PD fuze adaptive anti-interference strategy scheduling method based on zero-sum game

Abstract

The invention discloses a PD fuze adaptive anti-interference strategy scheduling method based on a zero-sum game, and belongs to the technical field of fuze electronic countermeasures. The implementation method comprises the following steps: constructing a revenue matrix of the fuze and jammer zero-sum game according to the zero-sum game; constructing the effective identification accuracy of the pulse Doppler fuze according to a fuze action efficiency criterion; constructing a profit criterion of the pulse Doppler fuze by combining the profit matrix of the fuze and jammer zero-sum game and the effective identification accuracy, and constructing an anti-interference profit matrix of the pulse Doppler fuze according to the profit criterion of the pulse Doppler fuze; and based on the income matrix under the income criterion, constructing a fuze anti-interference zero-sum game strategy, and realizing scheduling of the pulse Doppler fuze maximum income adaptive anti-interference strategy. According to the method, each anti-interference strategy can be adaptively scheduled, the anti-interference strategy with the maximum anti-interference benefit is selected as the current anti-interference strategy of the fuze, and the anti-interference capability of the pulse Doppler fuze under different anti-interference strategies is improved.

Description

Technical Field

[0001] The invention relates to a zero-sum game-based pulse Doppler PD fuze adaptive anti-interference strategy scheduling method, belonging to the technical field of fuze electronic countermeasures. Background Art

[0002] With the development of intelligent and integrated electronic jamming equipment, the electromagnetic interference patterns and power on the battlefield are gradually increasing, and the battlefield electromagnetic environment is becoming more and more complex, which brings severe tests to radio fuzes. According to the GJB6520-2008 battlefield electromagnetic environment classification and grading method, radio fuzes are in a moderate or severe complex electromagnetic environment. In a complex battlefield electromagnetic environment, fuzes may face the threat of multiple electromagnetic interferences at the same time, and different types of interference need to be countered by different interference suppression methods. At present, the new generation of jammers can complete the change from deceptive to suppressive interference in a very short time. If the jammer is in a deceptive interference state in the previous working cycle, it is entirely possible to be in a suppressive interference state in the next cycle, making the battlefield electromagnetic environment present a complex and changeable situation. If these changes cannot be kept up with, the fuze will find it difficult to effectively resist interference. Therefore, the fuze objectively needs to recognize the interference, environment and target, and make targeted adjustments to the anti-interference strategy and resources in a timely manner, so as to effectively improve its own anti-interference performance. Summary of the invention

[0003] Since each anti-interference strategy has different anti-interference effects under different interference conditions, in order to improve the anti-interference capability of the pulse Doppler fuze, the purpose of the present invention is to provide a PD fuze adaptive anti-interference strategy scheduling method based on zero-sum game, evaluate the anti-interference effectiveness of the anti-interference strategy under different interferences based on the benefit function, dynamically adjust the anti-interference strategy, and select the optimal anti-interference strategy in the current environment, so as to maintain the adaptability of the anti-interference performance of the pulse Doppler fuze under different interferences and improve the anti-interference capability of the pulse Doppler fuze.

[0004] The objective of the present invention is achieved through the following technical solutions:

[0005] The invention discloses a zero-sum game-based PD fuze adaptive anti-interference strategy scheduling method, constructs a zero-sum game model of a pulse Doppler fuze and a jammer; establishes a pulse Doppler fuze anti-interference efficiency evaluation method based on a zero-sum game benefit criterion; in order to improve the anti-interference capability of the pulse Doppler fuze, a dynamic scheduling method for the fuze anti-interference strategy is designed according to the anti-interference efficiency evaluation result, that is, a zero-sum game-based pulse Doppler fuze maximization benefit adaptive anti-interference strategy scheduling method, which can adaptively schedule each anti-interference strategy, select the one with the largest anti-interference benefit as the current anti-interference strategy of the fuze, and improve the anti-interference capability of the pulse Doppler fuze under different interference strategies.

[0006] The zero-sum game-based PD fuze adaptive anti-interference strategy scheduling method disclosed in the present invention comprises the following steps:

[0007] Step 1: Construct the payoff matrix of the zero-sum game between fuze and jammer according to the zero-sum game; construct the effective recognition accuracy of pulse Doppler fuze according to the fuze efficiency criterion; construct the payoff criterion of pulse Doppler fuze by combining the payoff matrix of the zero-sum game between fuze and jammer and the effective recognition accuracy, and construct the anti-interference payoff matrix of pulse Doppler fuze based on the payoff criterion of pulse Doppler fuze;

[0008] Step 1.1: Construct the payoff matrix of the zero-sum game between fuze and jammer based on the zero-sum game;

[0009] Game is a process in which multiple parties choose from the strategies they are allowed to choose under predetermined rules and conditions and obtain corresponding benefits. Game meets the following three necessary conditions:

[0010] 1) Participants in the game;

[0011] 2) The set of strategies that each game participant can choose;

[0012] 3) The corresponding benefits obtained by each participant based on the strategy they may choose.

[0013] In a game with n finite participants, the set of strategies that the lth participant can choose is S l , the specific strategy chosen is denoted as s l ,u l ,l=1,...,n is the profit function of the lth participant. If (s1,...,s n ) represents the combination of strategies adopted by each participant, u l (s1,...,s n ) is the profit obtained by the lth participant under this set of strategies, then the standard expression G of this game is

[0014] G={S1,...,S n ,u1,...,u n}(1)

[0015] According to whether there is an agreement between the game participants, the game is divided into cooperative game and non-cooperative game; according to the timeliness of the game behavior, the game is divided into static game and dynamic game; according to the degree of mutual understanding between the participants, the game is divided into complete information game and Bayesian game. The Bayesian game refers to the game in which the participants do not have complete information about each other's strategies. Non-cooperative games are divided into zero-sum games and non-zero-sum games according to the relationship between benefits. If the sum of the benefits of all participants is not zero, it is called a non-zero-sum game; if the sum of the benefits of all participants is zero, it is called a zero-sum game.

