Radar jamming decision method based on combination of order relation analysis and entropy weight game empowerment

Abstract

The application provides a radar jamming decision-making method based on sequence relation analysis and entropy weight game combination weighting, relates to the technical field of radar electronic countermeasure, and comprises the following steps: Nash equilibrium combination weighting is adopted to combine subjective weights of a sequence relation analysis method for calculating jamming evaluation indexes according to expert experience and objective weights solved by an entropy weight method based on jamming measured data, a linear expression of combined weights is constructed, an optimization model is constructed by taking the minimum Euclidean distance of the combined weights and the subjective weights and the objective weights as a target, optimal combination coefficients are solved, and a jamming pattern optimization result for radar jamming decision-making is obtained. The application introduces Nash equilibrium of game theory, constructs an optimization model by taking the minimum Euclidean distance of the combined weights and the subjective weights and the objective weights of the entropy weight method as a target, solves optimal combination coefficients and comprehensive index weights, calculates comprehensive scores of each jamming pattern in combination with standardized jamming data, and outputs an optimal jamming pattern.

Description

Technical Field

[0001] This invention relates to the field of radar electronic countermeasures technology, and more specifically, to a radar jamming decision-making method based on a combination of order relation analysis and entropy weight game. Background Technology

[0002] The electromagnetic environment of modern battlefields is becoming increasingly complex, with diversified radar systems and continuously improving detection and anti-jamming capabilities. Jammers need to quickly select the optimal jamming pattern based on enemy radar parameters, operational airspace, and equipment performance to achieve precise suppression. The selection of jamming patterns is a multi-indicator decision problem, with indicators including jamming power, time response, PRT response, signal bandwidth, spatial coverage, platform distance, signal coherence, and other multi-dimensional parameters. The weighting of these indicators directly determines the reliability of the jamming decision results.

[0003] Existing indicator weighting methods fall into two categories: Single-subjective weighting methods, such as the G1 method (or order relation analysis), are used to assign weights. For example, the numerical evaluation scheme for flight maneuvers based on the order relation analysis method proposed by Yuan Tao et al. relies on domain experts to rank the importance of indicators and manually assign weights. The advantage is that it can fully incorporate radar countermeasure experience; the disadvantage is that it depends on the subjective judgment of experts, has no experimental data constraints, is highly subjective, has large differences in scores among different experts, lacks objectivity of weights in complex electromagnetic scenarios, and is prone to decision-making bias.

[0004] Single objective weighting methods, represented by the entropy weighting method: For example, the entropy weight method for evaluating the competence of counselors, constructed by Zhou Lin et al., relies on a matrix of measured data to calculate the information entropy of indicators and generates weights based on data. Its advantages are objectivity, neutrality, and quantification of data differences; its disadvantages are that it cannot incorporate the commander's prior knowledge and relies solely on sample data. When battlefield data is missing or the sample is unbalanced, the weights lack battlefield adaptability and are difficult to match the needs of real combat.

[0005] Currently, the radar countermeasures and jamming decision-making field only uses the above-mentioned single weighting scheme, which cannot simultaneously take into account expert experience and objective data measured by equipment. This leads to a distortion in the comprehensive score of jamming patterns, and the jammer cannot quickly and accurately select the optimal jamming pattern that is suitable for the current electromagnetic scene. This results in practical shortcomings such as wasted jamming resources and insufficient suppression effect. Summary of the Invention

[0006] Therefore, the purpose of this invention is to propose a radar jamming decision-making method based on a combination of order relation analysis and entropy weight game. The method employs order relation analysis to calculate the subjective weights of jamming evaluation indicators based on expert experience, and uses the entropy weight method to solve for the objective weights based on measured jamming data. It introduces the Nash equilibrium concept from game theory, constructing an optimization model with the objective of minimizing the Euclidean distance between the combined weights and the individual subjective and objective weights, and solving for the optimal combination coefficients to obtain the comprehensive indicator weights. It combines standardized jamming data to calculate the comprehensive score of each jamming pattern, outputting the optimal jamming pattern. This method overcomes the shortcomings of existing methods, such as the strong subjectivity of single subjective weighting and the lack of battlefield adaptability of single entropy weight methods. It also integrates prior knowledge and measured data information, making the weight allocation more balanced and reliable. This enables rapid and accurate decision-making on jamming patterns in complex electromagnetic environments and can be widely applied to airborne, vehicle-mounted, and shipborne radar counter-jamming equipment.

[0007] This invention provides a radar jamming decision-making method based on a combination of order relation analysis and entropy weight game, comprising the following steps: By combining the subjective weights of the interference evaluation index calculated based on expert experience using the Nash equilibrium combination method, and the objective weights calculated based on the interference measured data using the entropy weight method, a linear expression for the combined weights is constructed. An optimization model is constructed with the objective of minimizing the Euclidean distance between the combined weights and the individual subjective and objective weights. The optimal combination coefficients are then solved to obtain the optimal interference pattern for radar interference decision-making.

