A Radar Cognitive Jamming Decision-making Method Based on Incomplete Information Game

Abstract

The present invention discloses a radar cognitive jamming decision-making method based on incomplete information game, including constructing and initializing a game model; quantifying the jamming benefits of the jamming party and the radar benefits of the radar according to the game model; obtaining the jamming action set of the jamming party in the state of reaching the mixed strategy Bayesian Nash equilibrium, predicting the working mode set of the radar according to the jamming action set, and calculating the jamming effectiveness set of the jamming party based on the jamming action set of the jamming party and the working mode set of the radar; sorting the values of the jamming effectiveness in the jamming effectiveness set in descending order, obtaining the jamming action corresponding to the maximum jamming effectiveness, and taking the jamming action as the optimal jamming action of the jamming party. It solves the problem that the existing jamming decision-making method based on game theory overly relies on prior knowledge, and improves the jamming decision-making ability for non-cooperative multi-functional radars in complex electromagnetic environments.

Description

Technical Field

[0001] The present invention relates to the field of radar jamming decision-making, and in particular to a radar cognitive jamming decision-making method based on incomplete information game. Background Art

[0002] Today, great progress has been made in radar technology, and the development of radar has been continuously intelligent and flexible. Multifunctional radars have reduced the probability of being intercepted by the jammer during operation through technologies such as controlling their own transmit power, reducing the antenna sidelobe gain, and using low-intercept waveforms; the research and development of multifunctional radars such as pulse compression radars, phase-coded radars, and phased array radars have increased the difficulty for the jammer to analyze radar signals and implement jamming actions. The new developments of the above radar systems have led the jammer to face an unprecedentedly complex electromagnetic field environment, unknown jamming scenarios, and unpredictable enemy threat signals. These all put higher requirements on the jammer's confrontation ability. Being able to conduct real-time battlefield situation analysis, autonomously and efficiently complete jamming decisions, and having the characteristics of "cognition, intelligence, and time-variation" are the highest levels of current electronic countermeasure development, that is, cognitive electronic warfare, and it is also an inevitable trend to adapt to the future strong game combat environment.

[0003] Cognitive interference decision-making is one of the key technologies in cognitive electronic warfare. Due to its characteristics such as closed-loop feedback, global optimization, and adaptive processing, cognitive interference technology provides new ideas for the design and development of electronic countermeasure equipment in future battlefields. Its tasks are mainly divided into three steps: (1) The jammer receives the target radar signal to complete the recognition of the target's working state; (2) The interference system judges the state, selects the best interference strategy based on experience and implements it; (3) The interference system evaluates the interference effect. Existing interference decision-making technologies mainly rely on summarizing past confrontation experiences to establish a priori knowledge bases, usually developed and loaded based on the obtained data during the equipment development process or before the mission. However, the battlefield situation changes rapidly, and the lagging interference decision-making methods cannot effectively cope with the complex battlefield environment with multi-dimensional changes. It is difficult to establish a one-to-one matching relationship between specific radar working states and interference methods in the short term, and it is difficult for interference equipment to perform effective interference in real time, which poses a severe challenge to the development of technologies and equipment in the field of electronic countermeasures. Therefore, the research on cognitive interference decision-making methods is urgent. Many scholars have conducted explorations, such as: (1) Introducing cognitive technology into the radar confrontation process, providing new ideas for radar interference decision-making; (2) Analyzing and studying the Q-learning theory to solve the problem of using the Q-learning algorithm for radar interference decision-making when the radar working mode is unknown; (3) Using deep Q neural networks to make the interference decision-making process of multi-functional radars more scientific and reasonable; (4) Using a priori knowledge to accelerate algorithm convergence to solve the problems of long training cycles and slow convergence rates in radar interference decision-making by reinforcement learning; (5) Designing an interference pattern selection method based on D-S evidence theory from the perspective of template matching; (6) Combining the idea of game theory with the a priori knowledge of radar confrontation to establish a profit matrix for interference decision-making and preliminarily discussing the selection problem of radar active interference patterns.

[0004] The above different methods have carried out theoretical research and practical analysis on the radar interference decision-making problem and achieved relatively ideal results, but the following problems have not been effectively solved: (1) The influence that various types of the two sides in the confrontation may bring to the decision-making effect is not considered in the modeling process; (2) The benefits are not analyzed in combination with the specific characteristics of radar confrontation, resulting in a lack of certain scientificity in the energy quantification of interference strategies; (3) Over-reliance on a priori knowledge, which can only be applied to radars with limited parameters and systems, lacking reliable timeliness and usability. To sum up, although the existing cognitive interference decision-making methods can provide references for radar interference decision-making, it is difficult to apply them to the actual confrontation process of multi-functional radars. Summary of the Invention

[0005] The present invention provides a radar cognitive interference decision-making method based on incomplete information game to overcome the above technical problems.