[0016] For pulse Doppler fuze and jammer, if the fuze is jammed, it means the "failure" of the fuze anti-jamming strategy and the "success" of the jammer's jamming strategy. Otherwise, it means the "success" of the fuze anti-jamming strategy and the "failure" of the jammer's jamming strategy. Therefore, the game relationship between the fuze and the jammer belongs to the category of zero-sum game. The anti-jamming performance of the pulse Doppler fuze is evaluated based on the benefits of the fuze in the zero-sum game process with the jammer.

[0017] The set of pure strategies for fuze anti-interference is S1 = {s 11 ,s 12 ,...,s 1m},{s 11 ,s 12 ,...,s 1m} represents the combination of anti-interference strategies adopted by the fuze, m is the number of anti-interference strategies of the fuze; the set of pure interference strategies of the jammer is S2={s 21 ,s 22 ,...,s 2n},{s 21 ,s 22 ,...,s 2n} represents the combination of jammer strategies, n is the number of jammer strategies; u1(s 1i ,s 2j ) is the payoff function of the fuze, u2(s 1i ,s 2j ) is the jammer's revenue function, and u2(s 1i ,s 2j )=-u1(s 1i ,s 2j ), where i represents the anti-interference strategy number and j represents the interference strategy number. The payoff matrix of the game between the fuze party and the jammer party is shown in Table 1.

[0018] Table 1 Fuze and jammer game payoff matrix

[0019]

[0020] Step 1.2: Construct the effective recognition accuracy of the pulse Doppler fuze according to the fuze efficiency criterion;

[0021] The jamming strategies of fuze jammers are mainly the following three strategies: 1) suppression jamming strategy a; 2) deception jamming strategy b; 3) combined jamming strategy a&b. According to the jamming strategies of fuze jammers, pulse Doppler fuzes adopt three corresponding anti-jamming strategies: 1) pulse Doppler fuze anti-suppression jamming strategy A based on identity recognition; 2) pulse Doppler fuze anti-deception jamming strategy B based on identity recognition; 3) combined anti-jamming method A&B, that is, the results of the first two anti-jamming strategies are "AND" operated. If the output result of one of the anti-jamming strategy channels is interference, the measured signal is judged to be a jamming signal. Only when the output results of the two anti-jamming strategy channels are both targets, the measured signal is judged to be a target and the start signal is output.

[0022] According to the efficiency criterion, if the fuze target and interference recognition rate is higher, its anti-interference efficiency is higher and its anti-interference performance is stronger. acc for

[0023]

[0024] Where: N R is the number of correctly identified signals, N T is the total number of signals used for testing.

[0025] The correct recognition rate of the target and the interference of the fuze under the three interference strategies and anti-interference strategy is:

[0026] 1) If the jammer takes jamming measure a: The correct recognition rate of the target and jammer of anti-jamming strategy A is The correct recognition rate of the target and interference of anti-interference strategy B is The correct recognition rate of target and interference of anti-interference strategy A&B is

[0027] 2) If the jammer takes jamming measure b: The correct recognition rate of the target and jammer of anti-jamming strategy A is The correct recognition rate of the target and interference of anti-interference strategy B is The correct recognition rate of target and interference of anti-interference strategy A&B is

[0028] 3) If the jammer takes jamming measures a&b: The correct recognition rate of the target and jammer of anti-jamming strategy A is The correct recognition rate of the target and interference of anti-interference strategy B is The correct recognition rate of target and interference of anti-interference strategy A&B is

[0029] The average target and interference recognition accuracy of the fuze under a specific signal-to-interference-noise ratio SJNR is defined as the effective recognition accuracy of the fuze under different anti-interference strategies and interference strategies, that is,

[0030]

[0031] Among them, X represents the anti-interference strategy A, B, A&B; Y represents the interference strategy a, b, a&b;

[0032] Anti-interference strategy A&B is to perform a logical AND on the identification results of the two channels. Only when both channels are identified as targets can it be determined to be a target. As long as the identification result of one of the two channels is interference, the measured signal is determined to be interference. If the fuze adopts anti-interference strategy A&B, its misidentification has the following situations:

[0033] 1) Channel A and channel B both recognize errors, and the probability is

[0034] 2) One of the channels A and B is misidentified. In this case, misidentification will occur only when the signal is the target, and the probability is

[0035] Therefore, the effective recognition accuracy of the fuze adopting the anti-interference strategy A&B is

[0036]

[0037] Step 1.3: Based on the benefit matrix of the zero-sum game between the fuze and the jammer in step 1.1 and the correct rate of effective fuze identification in step 1.2, the benefit criterion of the pulse Doppler fuze is constructed, and the anti-jamming benefit matrix of the pulse Doppler fuze is constructed based on the benefit criterion;

[0038] On the basis of the correct recognition rate of the fuze target and the interference, the difference between the correct recognition rate and the false recognition rate of the interference and the target after adopting the anti-interference strategy defines the benefit function of the fuze, that is:

[0039]

[0040] Where: is the target and interference recognition rate of the fuze using the i-th anti-interference strategy under the j-th interference.

[0041] The benefit criterion for evaluating the anti-interference effectiveness of the fuze is obtained through formula (5), that is, the greater the benefit obtained by the fuze taking a certain anti-interference measure, the stronger the anti-interference ability of the fuze after adopting the anti-interference strategy. The benefit criterion number can reflect the influence of different interference strategies on the anti-interference effect of the fuze and meet the requirements of the fuze anti-interference effectiveness evaluation criterion. The benefit criterion constructed by the benefit function of formula (5) and the effective correct recognition rate of formula (3) and formula (4) are combined to obtain the pulse Doppler fuze anti-interference benefit matrix, as shown in Table 2.