[0008] Furthermore, the method of combining the subjective weights of the order relation analysis method used to calculate the interference evaluation index based on expert experience with the objective weights obtained by the entropy weight method based on measured interference data includes: A basic weight set is constructed using the subjective weights of interference evaluation indicators obtained through order relation analysis based on expert experience and the objective weights of interference evaluation indicators obtained through entropy weight method based on measured interference data. A combined weight in the form of a linear superposition of the subjective and objective weights of the interference evaluation indicators is then constructed. Two sets of combination coefficients to be optimized, both with values ​​greater than zero, are set to correspond to the subjective and objective weights, respectively. A game-theoretic combination weighting method is used to solve for the equilibrium point between the subjective and objective weights. The equilibrium point is the weight value corresponding to the minimum overall deviation between the combined weight and the subjective and objective weights, respectively.

[0009] Specifically, the subjective weights of the order relation analysis method and the objective weights obtained by the entropy weight method are used as the basic weight set to construct a combined weight. The linear expression of the combined weight is as follows: ω=α1ω c +α2ω j ; Where, ωc The weights of the interference evaluation indexes obtained by the order relation analysis method, ω j Let α1 and α2 be the combined coefficients of the subjective and objective weights to be optimized, respectively, and α1 > 0 and α2 > 0. Using a game-theoretic combination weighting method, we seek a balance between the order relation analysis method and the entropy weight method. This balance point is the combination weight ω and the subjective weight ω of the order relation analysis method. c And the objective weight ω obtained by the entropy weight method j The point where the deviation between them is minimized.

[0010] Furthermore, the method for constructing an optimization model with the objective of minimizing the Euclidean distance between the combined weights and the individual subjective and objective weights includes: The optimization objective function is constructed by minimizing the Euclidean distance between the combined weights of the interference evaluation indicators obtained by linear superposition and the subjective weight row vectors output by the order relation analysis method and the objective weight row vectors output by the entropy weight method, respectively. The superscripts of the subjective and objective weight row vectors are used to identify the vector transpose, and the squared Euclidean distance between the two sets of vectors is represented by the squared L2 norm. The optimization objective function sets two types of minimum value solving objectives, respectively minimizing the squared Euclidean distance between the combined weights and the individual subjective and objective weights. Specifically, the optimization objective function is constructed with minimizing the Euclidean distance between the combined weights and each individual subjective and objective weight as the optimization objective: ; in, ω c T The subjective weight row vector obtained by the order relation analysis method, with superscript... T Represents transpose; ω j T This is the objective weight row vector obtained by the entropy weight method; ||2 2 is the square of the vector's 2-norm, i.e., the square of the Euclidean distance; min means to find the minimum value; The optimization objective function is a game-theoretic weighted bi-objective minimization optimization model, which aims to minimize the squared Euclidean distance between the combined weights and the subjective and objective weights, respectively.

[0011] Furthermore, the method for solving the optimal combination coefficients includes: Based on the constraint of finding the extremum using matrix differentiation, the first-order partial derivative of the objective function is calculated and set to zero, deriving a system of linear equations for solving the combination coefficients. The measured radar interference index data is substituted into the system of linear equations to calculate the initial combination coefficients. The initial combination coefficients are then normalized so that the sum of the two sets of combination coefficients equals 1, finally yielding the optimal combination coefficients assigned to the order relation analysis method and the entropy weight method, respectively.

[0012] Specifically, based on the extremum condition of matrix differentiation, the first-order partial derivative of the objective function is made equal to 0, resulting in the optimal system of linear equations: ; Based on the optimal linear equation system, the combination coefficients are calculated by substituting the data, and the combination coefficients are normalized so that α1 + α2 = 1. Finally, the optimal combination coefficients α1 and α2 are obtained, which are the weights allocated by the order relation analysis method and the entropy weight method.

[0013] Furthermore, the method for obtaining the optimal interference pattern for radar interference decision-making includes: Substitute the optimal combination coefficients obtained from the solution into the optimization model (linear combination model) to calculate the final game combination weight of the subjective weight of the fusion order relation analysis method and the objective weight of the entropy weight method; multiply the original data matrix of the interference evaluation index after standardization with the row vector of the final game combination weight with transpose label to obtain the comprehensive interference evaluation index corresponding to each type of interference pattern; determine the optimal interference pattern result corresponding to the radar interference decision based on the magnitude of the comprehensive interference evaluation index of each interference pattern.

[0014] Specifically, substituting the optimal combination coefficients into the optimization model (linear combination model) yields the final game combination weights, the expression for which is: ω final =α1ω c +α2ω j ; Where, ω final The final game combination weights; ω c Subjective weights obtained by order relation analysis; ω j The objective weights obtained by the entropy weight method; Multiply the final game combination weights by the standardized original data matrix of interference evaluation indicators to calculate the comprehensive score for each interference pattern: E=BωT final; Where E is the comprehensive interference evaluation index; B is the original data matrix of the standardized interference evaluation index; ωTfinal is the final game combination weight row vector, and the superscript T represents the vector transpose; Based on the comprehensive score, the optimal interference pattern is determined.