[0006] A radar cognitive jamming decision-making method based on incomplete information game, including:

[0007] Step 1: Construct and initialize a game model. The game model includes a set of participants, a set of participant types, a set of strategies, a set of prior knowledge, and a set of payoffs. The set of participants is used to represent the target radar and the jammer set participating in the game. The set of participant types is used to represent the set of participant types. The set of strategies is used to represent the operating modes that the radar can adopt during the game and the jamming actions that the jammer can adopt during the game. The set of prior knowledge is used to represent the set of prior knowledge of the participants. The set of payoffs is used to represent the set of payoffs of both participants;

[0008] Step 2: Obtain the game information of the jammer and the radar according to the initialized game model. The game information includes the radar type, the radar operating mode, the jammer type, and the jamming action taken by the jammer. Quantify the jamming payoff of the jammer and the radar payoff of the radar according to the game information, the success probability of the jamming action, and the anti-jamming success probability of the radar.

[0009] Step 3: Obtain the set of jamming actions of the jammer under the Bayesian Nash equilibrium. Predict the set of operating modes of the radar according to the set of jamming actions. Obtain the set of jamming effectiveness of the jammer based on the set of jamming actions of the jammer and the set of operating modes of the radar.

[0010] Step 4: Sort the values of the jamming effectiveness in the set of jamming effectiveness in descending order, obtain the jamming action corresponding to the maximum jamming effectiveness, and use the jamming action as the optimal jamming action of the jammer.

[0011] Preferably, Step 1 includes a game model M = <N, S, A, P, R>,

[0012] N is the set of participants, N = {N r , N j}, where N r is the radar in the game process, and N j is the jammer in the game process;

[0013] S is the set of participant types, S = {S r , S j} is the set of types of the radar and the jammer. Among them, is the set of jammer types, and n 1 is the total number of jammer types; is the set of radar types, and m 1 is the total number of radar types;

[0014] A is the set of strategies, is the jamming action that the jammer can take, and n2 is the total amount of interference actions; is the operating mode of the radar, m 2 is the total number of operating modes,

[0015] P is the set of prior knowledge, P = {P r , P j} is the set of prior knowledge of the participants, P r is the set of prior knowledge of the jammer, P j is the set of prior knowledge of the radar,

[0016] R is the set of payoffs, R = {R r , R j} is the set of payoffs of the participants, R r is the set of payoffs of the jammer, R j is the set of payoffs of the radar,

[0017] Initialize the values of the parameters in the game model M.

[0018] Preferably, the quantification of the interference payoff of the jammer and the radar payoff of the radar according to the game information, the success probability of the interference action, and the success probability of the radar's anti-jamming includes obtaining the type of the radar as S r，i , the radar operating mode is A r，q , q is the serial number of the operating mode, the type of the jammer is S j，i , the interference action taken by the jammer is A j，k , k is the serial number of the selected interference action; the success probability of the interference action is λ k , the success probability of the radar's own anti-jamming is β q ,

[0019] When the radar fails to resist jamming, reduce the threat level, and calculate the interference payoff of the jammer according to formula (1),

[0020]

[0021] where, W(D x ) is the influence weight of the interference action on the radar, x ∈ {a, b, c}, W(D a ), W(D b ), W(D c ) are the influence weights of the interference action on the real-time rate, accuracy rate, and false alarm rate of the radar's updated target information respectively; C(A j，k ) is the cost of initiating the interference action A j，k , the success probability of the interference action is λ k , the success probability of the radar's anti-jamming is β q , R = 100, indicating that the jammer obtains the interference payoff,

[0022] When the radar anti - jamming is successful, increase the threat level, and calculate the radar benefit of the radar according to formula (2).

[0023]

[0024] Among them, Y is the discount factor when the anti - jamming is successful, V(D x ) is the working value of the radar side, C(A r，q ) is the cost for the radar to actively change the working mode to A r，q , the success probability of the jamming operation is λ k , the success probability of the radar anti - jamming is β q , x ∈ {a, b, c}, V(D a ), V(D b ), V(D c ) are the values of the real - time rate, accuracy rate, and false - alarm rate of the radar for updating the information of the jammer respectively, R = - 100, indicating that the radar obtains the radar benefit.

[0025] Preferably, calculating the interference effectiveness set of the jammer based on the interference operation set of the jammer and the working mode set of the radar includes calculating the interference effectiveness of different interference operations taken by the jammer according to formula (3) respectively.