[0042] Table 2 Pulse Doppler fuze anti-interference benefit matrix

[0043]

[0044] Step 2: Based on the benefit matrix under the benefit criterion for evaluating the anti-interference effectiveness of the fuze constructed in step 1, a zero-sum game strategy for fuze anti-interference is constructed to realize the scheduling of the adaptive anti-interference strategy for maximizing the benefit of the pulse Doppler fuze.

[0045] According to the anti-interference benefit matrix of the pulse Doppler fuze constructed in step 1 and the Nash equilibrium theorem, there is no Nash equilibrium in the game between the pulse Doppler fuze and the jammer. Under different jamming strategies, the pulse Doppler fuze cannot always choose a constant anti-interference strategy as its optimal strategy. According to the maximum and minimum theorem, the two parties in the game should maximize their expected benefits when choosing strategies. When the jammer's jamming strategy is σ2=(σ 21 ,σ 22 ,σ 23 ), σ 21 ,σ 22 ,σ 23 They represent the probability that the jammer takes jamming measures a, b, and a&b respectively. Then the anti-jamming benefits of different anti-jamming strategies for pulse Doppler fuze are:

[0046]

[0047] Since the fuze jammer does not know what anti-jamming strategy the fuze adopts, according to Nash's theorem, in order to ensure its jamming effect, the jammer should not adopt a single constant jamming strategy, but a mixed jamming strategy. Therefore, the expected benefit of the fuze adopting each anti-jamming strategy is

[0048] u1(s 1i ,σ2)=x i1 σ 21 +x i2 σ 22 +x i3 σ 23

[0049] =x i1 σ 21 +x i2 σ 22 +x i3 (1-σ 21 -σ 22 )(7)

[0050] =x i3 +(x i1 -x i3 )σ 21 +(x i2 -x i3 )σ 22

[0051] The anti-interference benefit matrix under measured data is introduced to complete the expected benefit of each anti-interference strategy in formula (7). The greater the benefit of the fuze taking a certain anti-interference measure, the stronger the anti-interference ability after the anti-interference strategy is. Then the corresponding best anti-interference strategy of the fuze is selected to realize the scheduling of the adaptive anti-interference strategy for maximizing the benefit of the pulse Doppler fuze.

[0052] Beneficial effects:

[0053] 1. The zero-sum game-based PD fuze adaptive anti-interference strategy scheduling method disclosed in the present invention constructs a benefit matrix under the benefit criterion for evaluating the anti-interference effectiveness of the fuze, evaluates the impact of different interference strategies on the anti-interference effect of the fuze, and can meet the requirements of the fuze anti-interference effectiveness evaluation criterion.

[0054] 2. The zero-sum game-based PD fuze adaptive anti-interference strategy scheduling method disclosed in the present invention can adaptively schedule each anti-interference strategy and select the one with the largest anti-interference benefit as the current anti-interference strategy of the fuze, thereby effectively improving the anti-interference capability of the pulse Doppler fuze under different interference strategies.

[0055] 3. The zero-sum game-based PD fuze adaptive anti-interference strategy scheduling method disclosed in the present invention, in the process of constructing a benefit matrix under the benefit criterion for evaluating the anti-interference effectiveness of the fuze, the correct recognition rate and false recognition rate of the fuze for each interference strategy can be obtained through offline repeated experiments, so the benefit function of the fuze is known, and the evaluation of the anti-interference effectiveness of the fuze can be completed without the premise of "cooperation" between the fuze and the jammer. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a schematic diagram of the zero-sum game process between the pulse Doppler fuze and the jammer disclosed in the present invention;

[0057] Figure 2 The bit error rate of the pulse Doppler fuze identity recognition disclosed in the following embodiments;

[0058] Figure 3 is the target and interference correct recognition rate of fuze anti-interference strategy A under different signal-to-interference-noise ratios;

[0059] Figure 4 It is the joint feature space of target and interference in time and frequency domain;

[0060] Figure 5 The accuracy of target and interference identification of anti-interference strategy B under different signal-to-interference-noise ratios;

[0061] Figure 6 A linear programming diagram for the expected benefit of anti-jamming for pulse Doppler fuze;

[0062] Figure 7 Comparison of the correct recognition rate of interference between the targets of different pulse Doppler fuze anti-interference strategies; (a) is the comparison of the results of the maximization benefit anti-interference strategy and the random strategy; (b) is the comparison of the results of the maximization benefit anti-interference strategy and strategy A; (c) is the comparison of the results of the maximization benefit anti-interference strategy and strategy B; (d) is the comparison of the results of the maximization benefit anti-interference strategy and strategies A&B;

[0063] Figure 8 It is a workflow for evaluating the anti-jamming effectiveness of pulse Doppler fuze and scheduling of adaptive anti-jamming strategies. DETAILED DESCRIPTION

[0064] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0065] Embodiment 1:

[0066] Step 1: Based on the zero-sum game, the payoff matrix of the zero-sum game between the fuze and the jammer is constructed; then, the effective recognition accuracy of the pulse Doppler fuze is constructed according to the fuze efficiency criterion; then, the payoff matrix of the zero-sum game between the fuze and the jammer and the effective recognition accuracy are combined to construct the payoff criterion of the pulse Doppler fuze, and the anti-interference payoff matrix of the pulse Doppler fuze is constructed based on the payoff criterion of the pulse Doppler fuze;

[0067] Step 1.1: Construct the payoff matrix of the zero-sum game between fuze and jammer based on the zero-sum game;

[0068] Game is a process in which multiple parties choose from the strategies they are allowed to choose under predetermined rules and conditions and obtain corresponding benefits. Game meets the following three necessary conditions:

[0069] 1) Participants in the game;

[0070] 2) The set of strategies that each game participant can choose;

[0071] 3) The corresponding benefits obtained by each participant based on the strategy they may choose.