[0015] Furthermore, after obtaining the optimal interference pattern for radar interference decision-making, the method further includes: performing simulation analysis on the optimal interference pattern, wherein the configuration of the simulation analysis includes: setting multiple interference patterns and setting multiple interference evaluation indicators; The various interference patterns include: range decoy interference, velocity decoy interference, dense decoy interference, coherent interference, and intermittent sampling and forwarding interference; The various interference evaluation indicators include: interference power, time response, PRT response, signal bandwidth, spatial coverage, distance between the jammer and the radar, and signal coherence.

[0016] In the field of radar, PRT (Pulse Repetition Time) refers to the time interval between the start points of two adjacent transmitted pulses. The response characteristics of PRT are reflected in the decisive constraint on the maximum unambiguous range of the radar and the reciprocal relationship with PRF.

[0017] Furthermore, the simulation analysis method includes: The analysis process involves three steps: subjective weighting using the order relation analysis method, objective weighting using the entropy weight method, and game combination weighting. The order relation analysis method involves experts ranking seven types of interference evaluation indicators according to their importance, determining the importance ratio of adjacent indicators, and then calculating the subjective weights. The entropy weight method sequentially constructs the original data matrix, the normalized matrix, and the indicator ratio matrix, and calculates the objective weights using the indicator entropy values. The game combination weighting method constructs an optimization objective function, solves for the optimal combination coefficients, and combines the subjective and objective weights with an optimization model (linear combination model) to obtain the final game combination weights.

[0018] Specifically, the simulation analysis process is as follows: I. Subjective Weighting Analysis of the Order Relationship Analysis Method: The order relationship analysis method includes the following steps: determining the order relationship of each interference evaluation indicator, judging the importance of adjacent interference evaluation indicators, and calculating the weight coefficients of each interference evaluation indicator. Specifically: 1. Determine the order relationship of each interference evaluation index: Experts ranked the seven interference evaluation indicators from most important to least important as follows: x1>x2>x3>x4>x5>x6>x7; Where x1 represents the importance of time response, x2 represents the importance of PRT response, x3 represents the importance of signal coherence, x4 represents the importance of spatial coverage, x5 represents the importance of jamming power, x6 represents the importance of signal bandwidth, and x7 represents the importance of the distance between the jammer and the radar.

[0019] 2. Determine the importance of neighboring interference evaluation indicators: The formula for calculating the ratio of importance (relative importance) among neighboring interference evaluation indicators is as follows: r k =x k-1 / x k ; Where, x k-1 ≥x k (k=n,n-1,…,3,2),x k For the k-th indicator The importance of x k-1 For the (k-1)th indicator The importance of; r k The possible values ​​are shown in Table 1: Table 1r k Value table

[0020] Based on the formula for calculating relative importance and Table 1, the relative importance r among the interference evaluation indicators arranged in order of importance is obtained. k ; 3. Calculate the weighting coefficients of each interference evaluation index. The calculation formula is: ; Where m is the number of interference evaluation indicators and n is the number of interference patterns. Based on the weighting coefficient of each interference evaluation indicator The weight vector ω of the interference evaluation index in the order relation analysis method is calculated. c : ; in, T Indicates transpose; II. Objective Weighting Analysis using the Entropy Weight Method: Construct the original data matrix and set the evaluation object as... Various interference patterns are available, such as range decoy interference, velocity decoy interference, dense decoy interference, coherent interference, and intermittent sampling and forwarding interference. The interference evaluation metrics are set as follows: Types of data, such as jamming power, time response, PRT response, signal bandwidth, spatial coverage, distance between jammer and radar, and signal coherence, are used to construct the original data matrix. :

[0021] in, Indicates the first i The first interference pattern j Data values ​​corresponding to various interference evaluation indicators.

[0022] The original data matrix is ​​normalized to obtain the normalized matrix: For each element in the original data matrix The result was obtained by vector normalization. : ; all Normalization Then, the matrix is ​​obtained. That is, for the matrix After normalization, the matrix is ​​obtained. 】: ; Calculate objective weights: for the matrix The following processing is performed to calculate the proportion of different evaluation objects corresponding to the same evaluation indicator. : ; According to all This yields the proportion matrix.

[0023] Calculate the entropy value of each interference evaluation index to obtain the entropy value of each evaluation object in the first... Entropy value under the item index : ; Among them, when hour, .

[0024] Calculate the weights of the interference evaluation indicators using the entropy weight method, and obtain the results for each object in the first... Weights under each indicator : ; in , This yields the index weight column vector. : .

[0025] III. Combination Weighting Analysis of Game Theory Using Order Relation Analysis and Entropy Weighting: Construct the optimization objective function for the game combination: ; in, ω c T The subjective weight row vector obtained by the order relation analysis method, with superscript... T Represents transpose; ω j T This is the objective weight row vector obtained by the entropy weight method; ||2 2 is the square of the vector's 2-norm, i.e., the square of the Euclidean distance; min means to find the minimum value; The objective function is a game-theoretic weighted bi-objective minimization optimization model, which aims to minimize the squared Euclidean distance between the combined weights and the subjective and objective weights, respectively.