[0026]

[0027] Among them, S j，i is the type of the jammer, A j，k is the interference operation selected by the jammer from the interference operation set, E(A j，k ) is the interference effectiveness obtained by the jammer when selecting the interference operation A j，k , P j (S r，i |S j，i ) is the prior probability of the jammer, R j (S j，i , A j，k , A r，q ) is the interference benefit obtained by the jammer after implementing the interference operation A j，k , A r，q is the working mode selected by the radar from the working mode set, S r，i is the type of the radar,

[0028] Save the interference effectiveness of different interference operations to the interference effectiveness set.

[0029] Preferably, the obtaining of the interference action set of the interfering party under the Bayesian Nash equilibrium includes performing Bayesian Nash equilibrium analysis on the game model by means of a mixed strategy, obtaining a mixed strategy set with Bayesian Nash equilibrium, and taking the mixed strategy of the interfering party in the mixed strategy set as the interference action set.

[0030] The present invention provides a radar cognitive interference decision-making method based on incomplete information game. Combining the actual interference process, the influence of the type differences between the two game parties on the game process is added to the game model to achieve optimal decision-making in the case of partially known information; from the perspectives of the influence of interference actions on the working value of the radar and the radar anti-jamming ability, the decision-making benefits of both parties are quantified, making the calculation of the benefits more reasonable and conforming to the actual combat background; performing Bayesian Nash equilibrium analysis on the game model by means of a mixed strategy, obtaining a mixed strategy set with Bayesian Nash equilibrium, obtaining the unknown working mode of the multifunctional radar according to the mixed strategy set, dynamically adjusting the interfering party's strategy when the radar working mode changes, and making the interference system give full play to the cognitive advantage by selecting a pure strategy form of interference method, solving the problem that the existing game theory-based interference decision-making method overly relies on prior knowledge, and improving the interference decision-making ability for non-cooperative multifunctional radars in complex electromagnetic environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0032] Figure 1 is the flowchart of the method of the present invention;

[0033] Figure 2 is the flowchart of the implementation of the present invention;

[0034] Figure 3 is the attack and defense game tree of the present invention;

[0035] Figure 4 is the interference decision-making efficiency mean value diagram of the present invention;

[0036] Figure 5 is the diagram of the change of the efficiency mean value of both parties of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0038] Figure 1 This is the flowchart of the method of the present invention. As Figure 1 shown, the method of this embodiment may include:

[0039] Step 1: Construct a game model.

[0040] (1) Model assumptions

[0041] The establishment of the game model first needs to meet the following three assumptions:

[0042] Assumption 1 Rationality assumption. It is assumed that both the radar side and the jamming side are completely rational when making decisions, that is, the decisions made by themselves can maximize the benefits of their own sides.

[0043] Assumption 2 Prior knowledge assumption. Before the confrontation starts, both sides have some information about the other side and can have a preliminary judgment on the probability distribution of the strategies selected by the enemy, which is in line with the results of intelligence collection in reality.

[0044] Assumption 3 Benefit assumption. The two sides of the confrontation can evaluate the decision-making effects through their own systems and quantify the confrontation benefits.

[0045] With the increasing demand for radars in future wars, the purpose of radar detection is gradually strengthened, and the participants are mostly experienced, well-organized, and highly cooperative combatants; the complex electromagnetic environment and the changing decision-making habits make it impossible to judge the working characteristics of the radar side before the jamming decision; the ultimate goal of the jamming side is to reduce the threat level of the enemy's radar working state through jamming and thus gain the initiative of the electromagnetic spectrum. The characteristics of the radar jamming decision-making process itself meet the assumptions for the establishment of the incomplete information game model, providing a prerequisite for the establishment of the model.

[0046] The game model includes a set of participants, a set of participant types, a set of strategies, a set of prior knowledge, and a set of benefits. The set of participants is used to represent the set of the target radar and the jamming side participating in the game. The set of participant types is used to represent the set of participant types. The set of strategies is used to represent the working modes that the radar can adopt during the game and the jamming actions that the jamming side can adopt during the game. The set of prior knowledge is used to represent the set of prior knowledge of the participants. The set of benefits is used to represent the set of benefits of both sides of the participants. The game model M = <N, S, A, P, R>.