[0072] In a game with n finite participants, the set of strategies that the lth participant can choose is S l , the specific strategy chosen is denoted as s l ,u l ,l=1,...,n is the profit function of the lth participant. If (s1,...,s n ) represents the combination of strategies adopted by each participant, u l (s1,...,s n ) is the profit obtained by the lth participant under this set of strategies, then the standard expression G of this game is

[0073] G={S1,...,S n ,u1,...,u n}(1)

[0074] According to whether there is an agreement between the game participants, the game is divided into cooperative game and non-cooperative game; according to the timeliness of the game behavior, the game is divided into static game and dynamic game; according to the degree of mutual understanding between the participants, the game is divided into complete information game and Bayesian game. The Bayesian game refers to the game in which the participants do not have complete information about each other's strategies. Non-cooperative games are divided into zero-sum games and non-zero-sum games according to the relationship between benefits. If the sum of the benefits of all participants is not zero, it is called a non-zero-sum game; if the sum of the benefits of all participants is zero, it is called a zero-sum game.

[0075] For pulse Doppler fuze and jammer, if the fuze is jammed, it means the "failure" of the fuze anti-jamming strategy and the "success" of the jammer's jamming strategy. Otherwise, it means the "success" of the fuze anti-jamming strategy and the "failure" of the jammer's jamming strategy. Therefore, the game relationship between the fuze and the jammer belongs to the category of zero-sum game. The anti-jamming performance of the pulse Doppler fuze is evaluated based on the benefits of the fuze in the zero-sum game process with the jammer.

[0076] The set of pure strategies for fuze anti-interference is S1 = {s 11 ,s 12 ,...,s 1m},{s 11 ,s 12 ,...,s 1m} represents the combination of anti-interference strategies adopted by the fuze, m is the number of anti-interference strategies of the fuze; the set of pure interference strategies of the jammer is S2={s 21 ,s 22 ,...,s 2n},{s 21 ,s 22 ,...,s 2n} represents the combination of jammer strategies, n is the number of jammer strategies; u1(s 1i ,s 2j ) is the payoff function of the fuze, u2(s 1i ,s 2j ) is the jammer's revenue function, and u2(s 1i ,s 2j )=-u1(s 1i ,s 2j ), where i represents the anti-interference strategy number and j represents the interference strategy number. The payoff matrix of the game between the fuze party and the jammer party is shown in Table 1.

[0077] Table 1 Fuze and jammer game payoff matrix

[0078]

[0079] Step 1.2: Construct the effective recognition accuracy of the pulse Doppler fuze according to the fuze efficiency criterion;

[0080] The jamming strategies of fuze jammers are mainly the following three strategies: 1) suppression jamming strategy a; 2) deception jamming strategy b; 3) combined jamming strategy a&b. According to the jamming strategies of fuze jammers, pulse Doppler fuzes adopt three corresponding anti-jamming strategies: 1) pulse Doppler fuze anti-suppression jamming strategy A based on identity recognition; 2) pulse Doppler fuze anti-deception jamming strategy B based on identity recognition; 3) combined anti-jamming method A&B, that is, the results of the first two anti-jamming strategies are "AND" operated. If the output result of one of the anti-jamming strategy channels is interference, the measured signal is judged to be a jamming signal. Only when the output results of the two anti-jamming strategy channels are both targets, the measured signal is judged to be a target and the start signal is output.

[0081] According to the efficiency criterion, if the fuze target and interference recognition rate is higher, its anti-interference efficiency is higher and its anti-interference performance is stronger. acc for

[0082]

[0083] Where: N R is the number of correctly identified signals, N T is the total number of signals used for testing.

[0084] The correct recognition rate of the target and the interference of the fuze under the three interference strategies and anti-interference strategy is:

[0085] 1) If the jammer takes jamming measure a: The correct recognition rate of the target and jammer of anti-jamming strategy A is The correct recognition rate of the target and interference of anti-interference strategy B is The correct recognition rate of target and interference of anti-interference strategy A&B is

[0086] 2) If the jammer takes jamming measure b: The correct recognition rate of the target and jammer of anti-jamming strategy A is The correct recognition rate of the target and interference of anti-interference strategy B is The correct recognition rate of target and interference of anti-interference strategy A&B is

[0087] 3) If the jammer takes jamming measures a&b: The correct recognition rate of the target and jammer of anti-jamming strategy A is The correct recognition rate of the target and interference of anti-interference strategy B is The correct recognition rate of target and interference of anti-interference strategy A&B is

[0088] The average target and interference recognition accuracy of the fuze under a specific signal-to-interference-noise ratio SJNR is defined as the effective recognition accuracy of the fuze under different anti-interference strategies and interference strategies, that is,

[0089]

[0090] Among them, X represents the anti-interference strategy A, B, A&B; Y represents the interference strategy a, b, a&b;

[0091] Anti-interference strategy A&B is to perform a logical AND on the identification results of the two channels. Only when both channels are identified as targets can it be determined to be a target. As long as the identification result of one of the two channels is interference, the measured signal is determined to be interference. If the fuze adopts anti-interference strategy A&B, its misidentification has the following situations:

[0092] 1) Channel A and channel B both recognize errors, and the probability is

[0093] 2) One of the channels A and B is misidentified. In this case, misidentification will occur only when the signal is the target, and the probability is

[0094] Therefore, the effective recognition accuracy of the fuze adopting the anti-interference strategy A&B is

[0095]

[0096] The bit error rate of pulse Doppler fuze identity recognition system under different processing gains and signal-to-noise ratios is as follows Figure 2 As shown in the figure; the target and interference recognition accuracy of the pulse Doppler fuze identity recognition system under different processing gains and signal-to-noise ratios are shown in the figure below: Figure 3 shown.