[0026] The optimal combination coefficients are obtained by solving the problem; the optimal combination coefficients are then substituted into the linear combination model to calculate the final game combination weights.

[0027] Furthermore, after obtaining the final game combination weights, the final game combination weights that integrate subjective and objective weights are obtained. The final game combination weights are then calculated with the interference index data matrix that has undergone standardization to obtain a set of comprehensive evaluation scores corresponding to various interference patterns. The values ​​of all comprehensive evaluation scores are compared, and the interference pattern corresponding to the item with the highest score is selected as the optimal interference pattern. The optimal interference pattern for radar interference decision-making is output based on the optimal interference pattern, wherein the optimal interference pattern corresponding to the maximum value of the comprehensive evaluation score is dense false target interference.

[0028] Specifically, the final game combination weights are multiplied by the standardized interference evaluation index original data matrix to calculate the comprehensive score of each interference pattern. The element with the highest comprehensive score is the optimal interference pattern, which is determined as the preferred interference pattern.

[0029] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the program is executed by a processor, it implements the steps of the radar jamming decision-making method based on the combination of order relation analysis and entropy weight game as described above.

[0030] The present invention also provides a computer device, the computer device including a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, it implements the steps of the radar jamming decision-making method based on the combination of order relation analysis and entropy weight game as described above.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows: The radar jamming decision-making method based on a combination of order relation analysis and entropy weight game theory provided by this invention combines the subjective weights of the order relation analysis method with the objective weights of the entropy weight method through game theory Nash equilibrium. A linear expression for the combined weights is constructed, and the optimal combination coefficients are solved with the goal of minimizing Euclidean distance, achieving a Nash equilibrium of subjective and objective weights. Compared with existing technologies that only use a single weighting method, which struggles to balance subjective experience and objective data, this invention retains the guiding significance of expert experience while also considering the objective information content of the jamming evaluation index data itself. This effectively solves the problems of insufficient objectivity in single subjective weighting methods and lack of scenario adaptability in single objective weighting methods. Applying the combined weighting method to the jamming pattern decision-making scenario in radar countermeasures, the weight allocation and jamming pattern optimization for jamming performance indicators in radar countermeasures improve the rationality of multi-indicator weight allocation, enabling rapid and accurate selection of the optimal jamming pattern for jammers in complex electromagnetic environments. Attached Figure Description

[0032] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention.

[0033] In the attached diagram: Figure 1 This is a flowchart illustrating the order relation analysis method according to an embodiment of the present invention; Figure 2 This is a flowchart illustrating the entropy weight method according to an embodiment of the present invention; Figure 3 This is a flowchart illustrating the game combination weighting method according to an embodiment of the present invention. Figure 4 This is a schematic diagram of the configuration of a computer device according to an embodiment of the present invention. Detailed Implementation

[0034] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses and products consistent with some aspects of this disclosure as detailed in the appended claims.

[0035] The terminology used in this disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. The singular forms “a,” “the,” and “the” as used in this disclosure and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0036] It should be understood that although the terms first, second, third, etc., may be used in this disclosure to describe various information, such information should not be limited to these terms. These terms are used only to distinguish information of the same type from one another. For example, without departing from the scope of this disclosure, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0037] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0038] This invention provides a radar jamming decision-making method based on a combination of order relation analysis and entropy weight game, comprising the following steps: By combining the subjective weights of the interference evaluation index calculated based on expert experience using the Nash equilibrium combination method, and the objective weights calculated based on the interference measured data using the entropy weight method, a linear expression for the combined weights is constructed. Specifically, a basic weight set is constructed using the subjective weights of the interference evaluation indicators obtained from expert experience through order relation analysis and the objective weights of the interference evaluation indicators obtained from measured interference data through the entropy weight method. A combined weight in the form of a linear superposition of the subjective and objective weights of the interference evaluation indicators is then constructed. Two sets of combined coefficients to be optimized, both with values ​​greater than zero, are set to correspond to the subjective and objective weights, respectively. The game-theoretic combined weighting method is used to solve for the equilibrium point between the subjective and objective weights. The equilibrium point is the weight value corresponding to the minimum overall deviation between the combined weight and the subjective and objective weights, respectively.

[0039] In this embodiment, the subjective weights of the order relation analysis method and the objective weights obtained by the entropy weight method are used as the basic weight set to construct a combined weight. The linear expression of the combined weight is as follows: ω=α1ω c +α2ω j ; Where, ω c The weights of the interference evaluation indexes obtained by the order relation analysis method, ω jLet α1 and α2 be the combined coefficients of the subjective and objective weights to be optimized, respectively, and α1 > 0 and α2 > 0. Using a game-theoretic combination weighting method, we seek a balance between the order relation analysis method and the entropy weight method. This balance point is the combination weight ω and the subjective weight ω of the order relation analysis method. c And the objective weight ω obtained by the entropy weight method j The point where the deviation between them is minimized.