[0047] Let \(N\) be the set of participants, \(N = \{N r , N j \}\), where \(N r \) is the radar in the game process, and \(N j \) is the jammer in the game process;

[0048] Let \(S\) be the set of participant types, \(S = \{S r , S j \}\) is the set of types of the radar and the jammer, where \) is the set of types of the jammer, and \(n 1 \) is the total amount of jammer types; \) is the set of types of the radar, and \(m 1 \) is the total amount of radar types;

[0049] Let \(A\) be the set of strategies, \) are the jamming actions that the jammer can take, and \(n 2 \) is the total amount of jamming actions; \) is the operating mode of the radar, and \(m 2 \) is the total amount of operating modes,

[0050] Let \(P\) be the set of prior knowledge, \(P = \{P r , P j \}\) is the set of prior knowledge of the participants, \(P r \) is the set of prior knowledge of the jammer, and \(P j \) is the set of prior knowledge of the radar, representing the possibility of judging the other party as a certain type through confrontation experience, reflecting the uncertainty of information between the two sides,

[0051] Let \(R\) be the set of payoffs, \(R = \{R r , R j \}\) is the set of payoffs of the participants, \(R r \) is the set of payoffs of the jammer, and \(R j \) is the set of payoffs of the radar, representing the immediate return value after taking a certain action. In the jamming decision-making process, the change in the threat level of the radar after implementing different jamming methods is used to define the \(R\) value, as follows:

[0052]

[0053] Initializing the game model means initializing the values of the parameters in the game model \(M\);

[0054] Scientifically quantifying the payoffs of both sides in the confrontation will directly affect the selection of the optimal strategy. Starting from the actual situation of radar jamming decision-making, by comprehensively considering the impact of the jammer's strategy on the working value of the target radar and the radar's anti-jamming ability, the payoffs of the radar and the jammer are quantified.

[0055] (1) Concept of quantifying the benefits of interference decision-making

[0056] Definition 1: Radar working value. The radar working value can be reflected by the threat level of radar operation, and is represented by V = {V(D a ), V(D b ), V(D c )}, where V(D a ), V(D b ), V(D c ) are the values of the radar in terms of the real-time rate, accuracy rate, and false alarm rate of updating target information respectively.

[0057] Definition 2: Interference influence degree. The interference influence degree reflects the impact of the interference action on the radar working value of the target, and is represented by W = {W(D a ), W(D b ), W(D c )}, where W(D a ), W(D b ), W(D c ) are the influence weights brought by the interference action on the real-time rate, accuracy rate, and false alarm rate of the radar updating target information respectively.

[0058] Definition 3: Interference success rate. A successful interference will gradually reduce the threat level of the target radar working mode. The interference success rate reflects the probability that the interference means reduces the threat level of the target radar. The interference success rate θ is mainly affected by the interference success probability λ and the radar anti-interference success probability β.

[0059] Definition 4: Interference benefit. The interference benefit reflects the benefits obtained by the interfering party after implementing the interference action. This paper mainly studies the interference decision-making problem under incomplete information. Therefore, it is defined that when the interference fails or the effect is not good, while the interfering party obtains the relevant state information of the enemy radar, it will also leave some interference information in the radar system. The radar side will conduct key detection on similar interference signals based on historical anti-interference data. If the interfering party still adopts the same interference method in the new game process, the interference success rate will be greatly reduced.

[0060] Definition 5: Anti-interference benefit. The anti-interference benefit reflects the ability of the radar side to protect its own value by using anti-interference means. Whether the anti-interference is successful or not, the radar side can obtain benefits. The specific manifestations are as follows:

[0061] 1) When the anti-interference is successful, the threat level of the radar side is not affected and it transforms into a mode with a higher threat level, obtaining direct anti-interference benefits.

[0062] 2) When anti-jamming fails, the radar side loses some information about the target and switches to a low-threat state. However, during the anti-jamming process, it can obtain relevant data information of the jamming side, improve its own anti-jamming ability through the feedback evaluation system, and thus indirectly obtain anti-jamming benefits.

[0063] Step 2: Obtain the game information of the jamming side and the radar according to the initialized game model. The game information includes the radar type, radar working mode, jamming side type, and jamming action taken by the jamming side. Quantify the jamming benefits of the jamming side and the radar benefits of the radar according to the game information, the success probability of the jamming action, and the anti-jamming success probability of the radar. Quantifying the jamming benefits of the jamming side and the radar benefits of the radar according to the game information, the success probability of the jamming action, and the anti-jamming success probability of the radar includes obtaining the radar type as S r，i , the radar working mode as A r，q , q is the serial number of the working mode, the jamming side type is S j，i , the jamming action taken by the jamming side is A j，k , k is the serial number of the selected jamming action; the success probability of the jamming action is λ k , the anti-jamming success probability of the radar itself is β q ,

[0064] The jamming side can only obtain jamming benefits by implementing effective jamming actions. When the radar side fails in anti-jamming, the threat level is reduced. Calculate the jamming benefits of the jamming side according to formula (2).

[0065]

[0066] Among them, W(D x ) is the influence weight of the jamming action on the radar, x ∈ {a, b, c}, W(D a ), W(D b ), W(D c ) are the influence weights of the jamming action on the real-time rate, accuracy rate, and false alarm rate of the radar's updated target information respectively; C(A j，k ) is the cost of initiating the jamming action A j，k , the success probability of the jamming action is λ k , the radar anti-jamming success probability is β q , R = 100, indicating that the jamming side obtains jamming benefits.