[0097] Depend on Figure 2 and Figure 3 It can be seen that when the pulse Doppler fuze adopts the anti-deception jamming strategy A based on identity recognition, there are three different jamming situations:

[0098] 1) When the jammer adopts the suppression jamming strategy a, it mainly has a greater impact on the signal-to-noise ratio of the received information. When the signal-to-noise ratio is low, the fuze bit error rate increases, which leads to a decrease in the fuze's recognition rate of the identity code in the echo and an increase in the false recognition rate. At this time, the fuze benefit decreases.

[0099] 2) When the jammer adopts deceptive jamming strategy b, it mainly simulates the characteristics of the target so that the fuze misjudges it as the target, thereby achieving the deception effect on the fuze. However, since the jammer cannot intercept the random key of the fuze signal, the fuze will obtain the wrong identity code when decrypting the deceptive jamming, which can effectively counter deceptive jamming.

[0100] 3) When the jammer adopts the combined jamming strategy a&b, it will cause the fuze to be unable to identify the target and misidentify the deception jamming. However, the deterioration of the signal-to-noise ratio caused by the suppression jamming will also affect the effect of the deception jamming, resulting in a decrease in the deception effect on the fuze.

[0101] Through the measured data of the fuze jamming countermeasure experiment, the pulse Doppler fuze target and jamming joint feature space is obtained as follows: Figure 4 Under different signal-to-noise ratios, the accuracy of the anti-suppression jamming strategy B based on the spatial recognition of target and jamming signal characteristics for the pulse Doppler fuze target and jamming recognition is shown in Figure 5 shown.

[0102] Depend on Figure 4 and Figure 5 It can be seen that when the pulse Doppler fuze adopts the anti-suppression jamming strategy B based on the spatial recognition of target and jamming signal characteristics, there are also three situations:

[0103] 1) When the jammer adopts suppression jamming strategy a, since the difference between suppression jamming and pulse Doppler target feature space is large, while the difference between deceptive jamming and target feature space is relatively small, its effect against suppression jamming is better than deceptive jamming. Therefore, when the pulse Doppler fuze adopts anti-jamming strategy B, when the anti-jamming party adopts suppression strategy a, the fuze party will gain more;

[0104] 2) When the jammer adopts deceptive jamming strategy b, since the difference between the deceptive jamming and the pulse Doppler fuze target feature space is small and the overlap is high, its anti-suppression jamming effect is better than deceptive jamming. Therefore, when the pulse Doppler fuze adopts anti-jamming strategy B, when the jammer adopts deceptive jamming strategy b, the fuze party's benefits are reduced.

[0105] 3) When the jammer adopts the combined jamming strategy a&b, the characteristic distribution range of its jamming signal is between the suppression jamming and deception jamming. Therefore, when the pulse Doppler fuze adopts the anti-jamming strategy B, the jamming effect of the jamming strategy a&b on the fuze is between strategy a and strategy b.

[0106] The average target and interference recognition accuracy under the signal-to-interference-noise ratio (SJNR) of -5dB to 5dB is defined as: the effective recognition accuracy of the fuze under different anti-interference strategies and interference strategies, that is,

[0107]

[0108] Anti-interference strategy A&B is to perform a logical AND on the identification results of the two channels. Only when both channels are identified as targets can the signal be considered as a target. As long as the identification result of one of the two channels is interference, the measured signal is considered as interference. If the fuze adopts anti-interference strategy A&B, there are the following situations for its misidentification:

[0109] 1) Channel A and channel B both recognize errors, and the probability is

[0110] 2) One of the channels A and B is misidentified. In this case, misidentification will occur only when the signal is the target, and the probability is

[0111] Therefore, the effective recognition accuracy of the fuze adopting the anti-interference strategy A&B is

[0112]

[0113] Step 1.3: Based on the benefit matrix of the zero-sum game between the fuze and the jammer in step 1.1 and the correct rate of effective fuze identification in step 1.2, the benefit criterion of the pulse Doppler fuze is constructed, and the anti-jamming benefit matrix of the pulse Doppler fuze is constructed based on the benefit criterion;

[0114] On the basis of the correct recognition rate of the fuze target and the interference, the difference between the correct recognition rate and the false recognition rate of the interference and the target after adopting the anti-interference strategy defines the benefit function of the fuze, that is:

[0115]

[0116] Where: is the target and interference recognition rate of the fuze using the i-th anti-interference strategy under the j-th interference.

[0117] The benefit criterion for evaluating the anti-interference effectiveness of the fuze is obtained through formula (5), that is, the greater the benefit obtained by the fuze taking a certain anti-interference measure, the stronger the anti-interference ability of the fuze after adopting the anti-interference strategy. The benefit criterion number can reflect the influence of different interference strategies on the anti-interference effect of the fuze and meet the requirements of the fuze anti-interference effectiveness evaluation criterion. The benefit criterion constructed by the benefit function of formula (5) and the effective correct recognition rate of formula (3) and formula (4) are combined to obtain the pulse Doppler fuze anti-interference benefit matrix, as shown in Table 2.

[0118] Table 2 Pulse Doppler fuze anti-interference benefit matrix

[0119]

[0120] Will Figure 3 and Figure 5 By substituting the target and interference correct recognition rates of anti-interference strategy A and anti-interference strategy B into formula (4), we can obtain the effective recognition correct rates of fuzes under different anti-interference strategies and interference strategies, as shown in Table 3.

[0121] Table 3. Correct rate of effective identification of fuze under different strategies

[0122]

[0123] Table 3 and Figure 5 Substituting the data into equation (5), we can get the anti-interference benefit matrix of pulse Doppler fuze, as shown in Table 4.

[0124] Table 4 Pulse Doppler fuze anti-interference benefit matrix

[0125]

[0126] The benefit criterion for evaluating the anti-interference effectiveness of the fuze can be obtained by formula (5), that is, the greater the benefit obtained by the fuze by taking a certain anti-interference measure, the stronger the anti-interference ability of the fuze after adopting the anti-interference strategy. It can be seen that the benefit criterion number can reflect the influence of different interference strategies on the anti-interference effect of the fuze, and meet the requirements of the fuze anti-interference effectiveness evaluation criterion.

