two parties, and solves the Nash equilibrium through the PSRO (Policy Double Cyclic Iteration) method to ensure the robustness of the sensing system in effectively detecting and responding to noise interference sources in complex environments.

[0069] A schematic diagram of a terminal device according to 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, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0070] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention.

[0071] The terminal device can be a desktop computer, laptop computer, cloud server, or other device with strong computing power. The terminal device may include, but is not limited to, a processor and memory.

[0072] The optimal choice for the processor is a multi-core high-speed central processing unit (CPU).

[0073] The memory can be used to store the computer program and / or module. The processor implements various functions of the terminal device by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0074] If the modules / units integrated into the terminal device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed 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 electrical carrier signals and telecommunication signals.

[0075] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for deploying multi-sensor node locations based on zero-sum game theory, characterized in that, Includes the following steps: Obtain the movement positions of the sensing nodes and jammers, and initialize the policy pools of the multiple sensing nodes and jammers respectively based on their movement positions. Calculate the joint detection efficiency of multiple radar nodes against the jammer, define the payoffs of both sides of the game based on the joint detection efficiency, and construct a payoff matrix based on the payoffs of both sides of the game. Extract a portion of the policies from the policy pools of the multi-sensor node and the jammer respectively to obtain the meta-policies of the sensor node and the jammer. Based on the meta-policies of the sensing nodes and jammers, calculate the optimal response of the sensing nodes and jammers to each other's policies, and update the policy pools of the multi-sensing nodes and jammers based on the optimal responses. Based on the updated policy pools of the multi-sensor nodes and the jammer, update the payoff matrix, and solve for the updated meta-policies of the sensor nodes and the jammer based on the updated payoff matrix. Repeatedly iterate and update. When the preset conditions are met, stop updating, solve the meta-policy for updating the current sensing node and the jammer, and obtain the sensing node location deployment policy.

2. The multi-sensor node location deployment method based on zero-sum game theory according to claim 1, characterized in that, The process of acquiring the movement positions of the sensing nodes and jammers, and initializing the policy pools for the multiple sensing nodes and jammers based on their movement positions, includes: Define the radar's position strategy as follows Define the jammer's position strategy as follows: ; Based on the radar's position strategy Randomly initialize the policy pool of the sensing nodes ; The jammer's policy pool is randomly initialized based on the jammer's location strategy. .

3. The multi-sensor node location deployment method based on zero-sum game theory according to claim 1, characterized in that, The calculation of the joint detection efficiency of multiple radar nodes against the jammer, the definition of the payoffs for both sides of the game based on the joint detection efficiency, and the construction of a payoff matrix based on the payoffs of both sides include: Calculate the signal-to-interference-plus-noise ratio (SINR); The detection probability of a single sensing node for a target is calculated based on the signal-to-interference-plus-noise ratio (SINR). ; Based on the detection probability of a target by a single sensing node Calculate the joint detection probability ; Joint detection probability Benefits as a sensing node The benefits of the jammer Defined as joint detection probability The opposite number; Construct a payment matrix based on the revenue of the sensing node and the revenue of the jamming machine.

4. The multi-sensor node location deployment method based on zero-sum game theory according to claim 3, characterized in that, The calculation of signal-to-interference-plus-noise ratio (SINR) includes: When an interference source exists and the interference source is located within the beam of the sensing node: When there is no interference source or the interference source is not within the sensing node beam: in, Indicates echo signal power, Indicates the power of the interference signal and Indicates noise power.

5. The multi-sensor node location deployment method based on zero-sum game theory according to claim 3, characterized in that, The joint detection probability ,include: in, To detect the number of nodes. For the first The detection probability of each sensing node.

6. The multi-sensor node location deployment method based on zero-sum game theory according to claim 1, characterized in that, The step of calculating the optimal response of the sensing node and the jammer to each other's policies based on their meta-policies, and updating the policy pools of the multi-sensing node and the jammer based on the optimal responses, includes: Calculate the optimal response of the sensing node to the jammer: The optimal response of the computational jammer to the sensing node: in, The strategy for representing the sensing node. This represents the jammer's meta-policy; This represents the benefit of the sensing node. This indicates the benefits of the jammer; The meta-policy representing the sensing node; The best response of the sensing node Add to the policy pool of the perception node The best response of the jammer Add the jammer's policy pool Complete the policy pool update.

7. The multi-sensor node location deployment method based on zero-sum game theory according to claim 1, characterized in that, The step of updating the payoff matrix based on the updated policy pools of the multi-sensor nodes and the jammer, and solving for the updated meta-policies of the sensor nodes and the jammer based on the updated payoff matrix, includes: All newly added strategies are pitted against existing strategies, and the payoff matrix is ​​filled based on the results of the pitfalls to obtain the updated payoff matrix. Based on the updated payoff matrix, solve for the Nash equilibrium and update the meta-policy: in, This represents the jammer's meta-policy; The meta-policy of the sensing node.

8. A method for deploying multi-sensor node locations based on zero-sum game theory, characterized in that, Includes the following steps: The strategy set construction module is used to obtain the movement positions of the sensing nodes and jammers, and initialize the strategy pools of the multiple sensing nodes and jammers respectively based on the movement positions of the sensing nodes and jammers. The payment matrix construction module is used to calculate the joint detection efficiency of multiple radar nodes against the jammer, define the payoffs of both sides of the game based on the joint detection efficiency, and construct the payment matrix based on the payoffs of both sides of the game. The meta-policy construction module is used to extract partial policies from the policy pools of the multi-sensor nodes and the jammer respectively to obtain the meta-policies of the sensor nodes and the jammer. The policy pool update module is used to calculate the best response of the sensing node and the jammer to each other's policies based on the meta-policies of the sensing node and the jammer, and update the policy pool of the multi-sensing node and the jammer based on the best response. The meta-policy update module is used to update the payment matrix based on the updated policy pools of the multi-sensor nodes and jammers, and to update the meta-policies of the sensor nodes and jammers based on the updated payment matrix. The iterative update module is used for repeated iterative updates. When a preset condition is met, the update stops. It solves the meta-policy for updating the current sensing node and the jammer, and obtains the deployment strategy for the sensing node location.

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, it implements the steps of the method as described in any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-7.

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