[0067] When the radar successfully resists jamming, the radar will actively change the working mode to improve its own threat level to better perform deep-level tasks. When the radar successfully resists jamming and improves the threat level, calculate the radar benefits of the radar according to formula (3).

[0068]

[0069] Among them, Y is the discount factor when anti-interference is successful, V(D x ) is the working value of the radar side, C(A r，q ) is the cost for the radar to actively change the working mode to A r，q , the success probability of the interference action is λ k , the success probability of the radar's anti-interference is β q , x ∈ {a, b, c}, V(D a ), V(D b ), V(D c ) are the values of the real-time rate, accuracy rate, and false alarm rate of the radar to update the information of the interference side respectively, R = -100, indicating that the radar obtains the radar benefit.

[0070] When the two opposing sides in the model each select strategies (A j，k , A r，q ) to conduct the confrontation, the following formula is used to quantify their respective benefits:

[0071]

[0072]

[0073] Radar interference decision-making is a process with strong purpose and intense confrontation. Effective interference can gradually reduce the threat level of the radar's working state. Therefore, the selection of the decision should be unique. However, traditional interference decision-making methods based on game theory basically output interference strategies in the form of probability distributions, and the form of mixed strategies is difficult to be actually applied to interference decision-making problems. To solve the above problems and realize the cognitive attribute of interference decision-making, first, the possible modes of the radar side are predicted through the Bayesian Nash equilibrium of mixed strategies, and then the interference effect of the interference strategy on the radar is quantified by taking the change in the threat level of the radar's working mode after the implementation of the interference as the standard, and the magnitude of the interference effectiveness is used as the standard for selecting the optimization strategy. Compared with the traditional interference strategy selection method, this process outputs the interference strategy in the form of pure strategies and has the characteristics of learning while confronting, realizing the function of cognitive decision-making.

[0074] In the process of the interference decision-making game, both sides of the game hope to maximize their own interests. Under the guidance of this principle, as the game process progresses, finally, neither the radar nor the interference side can improve their unilateral benefits by adjusting their own strategies. At this time, the system reaches an equilibrium. Due to the complexity of the multi-functional radar, the present invention uses the method of mixed strategies to conduct equilibrium analysis on the game model of incomplete information.

[0075] Definition 6 Bayesian Nash equilibrium of mixed strategies. When the two opposing sides meet the following conditions:

[0076] For and

[0077] For

[0078] The interference party's mixed strategy is F(S j,i ) = {f 1 (S j,i ), f 2 (S j,i ), …, f n (S j,i )},

[0079] The radar party's mixed strategy is F(S r,i ) = {f 1 (S r,i ), f 2 (S r,i ), …, f n (S r,i )},

[0080] At this time, the mixed strategy (F * (S j,i ), F * (S r,i )) has a Bayesian Nash equilibrium.

[0081] Since the number of working modes of the multifunctional radar and the number of interference methods of the interference party are both finite in the actual situation, the model belongs to a two-person finite strategy game. And there is at least one mixed strategy Nash equilibrium in the finite strategy game. Therefore, there is a mixed strategy Bayesian Nash equilibrium in the constructed interference decision model. According to Definition 6, there is always a set of mixed strategies in the equilibrium state. Using the global search method to effectively handle the problem of solving the Bayesian Nash equilibrium of the mixed strategy, and then an optimal solution set (F * (S j,i ), F * (S r,i )) that maximizes the interests of both parties can be obtained.

[0082] Step 3: Obtain the interference action set of the interference party under the Bayesian Nash equilibrium. The obtaining of the interference action set of the interference party under the Bayesian Nash equilibrium includes performing Bayesian Nash equilibrium analysis on the game model by the method of mixed strategy, obtaining the mixed strategy set with the Bayesian Nash equilibrium, taking the mixed strategy of the interference party in the mixed strategy set as the interference action set, predicting the working mode set of the radar based on the interference action set, and calculating the interference effectiveness set of the interference party based on the interference action set and the working mode set of the radar, including calculating the interference effectiveness of the interference party taking different interference actions respectively according to formula (6),

[0083]

[0084] Among them, S j,i is the type of the interfering party, A j,k is the interference action selected by the interfering party from the set of interference actions, and E(A j,k ) is the interference effectiveness obtained by the interfering party when selecting the interference action A j,k . P j (S r,i |S j,i ) is the prior probability of the interfering party, and R j (S j,i , A j,k , A r,q ) is the interference benefit obtained by the interfering party after implementing the interference action A j,k . A r,q is the operating mode selected by the radar from the set of operating modes, and S r,i is the type of the radar.