[0127] Step 2: Through the benefit matrix under the benefit criterion for evaluating the anti-interference effectiveness of the fuze constructed in step 1, a zero-sum game strategy for fuze anti-interference is constructed to realize the scheduling of the adaptive anti-interference strategy for maximizing the benefit of the pulse Doppler fuze.

[0128] According to the anti-interference benefit matrix of the pulse Doppler fuze constructed in step 1 and the Nash equilibrium theorem, there is no Nash equilibrium in the game between the pulse Doppler fuze and the jammer. Under different jamming strategies, the pulse Doppler fuze cannot always choose a constant anti-interference strategy as its optimal strategy. According to the maximum and minimum theorem, the two parties in the game should maximize their expected benefits when choosing strategies. When the jammer's jamming strategy is σ2=(σ 21 ,σ 22 ,σ 23 ), σ 21 ,σ 22 ,σ 23 They represent the probability that the jammer takes jamming measures a, b, and a&b respectively. Then the anti-jamming benefits of different anti-jamming strategies for pulse Doppler fuze are:

[0129]

[0130] Since the fuze jammer does not know what anti-jamming strategy the fuze adopts, according to Nash's theorem, in order to ensure its jamming effect, the jammer should not adopt a single constant jamming strategy, but a mixed jamming strategy. Therefore, the expected benefit of the fuze adopting each anti-jamming strategy is

[0131] u1(s 1i ,σ2)=x i1 σ 21 +x i2 σ 22 +x i3 σ 23

[0132] =x i1 σ 21 +x i2 σ 22 +x i3 (1-σ 21 -σ 22 )(7)

[0133] =x i3 +(x i1 -x i3 )σ 21 +(x i2 -x i3 )σ 22

[0134] Substituting the data in Table 4 into equation (7), we get the linear programming equations shown in equation (8):

[0135]

[0136] According to linear programming theory, the problem shown in formula (8) can be transformed into a linear programming problem as shown in formula (9).

[0137]

[0138] The graphical solution of the linear programming problem in formula (9) is as follows Figure 6 shown.

[0139] Depend on Figure 6 It can be seen that when σ is satisfied 21 -1.81σ 22 >0.222, the optimal strategy of the fuze is s 12 , that is, anti-interference strategy B; when σ 21 -1.81σ 22 <0.222&σ 21 -1.018σ 22 >0.115, the optimal strategy for the fuze is s 13 , that is, anti-interference strategy A&B, when σ 21-1.018σ 22 <0.115, the optimal strategy for the fuze is s 11 , that is, anti-interference strategy A.

[0140] When interference exists, the output of channel A and channel B of the pulse Doppler fuze anti-interference strategy has the following four situations.

[0141] 1) Fuze anti-interference strategy When the output results of channel A and channel B are both interference, recorded as A:0, and the output result of channel B is the target, recorded as B:0, then

[0142]

[0143] At this time σ 21 -1.018σ 22 =0.047<0.115, the fuze takes anti-interference strategy A for maximum benefit;

[0144] 2) Fuze anti-interference strategy When the output results of channel A and channel B are both the target

[0145]

[0146] At this time σ 21 -1.018σ 22 =-0.059<0.115, the fuze adopts anti-interference strategy A to obtain the greatest benefit;

[0147] 3) When the output result of channel A is interference and the output result of channel B is target

[0148]

[0149] At this time σ 21 -1.018σ 22 =-0.511<0.115, so when A:0, B:1, the fuze selects anti-interference strategy A to achieve the greatest benefit.

[0150] 4) When the output result of channel A is the target and the output result of channel B is the interference:

[0151]

[0152] At this time σ 21 -1.018σ 22 =0.461>0.115&σ 21 -1.81σ 22 =0.389>0.222, the fuze selects anti-interference strategy B for maximum benefit.

[0153] In order to verify the improvement effect of the proposed anti-interference effectiveness evaluation and adaptive anti-interference strategy scheduling on the anti-interference performance of pulse Doppler fuze, the effectiveness of the adaptive anti-interference strategy scheduling was verified.

[0154] 1) Anti-interference success rate verification

[0155] Under the condition that the fuze can be interfered, 100 sets of suppression, deception and combination interference with random setting parameters are used to randomly test the fuze. The results are as follows: Figure 7 As shown. Bars of different colors represent different anti-interference strategies: blue represents that the fuze adopts the adaptive anti-interference strategy scheduling method of maximizing benefits proposed in the paper; yellow represents that the fuze adopts a random anti-interference strategy; green represents that the fuze only adopts anti-interference strategy A; red represents that the fuze only adopts anti-interference strategy B; and gray represents that the fuze only adopts anti-interference strategies A&B.

[0156] Depend on Figure 7 It can be seen that under the three interference strategies, the anti-interference effect of the maximum benefit adaptive anti-interference strategy scheduling method is better than that of the random anti-interference strategy. For a single anti-interference strategy, under a certain interference, its target and interference correct identification rate is equivalent to the dynamic anti-interference strategy based on maximum benefit. For example, when the anti-interference strategy A targets the deceptive interference strategy B, its anti-interference success rate is 95.1%, which is slightly higher than the maximum benefit dynamic anti-interference strategy, but in the face of other types of interference strategies, its target and interference correct identification rate is much lower than the maximum benefit dynamic anti-interference strategy proposed in the paper. Therefore, the pulse Doppler fuze maximization benefit adaptive anti-interference strategy scheduling method based on zero-sum game can reasonably schedule different anti-interference strategies according to the anti-interference benefit, and significantly improve the anti-interference effect of the pulse Doppler fuze.