[0040] An optimization model is constructed with the objective of minimizing the Euclidean distance between the combined weights and the individual subjective and objective weights. The optimal combination coefficients are solved to obtain the best interference pattern selection results for radar interference decision-making.

[0041] Specifically, the combined weights of the interference evaluation indicators obtained by linear superposition are used as optimization objectives to minimize the Euclidean distance between the subjective weight row vectors output by the order relation analysis method and the objective weight row vectors output by the entropy weight method. A dual-objective minimization optimization objective function corresponding to game weighting is constructed. The superscripts of the subjective weight row vectors and the objective weight row vectors are used to identify the transpose of the vectors. The square of the second norm of the vectors is used to represent the square of the Euclidean distance between the two sets of vectors. The optimization objective function sets two types of minimum value solutions to minimize the square of the Euclidean distance between the combined weights and the subjective weights and the objective weights respectively.

[0042] In this embodiment, the optimization objective is to minimize the Euclidean distance between the combined weight and each individual weight (subjective weight, objective weight), and the optimization objective function is constructed as follows: ; in, ω c T The subjective weight row vector obtained by the order relation analysis method, with superscript... T Represents transpose; ω j T This is the objective weight row vector obtained by the entropy weight method; ||2 2 is the square of the vector's 2-norm, i.e., the square of the Euclidean distance; min means to find the minimum value; The objective function is a game-theoretic weighted bi-objective minimization optimization model, which aims to minimize the squared Euclidean distance between the combined weights and the subjective and objective weights, respectively.

[0043] Based on the constraint of finding the extremum using matrix differentiation, the first-order partial derivatives of the objective function are calculated and set to zero, deriving a system of linear equations for solving the combination coefficients. The measured radar interference index data are substituted into this system of linear equations to calculate the initial combination coefficients. The initial combination coefficients are then normalized so that the sum of the two sets of combination coefficients equals 1, finally yielding the optimal combination coefficients assigned to the order relation analysis method and the entropy weight method, respectively.

[0044] In this embodiment, based on the extremum condition of matrix differentiation, the first-order partial derivative of the objective function is made equal to 0, resulting in the optimal system of linear equations: ; Substitute the data into the optimal linear equation system to calculate the combination coefficients. Normalize the combination coefficients so that α1 + α2 = 1. Finally, obtain the optimal combination coefficients α1 and α2, which are the weights allocated by the order relation analysis method and the entropy weight method.

[0045] Substitute the optimal combination coefficients obtained from the solution into the optimization model (linear combination model) to calculate the final game combination weight of the subjective weight of the fusion order relation analysis method and the objective weight of the entropy weight method; multiply the original data matrix of the standardized interference evaluation index with the row vector of the final game combination weight with transpose label to obtain the comprehensive interference evaluation index corresponding to each type of interference pattern; based on the magnitude of the comprehensive interference evaluation index of each interference pattern, determine the optimal interference pattern corresponding to the radar interference decision.

[0046] In this embodiment, the optimal combination coefficients are substituted into the linear combination model to obtain the final game combination weights, which are: ω final =α1ω c +α2ω j ; Where, ω final The final game combination weights; ω c Subjective weights obtained by order relation analysis; ω j The objective weights obtained by the entropy weight method; Multiply the final game combination weights by the standardized original data matrix of interference evaluation indicators to calculate the comprehensive score for each interference pattern: E=BωT final; Where E is the comprehensive interference evaluation index; B is the original data matrix of the standardized interference evaluation index; ωTfinal is the final game combination weight row vector, and the superscript T represents the vector transpose; Based on the overall score, the optimal interference pattern is determined.

[0047] After obtaining the optimal interference pattern for radar interference decision-making, simulation analysis is performed on the optimal interference pattern. The configuration for simulation analysis includes: setting multiple interference patterns and setting multiple interference evaluation indicators; Among them, various jamming patterns include: range decoy jamming, velocity decoy jamming, dense decoy jamming, coherent jamming, and intermittent sampling and forwarding jamming; Multiple interference evaluation indicators include: interference power, time response, PRT response, signal bandwidth, spatial coverage, distance between jammer and radar, and signal coherence.

[0048] Sequential execution of the order relation analysis method (e.g.) Figure 1 Subjective weighting and entropy weighting methods (as shown) Figure 2 Objective empowerment (as shown) and game-theoretic combination empowerment (such as...) Figure 3 The three-step analysis process (as shown) involves: First, the order relation analysis method, where experts rank seven types of interference evaluation indicators according to their importance, determine the importance ratio of adjacent indicators, and then calculate the subjective weights. Second, the entropy weight method sequentially constructs the original data matrix, normalized matrix, and indicator ratio matrix, and calculates the objective weights using the indicator entropy values. Third, the game combination weighting constructs an optimization objective function, solves for the optimal combination coefficients, and combines the subjective and objective weights with the optimization model (linear combination model) to obtain the final game combination weights.