[0085] Save the interference effectiveness of different interference actions to the interference effectiveness set.

[0086] By quantifying the interference effectiveness, the strength of the impact of the interference strategy on the radar side can be obtained. The interfering party actively adjusts its own deployment according to the change of the enemy radar's operating mode, so that the interfering party has more initiative in confrontation to achieve the best interference effect.

[0087] Step 4: Sort the values of the interference effectiveness in the interference effectiveness set in descending order, obtain the interference action corresponding to the maximum interference effectiveness, and use the interference action as the optimal interference action of the interfering party.

[0088] The following takes the radar cognitive interference decision as an example to illustrate the implementation process of the present invention. The input data are the parameters of the game model, including: participants N, type S, strategy A, prior knowledge P and benefit R. Construct the type characteristics of both sides of the game, generate interference effectiveness, select the interference pattern based on the interference effectiveness. When the radar switches to a low threat level, the output result is the optimal interference strategy. The process block diagram is as Figure 2 shown.

[0089] 1. Quantification of interference decision benefits in the radar confrontation process

[0090] There are various classification methods for interference patterns. By comprehensively considering the success rate of the interference action and the cost paid, the types of the interfering party are divided into three categories: adventurous, balanced, and conservative.

[0091] The adventurous interference can obtain a better interference effect by adopting high-cost interference patterns, but at the same time, the probability of its own exposure is large. It is easy to become the key target of the enemy's attack during long-term operation, and the technical level requirements for the interference equipment are high, and it is considered that a higher interference cost is required;

[0092] Balanced interference balances the relationship between the cost and benefit of an attack, with a medium success rate; conservative interference is more willing to use methods with lower costs to implement interference. The equipment is simple and the concealment of the interference process is better. Although the interference success rate is low, the cost is also low. The strategies of different types of interference patterns of the interfering party are shown in Table 1.

[0093] Table 1

[0094]

[0095] Taking the effect and cost of the radar working mode as the criteria, the radar types are similarly divided into two categories: high-threat radar mode and low-threat radar mode. Compared with the low-threat radar mode, the threat level and cost of the working mode adopted by the high-threat radar mode are both higher. According to the order of decreasing radar threat level, different types of radar modes are classified as shown in Table 2.

[0096] Table 2

[0097]

[0098] Suppose that in a certain interference process, the prior belief of the interfering party is (adventurous type, balanced type, conservative type) = (0.4, 0.3, 0.3); the prior belief of the radar party is (high-threat radar mode, low-threat radar mode) = (0.4, 0.6). According to the strategy types of the radar and the interfering party, the costs of the interference strategy and the anti-interference strategy are set to 50, and the success probability λ k =(0.9, 0.8, 0.7, 0.6, 0.5, 0.4) of the interference action, and the success probability β q =(0.8, 0.8, 0.7, 0.6, 0.5, 0.5) of the radar anti-interference. The values V(D a ), V(D b ), V(D c ) of the real-time rate, accuracy rate, and false alarm rate of the radar to update the target information are respectively set to 0.7, 0.3, 0.2. The influence weights W(D a ), W(D b ), W(D c ) of the interference action on the real-time rate, accuracy rate, and false alarm rate of the radar to update the target information are respectively set to 0.6, 0.5, 0.4. The discount factor γ = 0.5 when the radar anti-interference is successful. The attack and defense game tree is constructed through the Harsanyi transformation. The interference effectiveness of the interfering party is defined as a positive value, and the effectiveness of the radar party is defined as a negative value. The calculation results are as Figure 3 shown. According to the constructed simulation conditions, taking the strategy selected by the interfering party as an example, the process of effectiveness conversion is calculated as follows:

[0099] (1) Calculate the interference benefit and the radar anti-interference benefit.

[0100] From the formula we get:

[0101]

[0102]

[0103]

[0104] Similarly

[0105] From the formula we get:

[0106]

[0107]

[0108]

[0109] Similarly

[0110] (2) Calculate the interference effectiveness and the radar anti - interference effectiveness.

[0111] From the formula we get:

[0112]

[0113]

[0114]

[0115] Similarly: E(A j,4 ) = 51.46, E(A j,5 ) = 53.95, E(A j,4 ) = 63.91.

[0116] E(A r,1 ) = - 51.3, E(A r,2 ) = - 66.4, E(A r,1 ) = - 61.244, E(A r,1 ) = - 67.34, E(A r,1 ) = - 71.9, E(A r,1 ) = - 75.6.