[0157] 2) Real-time analysis

[0158] Since the pulse Doppler fuze has a very short working time, it has a very high requirement for the real-time signal processing. Therefore, the pulse Doppler fuze anti-interference performance evaluation and adaptive anti-interference strategy scheduling must have a high real-time performance. Therefore, the pulse Doppler fuze anti-interference performance evaluation and adaptive anti-interference strategy scheduling both adopt the offline training and online decision-making mode. For the pulse Doppler fuze signal processing, it only increases the time consumption of the online decision-making stage. The workflow is as follows: Figure 8 shown.

[0159] During offline training, the effective recognition accuracy of sample data for anti-interference strategy A, anti-interference strategy B, and anti-interference strategy A&B is calculated respectively, and the anti-interference benefit matrix is ​​obtained through the calculation of the effective recognition accuracy. According to the benefit matrix, the solution space of the offline programming equation of the pulse Doppler fuze anti-interference expected benefit is obtained to provide support for online decision-making. In the online decision-making stage, the solution space of the linear programming equation of the expected benefit of the fuze obtained by offline training is used as the basis. According to the recognition results of the anti-interference strategy A channel and the anti-interference strategy B channel, dynamic decision-making and scheduling are performed on the anti-interference strategy. For the four combinations of the recognition results of the anti-interference strategy A channel and the anti-interference strategy B channel, only one digital logic operation is required. Taking the typical 74 series logic gate device as an example, its response time to the input is only tens of nanoseconds. Assuming that the pulse width of the pulse Doppler fuze is not less than 20ns, the rendezvous speed of the missile is not higher than 2000m / s, and the envelope duration of the target signal output by the fuze baseband filter is greater than 3ms, the dynamic decision-making and scheduling of the fuze only takes tens of nanoseconds, so it fully meets the real-time requirements of the pulse Doppler fuze signal processing.

[0160] In summary, the adaptive anti-interference strategy scheduling of pulse Doppler fuze maximizing benefits based on zero-sum game is very effective for different anti-interference strategies under different interference strategies, has high real-time performance, and can significantly improve the adaptability of pulse Doppler fuze anti-interference system to different interference strategies. Through the above method, the fuze can always gain an advantageous position and obtain the maximum benefit in the game with the jammer. This method can effectively improve the anti-interference ability of radio fuze under different interference strategies.

[0161] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A zero-sum game-based PD fuze adaptive anti-interference strategy scheduling method, characterized by: The steps include: Step 1: Construct the payoff matrix of the zero-sum game between fuze and jammer according to the zero-sum game; construct the effective recognition accuracy of pulse Doppler fuze according to the fuze efficiency criterion; Combining the benefit matrix of zero-sum game between fuze and jammer and the effective recognition accuracy, the benefit criterion of pulse Doppler fuze is constructed, and the anti-jamming benefit matrix of pulse Doppler fuze is constructed based on the benefit criterion of pulse Doppler fuze. Step 2: Based on the benefit matrix under the benefit criterion for evaluating the anti-interference effectiveness of the fuze constructed in step 1, a zero-sum game strategy for fuze anti-interference is constructed to realize the scheduling of the adaptive anti-interference strategy for maximizing the benefit of the pulse Doppler fuze.