[0049] In this embodiment, the simulation analysis process is as follows: I. Subjective weighting analysis of the order relation analysis method, as detailed below: Determining the order of the various interference evaluation indicators: Experts ranked the seven interference evaluation indicators from most important to least important as follows: x1>x2>x3>x4>x5>x6>x7; Where x1 represents the importance of time response, x2 represents the importance of PRT response, x3 represents the importance of signal coherence, x4 represents the importance of spatial coverage, x5 represents the importance of jamming power, x6 represents the importance of signal bandwidth, and x7 represents the importance of the distance between the jammer and the radar.

[0050] Determining the importance of neighboring interference evaluation indicators: The ratio of the importance of neighboring interference evaluation indicators, i.e., the relative importance, is expressed as: r k =x k-1 / x k ; Where, x k-1 ≥x k (k=n,n-1,…,3,2),x k For the k-th indicator The importance of x k-1 For the (k-1)th indicator The importance of.

[0051] r k The possible values ​​are shown in Table 1: Table 1r k Value table

[0052] Based on the formula for calculating relative importance and Table 1, the relative importance r among the indicators arranged in order can be obtained. k ; In this embodiment of the invention, r k The assignments are shown in Table 2: Table 2r k Assignment table

[0053] Calculate the weighting coefficients of each interference evaluation index. : ; Where m is the number of interference evaluation indicators and n is the number of interference patterns. The weight vector ω of the interference evaluation index in the order relation analysis method is calculated. c : ; in, T Indicates transpose; In this embodiment, ω c =【0.084,0.349,0.194,0.060,0.101,0.050,0.162】; II. Objective Weighting Analysis Using the Entropy Weight Method: Constructing the original data matrix and setting the evaluation object as... Various jamming patterns (range-based decoy jamming, velocity-based decoy jamming, dense decoy jamming, coherent jamming, intermittent sampling and forwarding jamming, etc.) are used, and the jamming evaluation index is set as follows: (various parameters including jamming power, time response, PRT response, signal bandwidth, spatial coverage, distance between jammer and radar, signal coherence, etc.) to construct the original data matrix. :

[0054] in, Indicates the first i The first interference pattern j Data values ​​corresponding to various interference evaluation indicators.

[0055] The original data matrix in this embodiment is shown in Table 3: Table 3 Original Data Matrix

[0056] Normalization of the original data matrix: For each element in the original data matrix... The result was obtained by vector normalization. : ; all Normalization Then, the matrix is ​​obtained. : ; For matrix After normalization, the matrix is ​​obtained. In this embodiment, the obtained normalized matrix is ​​shown in Table 4: Table 4 Normalized Matrix Table

[0057] Calculate objective weights: Calculate the proportion of different interference patterns (evaluation objects) corresponding to the same evaluation indicator. : ; According to all This yields the proportion matrix.

[0058] The proportion matrix obtained in this embodiment is shown in Table 5: Table 5 Proportion Matrix

[0059] Calculate the entropy value of each interference evaluation index to obtain the entropy value of each evaluation object in the first... Entropy value under the item index : ; Among them, when hour, .

[0060] In this embodiment, =【0.9990,0.7321,0.9783,0.6826,0.9061,0.9890,0.9712】; Calculate the weights of the interference evaluation indicators using the entropy weight method, and obtain the results for each object in the first... Weights under each indicator : ; in, , This yields the index weight column vector. : ; In this embodiment, =【0.0013,0.3612,0.0293,0.4279,0.1266,0.0149,0.0388】; III. Combination Weighting Analysis of Game Theory Using Order Relation Analysis and Entropy Weighting: Construct the optimization objective function for the game combination: ; in, ω c T The subjective weight row vector obtained by the order relation analysis method, with superscript... T Represents transpose; ω j T This is the objective weight row vector obtained by the entropy weight method; ||2 2 is the square of the vector's 2-norm, i.e., the square of the Euclidean distance; min means to find the minimum value; The objective function is a game-theoretic weighted bi-objective minimization optimization model, which aims to minimize the squared Euclidean distance between the combined weights and the subjective and objective weights, respectively.

[0061] By solving, the optimal combination coefficients are obtained as follows: , .

[0062] Substituting the optimal combination coefficients into the linear combination model, we can calculate the final game combination weights: ω final =【0.0216,0.3583,0.0696,0.3379,0.1203,0.0235,0.0688】; After obtaining the final game combination weights, the final game combination weights that integrate subjective and objective weights are obtained. The final game combination weights are then calculated with the interference index data matrix that has undergone standardization to obtain a set of comprehensive evaluation scores corresponding to various interference patterns. The values ​​of all comprehensive evaluation scores are compared, and the interference pattern corresponding to the item with the highest score is selected as the optimal interference pattern. The optimal interference pattern for radar interference decision is output based on the optimal interference pattern, where the optimal interference pattern corresponding to the maximum value of the comprehensive evaluation score is dense false target interference.

[0063] In this embodiment, the final game combination weights are multiplied by the standardized original data matrix of interference evaluation indicators to calculate the comprehensive score for each interference pattern: E=[0.422,0.424,0.526,0.175,0.179]; The third element value, E3=0.526, is the highest in the overall score and is determined to be the optimal interference pattern, indicating that the best interference pattern is dense false target interference.