[0117] 2. Selection of interference strategies

[0118] By calculating the interference effectiveness and radar effectiveness when the opposing sides adopt different types, the following conclusions can be intuitively drawn from the results of the game tree: (1) Different interference patterns have different interference effects on the same radar operating mode. The selection of interference decisions needs to comprehensively consider the radar's anti-interference ability and the game type of the participants; (2) According to the actual battlefield environment, dynamically adjusting its own interference strategy can achieve better interference effects. Combining the strategy benefits and prior beliefs of the interfering party to calculate the average value of the interference decision effectiveness, the average value of the interference effectiveness is obtained from the calculation results in the game tree. It is the average value of all interference effectiveness values obtained by adopting a certain interference method and can reflect the quality of this strategy under the current conditions. It can be seen from Figure 4 that the descending order of the interference effectiveness is:

[0119] Interference effectiveness set = [E(A j,3 ), E(A j,6 ), E(A j,2 ), E(A j,1 ), E(A j,4 ), E(A j,5 )],

[0120] When the interference resources are limited, considering the interference effect and interference cost comprehensively, the interfering party should actively and preferentially implement the interference strategy A j,3 in order to achieve the best interference effect. Thus, it can be seen that the method proposed by the present invention can provide guidance for radar interference decision-making. On the basis of predicting the radar operating mode, it further quantifies the interference effect of the interference strategy and outputs the optimal decision in the form of a pure strategy, which has better operability.

[0121] 3. Verification of the optimal strategy

[0122] By changing the prior belief sets of the opposing sides and resetting the experimental parameters, 500 independent experiments are carried out, and the effectiveness results of the interference decision game tree are calculated. The changes in the average effectiveness values of both sides are recorded as Figure 5 shown. As the number of decisions increases, the probabilities of the opposing sides choosing a certain strategy gradually stabilize and finally reach a convergent state, obtaining the optimal solution set (F * (S j,i ), F * (S r,i )) that can maximize the interests of the opposing sides, proving that the new game method has a Nash equilibrium, solving the problem that the traditional interference decision-making method based on game theory highly depends on constructing a profit matrix, resulting in the interference strategy under Nash equilibrium not necessarily being the optimal solution, and avoiding the problem of a large increase in the algorithm complexity and the occurrence of the "curse of dimensionality" as the number of participants of the opposing sides increases.

[0123] In summary, for the radar jamming decision-making problem in cognitive electronic warfare, a radar jamming game model based on incomplete information is constructed. By reasonably quantifying the effectiveness, the influence of incomplete information on radar countermeasures is effectively avoided. The increase in the number of radar modes does not affect the convergence of the Nash equilibrium. At the same time, the uniqueness of actual combat command issuance is fully considered, and the optimal strategy is output in the form of a pure strategy, greatly improving the decision-making accuracy.

[0124] Overall beneficial effects:

[0125] The present invention provides a radar cognitive jamming decision-making method based on incomplete information game. Combining the actual jamming process, the influence of the type difference between the two game parties on the game process is added to the game model to achieve the optimal decision-making under the condition of partially known information. From the perspectives of the influence of jamming actions on the working value of the radar and the radar anti-jamming ability, the decision-making benefits of both parties are quantified to make the calculation of benefits more reasonable and in line with the actual combat background. Through the method of mixed strategy, the Bayesian Nash equilibrium analysis of the game model is carried out to obtain the set of mixed strategies with Bayesian Nash equilibrium. According to the set of mixed strategies, the unknown working modes of the multifunctional radar are obtained, and the strategies of the jamming party are dynamically adjusted when the radar working mode changes. By selecting a pure strategy form of jamming method, the cognitive advantage of the jamming system is fully exerted, solving the problem that the existing jamming decision-making method based on game theory overly relies on prior knowledge, and improving the jamming decision-making ability for non-cooperative multifunctional radars in complex electromagnetic environments.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A radar cognitive jamming decision-making method based on incomplete information game, characterized in that, it includes, Step 1: Construct and initialize a game model, which includes a set of participants, a set of participant types, a set of strategies, a set of prior knowledge, and a set of payoffs. The set of participants is used to represent the target radar and the jammer set participating in the game. The set of participant types is used to represent the set of participant types. The set of strategies is used to represent the operating modes that the radar can adopt during the game and the jamming actions that the jammer can adopt during the game. The set of prior knowledge is used to represent the set of prior knowledge of the participants. The set of payoffs is used to represent the set of payoffs of both participants; Step 2: Obtain the game information of the jammer and the radar according to the initialized game model. The game information includes radar type, radar operating mode, jammer type, and jamming actions taken by the jammer. Quantify the jamming payoff of the jammer and the radar payoff of the radar according to the game information, the success probability of the jamming action, and the anti-jamming success probability of the radar. Step 3: Obtain the set of jamming actions of the jammer under the Bayesian Nash equilibrium, predict the set of operating modes of the radar according to the set of jamming actions, and obtain the set of jamming effectiveness of the jammer based on the set of jamming actions of the jammer and the set of operating modes of the radar. Step 4: Sort the values of the jamming effectiveness in the set of jamming effectiveness in descending order, obtain the jamming action corresponding to the maximum jamming effectiveness, and use the jamming action as the optimal jamming action of the jammer.