2. The method for scheduling a PD fuze adaptive anti-interference strategy based on zero-sum game as claimed in claim 1, characterized in that: The implementation method of step one is: Step 1.1: Construct the payoff matrix of the zero-sum game between fuze and jammer based on the zero-sum game; Game is a process in which multiple parties choose from the strategies they are allowed to choose under predetermined rules and conditions and obtain corresponding benefits; the game meets the following three necessary conditions: 1) Participants in the game; 2) The set of strategies that each game participant can choose; 3) The corresponding benefits of each participant's possible strategy; In a game with n finite participants, the set of strategies that the lth participant can choose is S l , the specific strategy chosen is denoted as s l ,u l ,l=1,...,n is the profit function of the lth participant; if (s1,...,s n ) represents the combination of strategies adopted by each participant, u l (s1,...,s n ) is the profit obtained by the lth participant under this set of strategies, then the standard expression G of this game is G={S1,...,S n ,u1,...,u n } (1) According to whether there is an agreement between the game participants, the game is divided into cooperative game and non-cooperative game; according to the timeliness of the game behavior, the game is divided into static game and dynamic game; according to the degree of mutual understanding between the participants, the game is divided into complete information game and Bayesian game. The Bayesian game refers to the game in which the participants do not have complete information about each other's strategies; non-cooperative games are divided into zero-sum games and non-zero-sum games according to the relationship between benefits. If the sum of the benefits of all participants is not zero, it is called a non-zero-sum game; if the sum of the benefits of all participants is zero, it is called a zero-sum game; For pulse Doppler fuze and jammer, if the fuze is jammed, it means the "failure" of the fuze anti-jamming strategy and the "success" of the jammer's jamming strategy. Otherwise, it means the "success" of the fuze anti-jamming strategy and the "failure" of the jammer's jamming strategy. Therefore, the game relationship between the fuze and the jammer belongs to the category of zero-sum game. The anti-jamming performance of the pulse Doppler fuze is evaluated based on the benefits of the fuze in the zero-sum game process with the jammer. The set of pure strategies for fuze anti-interference is S1 = {s 11 ,s 12 ,...,s 1m },{s 11 ,s 12 ,...,s 1m } represents the combination of anti-interference strategies adopted by the fuze, m is the number of anti-interference strategies of the fuze; the set of pure interference strategies of the jammer is S2={s 21 ,s 22 ,...,s 2n },{s 21 ,s 22 ,...,s 2n } represents the combination of jammer strategies, n is the number of jammer strategies; u1(s 1i ,s 2j ) is the payoff function of the fuze, u2(s 1i ,s 2j ) is the jammer's revenue function, and u2(s 1i ,s 2j )=-u1(s 1i ,s 2j ), where i represents the anti-interference strategy number, and j represents the interference strategy number. The payoff matrix of the game between the fuze party and the jammer party is shown in Table 1; Table 1 Fuze and jammer game payoff matrix Step 1.2: Construct the effective recognition accuracy of the pulse Doppler fuze according to the fuze efficiency criterion; The jamming strategies of fuze jammers are mainly the following three strategies: 1) suppression jamming strategy a; 2) deception jamming strategy b; 3) combined jamming strategy a&b; According to the jamming strategies of fuze jammers, pulse Doppler fuzes adopt three corresponding anti-jamming strategies: 1) pulse Doppler fuze anti-suppression jamming strategy A based on identity recognition; 2) pulse Doppler fuze anti-deception jamming strategy B based on identity recognition; 3) combined anti-jamming method A&B, that is, the results of the first two anti-jamming strategies are "AND" operated. If the output result of one of the anti-jamming strategy channels is interference, the measured signal is judged to be a jamming signal. Only when the output results of the two anti-jamming strategy channels are both targets, the measured signal is judged to be the target and the start signal is output; According to the efficiency criterion, if the fuze target and interference recognition rate is higher, its anti-interference efficiency is higher and its anti-interference performance is stronger; the fuze target and interference correct recognition rate P acc for Where: N R is the number of correctly identified signals, N T is the total number of signals used for testing; The correct recognition rate of the target and the interference of the fuze under the three interference strategies and anti-interference strategy is: 1) If the jammer takes jamming measure a: The correct recognition rate of the target and jammer of anti-jamming strategy A is The correct recognition rate of the target and interference of anti-interference strategy B is The correct recognition rate of target and interference of anti-interference strategy A&B is 2) If the jammer takes jamming measure b: The correct recognition rate of the target and jammer of anti-jamming strategy A is The correct recognition rate of the target and interference of anti-interference strategy B is The correct recognition rate of target and interference of anti-interference strategy A&B is 3) If the jammer takes jamming measures a&b: The correct recognition rate of the target and jammer of anti-jamming strategy A is The correct recognition rate of the target and interference of anti-interference strategy B is The correct recognition rate of target and interference of anti-interference strategy A&B is The average target and interference recognition accuracy of the fuze under a specific signal-to-interference-noise ratio SJNR is defined as the effective recognition accuracy of the fuze under different anti-interference strategies and interference strategies, that is, Among them, X represents the anti-interference strategy A, B, A&B; Y represents the interference strategy a, b, a&b; Anti-interference strategy A&B is to perform a logical AND on the identification results of the two channels. Only when both channels are identified as targets can it be determined to be a target. As long as the identification result of one of the two channels is interference, the measured signal is determined to be interference. If the fuze adopts anti-interference strategy A&B, its misidentification has the following situations: 1) Channel A and channel B both recognize errors, and the probability is 2) One of the channels A and B is misidentified. In this case, misidentification will occur only when the signal is the target, and the probability is Therefore, the effective recognition accuracy of the fuze adopting the anti-interference strategy A&B is Step 1.3: Based on the benefit matrix of the zero-sum game between the fuze and the jammer in step 1.1 and the correct rate of effective fuze identification in step 1.2, the benefit criterion of the pulse Doppler fuze is constructed, and the anti-jamming benefit matrix of the pulse Doppler fuze is constructed based on the benefit criterion; On the basis of the correct recognition rate of the fuze target and the interference, the difference between the correct recognition rate and the false recognition rate of the interference and the target after adopting the anti-interference strategy defines the benefit function of the fuze, that is: Where: is the target and interference recognition rate of the fuze using the i-th anti-interference strategy under the j-th interference; The benefit criterion for evaluating the anti-interference effectiveness of the fuze is obtained through formula (5), that is, the greater the benefit obtained by the fuze by taking a certain anti-interference measure, the stronger the anti-interference ability of the fuze after adopting the anti-interference strategy; the benefit criterion number can reflect the influence of different interference strategies on the anti-interference effect of the fuze, and meet the requirements of the fuze anti-interference effectiveness evaluation criterion; and the benefit criterion constructed by the benefit function of formula (5) and the effective correct recognition rate of formula (3) and formula (4) are combined to obtain the pulse Doppler fuze anti-interference benefit matrix, as shown in Table 2; Table 2 Pulse Doppler fuze anti-interference benefit matrix 3. The method for scheduling the PD fuze adaptive anti-interference strategy based on zero-sum game as claimed in claim 2 is characterized by: The implementation method of step 2 is: According to the anti-interference benefit matrix of the pulse Doppler fuze constructed in step 1 and the Nash equilibrium theorem, there is no Nash equilibrium in the game between the pulse Doppler fuze and the jammer. Under different jamming strategies, the pulse Doppler fuze cannot always choose a constant anti-interference strategy as its optimal strategy. According to the maximum and minimum theorem, the two parties in the game should maximize their expected benefits when choosing strategies. When the jammer's jamming strategy is σ2=(σ 21 ,σ 22 ,σ 23 ), σ 21 ,σ 22 ,σ 23 They represent the probability that the jammer takes jamming measures a, b, and a&b respectively. Then the anti-jamming benefits of different anti-jamming strategies for pulse Doppler fuze are: Since the fuze jammer does not know what anti-jamming strategy the fuze adopts, according to Nash's theorem, in order to ensure its jamming effect, the jammer should not adopt a single constant jamming strategy, but a mixed jamming strategy; therefore, the expected benefit of the fuze adopting each anti-jamming strategy is The anti-interference benefit matrix under measured data is introduced to complete the expected benefit of each anti-interference strategy in formula (7). The greater the benefit of the fuze taking a certain anti-interference measure, the stronger the anti-interference ability after the anti-interference strategy is. Then the corresponding best anti-interference strategy of the fuze is selected to realize the scheduling of the adaptive anti-interference strategy for maximizing the benefit of the pulse Doppler fuze.

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