[0064] This embodiment presents a radar jamming decision-making method based on a combination of order relation analysis and entropy weight game. It employs order relation analysis to calculate subjective weights of jamming evaluation indicators based on expert experience, and uses entropy weight method to solve for objective weights based on measured jamming data. By introducing the Nash equilibrium concept from game theory, an optimization model is constructed with the objective of minimizing the Euclidean distance between the combined weights and the individual subjective and objective weights. The optimal combination coefficients are then solved to obtain the comprehensive indicator weights. Combined with standardized jamming data, the comprehensive score for each jamming pattern is calculated, and the optimal jamming pattern is output. This method effectively addresses the shortcomings of existing methods, such as the strong subjectivity of single subjective weighting and the lack of battlefield adaptability of single entropy weight method. By integrating prior knowledge and measured data, the weight allocation becomes more balanced and reliable. All calculations are linear analytical calculations, allowing for embedded deployment in various jamming devices. This enables rapid and accurate decision-making on jamming patterns in complex electromagnetic environments and can be widely applied to airborne, vehicle-mounted, and shipborne radar counter-jamming equipment.

[0065] This invention also provides a computer device. Figure 4 This is a schematic diagram of the structure of a computer device provided in an embodiment of the present invention; see the accompanying drawings. Figure 4 As shown, the computer device includes: an input device 23, an output device 24, a memory 22, and a processor 21; the memory 22 is used to store one or more programs; when the one or more programs are executed by the one or more processors 21, the one or more processors 21 implement the radar jamming decision-making method based on a combination of order relation analysis and entropy weight game as provided in the above embodiment; wherein the input device 23, the output device 24, the memory 22, and the processor 21 can be connected via a bus or other means. Figure 4 Taking the example of a connection between China and Israel via a bus.

[0066] The memory 22, as a read / write storage medium for a computing device, can be used to store software programs and computer-executable programs, such as the program instructions corresponding to the radar interference decision-making method based on a combination of order relation analysis and entropy weight game as described in this embodiment of the invention. The memory 22 may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a function; the data storage area may store data created based on the use of the device. Furthermore, the memory 22 may include high-speed random access memory and non-volatile memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some instances, the memory 22 may further include memory remotely located relative to the processor 21, and these remote memories can be connected to the device via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0067] Input device 23 can be used to receive input digital or character information, and generate key signal inputs related to user settings and function control of the device; output device 24 may include display devices such as a display screen.

[0068] The processor 21 executes various functional applications and data processing of the device by running software programs, instructions and modules stored in the memory 22, thereby realizing the radar jamming decision-making method based on the combination of order relation analysis and entropy weight game as described above.

[0069] The computer equipment provided above can be used to execute the radar jamming decision-making method based on a combination of order relation analysis and entropy weight game provided in the above embodiments, and has corresponding functions and beneficial effects.

[0070] This invention also provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to execute the radar jamming decision-making method based on a combination of order relation analysis and entropy weight game as provided in the above embodiments. The storage medium can be any type of memory device or storage device, including: mounting media such as CD-ROM, floppy disk, or magnetic tape; computer system memory or random access memory such as DRAM, DDRRAM, SRAM, EDORAM, Rambus RAM, etc.; non-volatile memory such as flash memory, magnetic media (e.g., hard disk or optical storage); registers or other similar types of memory components; the storage medium may also include other types of memory or combinations thereof; furthermore, the storage medium may reside in a first computer system in which the program is executed, or it may reside in a different second computer system connected to the first computer system via a network (such as the Internet); the second computer system can provide program instructions to the first computer for execution. The storage medium includes two or more storage media that can reside in different locations (e.g., in different computer systems connected via a network). The storage medium can store program instructions (e.g., specifically implemented as a computer program) executable by one or more processors.

[0071] Of course, the computer-executable instructions provided in the embodiments of the present invention are not limited to the radar jamming decision-making method based on the combination of order relation analysis and entropy weight game as described in the above embodiments, but can also execute related operations in the radar jamming decision-making method based on the combination of order relation analysis and entropy weight game provided in any embodiment of the present invention.

[0072] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

[0073] The above description is merely a preferred embodiment of the present invention and is not intended to limit the 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 radar jamming decision-making method based on a combination of order relation analysis and entropy weight game, characterized in that, include: By combining the subjective weights of the interference evaluation index calculated based on expert experience using the Nash equilibrium combination method, and the objective weights calculated based on the interference measured data using the entropy weight method, a linear expression for the combined weights is constructed. An optimization model is constructed with the objective of minimizing the Euclidean distance between the combined weights and the individual subjective and objective weights. The optimal combination coefficients are then solved to obtain the optimal interference pattern for radar interference decision-making.