2. The radar cognitive jamming decision-making method based on incomplete information game according to claim 1, characterized in that, Step 1 includes a game model M = <N, S, A, P, R>, N is the set of participants, N = {N r , N j}, where N r is the radar in the game process, and N j is the interferer in the game process; Let \(S\) be the set of participant types, \(S=\{S r ,S j \}\) is the set of types of the radar and the jammer, where is the set of types of the jammer, and \(n 1 is the total number of jammer types; is the set of types of the radar, and \(m 1 is the total number of radar types; $A$ is the set of strategies, is the interference actions that the interfering party can take, $n$ 2 is the total amount of interference actions; is the working mode in which the radar is located, $m$ 2 is the total amount of working modes, Let \(P\) be the set of prior knowledge, \(P = \{P r , P j \}\) is the set of prior knowledge of the participants, \(P r \) is the set of prior knowledge of the interfering party, \(P j \) is the set of prior knowledge of the radar. Let \(R\) be the set of payoffs, \(R = \{R r , R j \}\) is the set of payoffs for the participants, \(R r \) is the set of payoffs for the jammer, \(R j \) is the set of payoffs for the radar. Initialize the values of each parameter in the game model M.

3. The radar cognitive jamming decision-making method based on incomplete information game according to claim 2, characterized in that, Quantifying the interference benefit of the interfering party and the radar benefit of the radar according to the game information, the success probability of the interference action, and the anti-interference success probability of the radar includes obtaining that the type of the radar is S r,i , the radar operating mode is A r,q , q is the serial number of the operating mode, the type of the interfering party is S j,i , the interference action taken by the interfering party is A j,k , k is the serial number of the selected interference action; the success probability of the interference action is λ k , the anti-interference success probability of the radar itself is β q , When the radar fails to resist jamming, reduce the threat level, and calculate the jamming payoff of the jammer according to formula (1), Among them, W(D x ) is the influence weight of the interference operation on the radar, x ∈ {a, b, c}, W(D a ), W(D b ), W(D c ) are the influence weights brought by the interference operation on the real-time rate, accuracy rate, and false alarm rate of the radar's updated target information respectively; C(A j,k ) is the cost of initiating the interference operation A j,k , the success probability of the interference operation is λ k , the success probability of the radar's anti-jamming is β q , R = 100, indicating the interference gain obtained by the interfering party, When the radar successfully resists jamming, increase the threat level, and calculate the radar payoff of the radar according to formula (2), Among them, γ is the discount factor when anti-jamming is successful, and V(D x ) is the working value of the radar side. C(A r,q ) is the cost for the radar to actively change its working mode to A r,q . The success probability of the jamming operation is λ k , and the success probability of the radar's anti-jamming is β q . x ∈ {a, b, c}, and V(D a ), V(D b ), and V(D c ) are the values of the real-time rate, accuracy rate, and false alarm rate of the radar for updating the information of the jamming side respectively. R = -100 indicates the radar's gain.

4. The radar cognitive jamming decision-making method based on incomplete information game according to claim 3, characterized in that, Calculating the set of jamming effectiveness of the jammer based on the set of jamming actions of the jammer and the set of operating modes of the radar includes calculating the jamming effectiveness of the jammer taking different jamming actions according to formula (3) respectively, Among them, S j,i is the type of the interfering party, A j,k is the interference action selected by the interfering party from the set of interference actions, E(A j,k ) is the interference effectiveness obtained by the interfering party when selecting the interference action A j,k P j (S r,i |S j,i ) is the prior probability of the interfering party, R j (S j,i , A j,k , A r,q ) is the interference gain obtained by the interfering party after implementing the interference action A j,k . A r,q is the operating mode selected by the radar from the set of operating modes, S r,i is the type of the radar. Save the jamming effectiveness of different jamming actions to the set of jamming effectiveness.

5. The radar cognitive jamming decision-making method based on incomplete information game according to claim 1, characterized in that, Obtaining the set of jamming actions of the jammer under the Bayesian Nash equilibrium includes performing Bayesian Nash equilibrium analysis on the game model by the method of mixed strategy, obtaining a set of mixed strategies with Bayesian Nash equilibrium, and using the mixed strategy of the jammer in the set of mixed strategies as the set of jamming actions.

Images