2. The radar jamming decision-making method based on a combination of order relation analysis and entropy weight game as described in claim 1, characterized in that, The method of combining the subjective weights of the order relation analysis method used to calculate interference evaluation indicators based on expert experience with the objective weights obtained by the entropy weight method based on measured interference data includes: A basic weight set is constructed using the subjective weights of interference evaluation indicators obtained through order relation analysis based on expert experience and the objective weights of interference evaluation indicators obtained through entropy weight method based on measured interference data. A combined weight in the form of a linear superposition of the subjective and objective weights of the interference evaluation indicators is then constructed. Two sets of combination coefficients to be optimized, both with values ​​greater than zero, are set to correspond to the subjective and objective weights, respectively. A game-theoretic combination weighting method is used to solve for the equilibrium point between the subjective and objective weights. The equilibrium point is the weight value corresponding to the minimum overall deviation between the combined weight and the subjective and objective weights, respectively.

3. The radar jamming decision-making method based on a combination of order relation analysis and entropy weight game as described in claim 2, characterized in that, The method for constructing an optimization model with the objective of minimizing the Euclidean distance between the combined weights and the individual subjective and objective weights includes: The combined weights of the interference evaluation indicators obtained by linear superposition are used as optimization objectives to minimize the Euclidean distance between the subjective weight row vectors output by the order relation analysis method and the objective weight row vectors output by the entropy weight method. A dual-objective minimization optimization objective function corresponding to game weighting is constructed. The superscripts of the subjective weight row vectors and objective weight row vectors are used to identify the transpose of the vectors. The square of the second norm of the vectors is used to represent the square of the Euclidean distance between the two sets of vectors. The optimization objective function sets two types of minimum value solving objectives to minimize the square of the Euclidean distance between the combined weights and the subjective weights and objective weights respectively.

4. The radar jamming decision-making method based on a combination of order relation analysis and entropy weight game as described in claim 3, characterized in that, The method for solving the optimal combination coefficients includes: Based on the constraint of finding the extremum using matrix differentiation, the first-order partial derivative of the objective function is calculated and set to zero, deriving a system of linear equations for solving the combination coefficients. The measured radar interference index data is substituted into the system of linear equations to calculate the initial combination coefficients. The initial combination coefficients are then normalized so that the sum of the two sets of combination coefficients equals 1, finally yielding the optimal combination coefficients assigned to the order relation analysis method and the entropy weight method, respectively.

5. The radar jamming decision-making method based on a combination of order relation analysis and entropy weight game as described in claim 4, characterized in that, The method for obtaining the optimal interference pattern for radar interference decision-making includes: Substituting the optimal combination coefficients obtained from the solution into the optimization model, the final game combination weights of the subjective weights of the fusion order relation analysis method and the objective weights of the entropy weight method are calculated. The original data matrix of the interference evaluation index after standardization is multiplied by the row vector of the final game combination weights with transpose label to obtain the comprehensive interference evaluation index corresponding to each type of interference pattern. Based on the magnitude of the comprehensive interference evaluation index of each interference pattern, the optimal interference pattern corresponding to the radar interference decision is determined.

6. The radar jamming decision-making method based on a combination of order relation analysis and entropy weight game as described in claim 1, characterized in that, After obtaining the optimal interference pattern for radar interference decision-making, the method further includes: performing simulation analysis on the optimal interference pattern, wherein the configuration of the simulation analysis includes: setting multiple interference patterns and setting multiple interference evaluation indicators. The various interference patterns include: range decoy interference, velocity decoy interference, dense decoy interference, coherent interference, and intermittent sampling and forwarding interference; The various interference evaluation indicators include: interference power, time response, PRT response, signal bandwidth, spatial coverage, distance between the jammer and the radar, and signal coherence.

7. The radar jamming decision-making method based on a combination of order relation analysis and entropy weight game as described in claim 6, characterized in that, The simulation analysis method includes: The analysis process involves three steps: subjective weighting using the order relation analysis method, objective weighting using the entropy weight method, and game combination weighting. The order relation analysis method involves experts ranking seven types of interference evaluation indicators according to their importance, determining the importance ratio of adjacent indicators, and then calculating the subjective weights. The entropy weight method sequentially constructs the original data matrix, the normalized matrix, and the indicator ratio matrix, and calculates the objective weights using the indicator entropy values. The game combination weighting method constructs an optimization objective function, solves for the optimal combination coefficients, and combines the subjective and objective weights with the optimization model to obtain the final game combination weights.

8. The radar jamming decision-making method based on a combination of order relation analysis and entropy weight game as described in claim 7, characterized in that, After obtaining the final game combination weights, the final game combination weights that integrate subjective and objective weights are obtained. The final game combination weights are then calculated with the interference index data matrix that has undergone standardization to obtain a set of comprehensive evaluation scores corresponding to various interference patterns. The values ​​of all comprehensive evaluation scores are compared, and the interference pattern corresponding to the item with the highest score is selected as the optimal interference pattern. The optimal interference pattern for radar interference decision-making is output based on the optimal interference pattern, wherein the optimal interference pattern corresponding to the maximum value of the comprehensive evaluation score is dense false target interference.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the radar jamming decision-making method based on the combination of order relation analysis and entropy weight game as described in any one of claims 1-8.

10. A computer device, the computer 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 program, it implements the steps of the radar jamming decision-making method based on the combination of order relation analysis and entropy weight game as described in any one of claims 1-8.

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