Satellite navigation confrontation dynamic game performance evaluation method and system

Abstract

The invention relates to the field of satellite navigation effectiveness evaluation, in particular to a satellite navigation confrontation dynamic game effectiveness evaluation method and system, which combines attacker and defender strategies and different scheme combinations to construct a triple game situation that a protection system completely masters, partially obtains and completely knows interference information of a threat party during confrontation. Remodeling a dynamic game model suitable for satellite navigation confrontation; introducing a hybrid evolutionary algorithm to solve a profit equation of linear programming, and proposing an artificial intelligence algorithm based on data envelope, krill group and bootstrap method joint optimization to obtain a globally optimal solution, determine a consistent convergence profit result, complete an optimal decision, and prevent the equation solution from falling into local optimum; finally, dynamic games under different information confrontation situations are achieved through example analysis, the protection benefit of the own navigation system is expanded, and safe application of the navigation system is guaranteed. The method can improve the quantification precision of the game model, changes the previous static performance evaluation mode, and is more suitable for the satellite navigation confrontation dynamic game.

Description

Technical Field

[0001] The present invention relates to the field of satellite navigation effectiveness evaluation, and particularly to a method and system for evaluating the dynamic game effectiveness of satellite navigation countermeasure. Background Art

[0002] The Global Navigation Satellite System (GNSS) is an important space infrastructure, which is widely used in the core fields of the national economy and has increasingly become the basic resource for ensuring the real-time dynamic and safe operation of the modern social system. Due to the vulnerability and susceptibility of the system itself, various institutions are sparing no effort to promote the performance improvement and technology upgrade of the satellite navigation system, aiming to gain the advantage of information control. Therefore, satellite navigation countermeasure, which ensures the effective use of satellite navigation information by oneself while preventing the enemy from using such information, has become the focus of competition in the navigation field. The concept of satellite navigation countermeasure is the concentrated manifestation of electronic countermeasure operations in the navigation application field, with the core being protection and prevention. In recent years, GNSS interference has occurred frequently, and the research on GNSS anti-jamming has become a hot topic. Satellite navigation countermeasure has gradually shifted from the confrontation between damage and anti-damage to the offensive and defensive confrontation between interference and anti-jamming. To cope with the growing security threats and ensure the safe application of GNSS, relevant units have successively built navigation countermeasure equipment and various carrying platforms, hoping to promote the maturity of countermeasure technology and the upgrade of its equipment, as well as to realize the update of the internal system of GNSS and the maintenance of external facilities through the research on satellite navigation countermeasure evaluation, so as to evaluate the countermeasure effect, equipment performance, and algorithm advantages and disadvantages.

[0003] The existing evaluations are mainly classified into two categories: one is the performance evaluation of satellite navigation countermeasure, which conducts performance evaluation by determining the evaluation model and detection method to obtain quantitative results and complete performance optimization; the other is the effectiveness evaluation of satellite navigation countermeasure, which determines the weights of indicators and selects the optimal solution through operations research methods to obtain the optimal solution, gives countermeasures, and expands the protection benefits. Performance evaluation is the basis of effectiveness evaluation. However, since the framework of the satellite navigation countermeasure system has just taken shape, there are few evaluation studies on it, and it is still in the stage of sub-item performance evaluation research with single scenarios and single interference sources, lacking systematic and dynamic effectiveness evaluation research, and the existing effectiveness evaluation methods have insufficient adaptability for satellite navigation countermeasure effectiveness evaluation. Considering that satellite navigation countermeasure belongs to the dynamic game problem under incomplete information conditions, therefore, the present invention conducts research on the effectiveness evaluation method of satellite navigation countermeasure dynamic game to promote the paradigm change of the evaluation method from static parameter analysis to dynamic effectiveness evaluation. Summary of the Invention

[0004] To this end, the present invention provides a satellite navigation confrontation dynamic game effectiveness evaluation method and system, which solves the problem that the existing effectiveness evaluation is a static mode and the method has insufficient adaptability, which is specifically reflected in the problem that the game model is not applicable and the core elements such as the profit matrix are not interoperable. The effectiveness evaluation of the satellite navigation confrontation dynamic game is performed based on the effectiveness evaluation result of multi-attribute decision-making to maximize the protection benefit of one's own navigation system during confrontation, and can realize dynamic game in blind information, partial information and complete information satellite navigation confrontation situations.

[0005] According to the design scheme provided by the present invention, on the one hand, a method for evaluating the effectiveness of satellite navigation against dynamic game is provided, comprising:

[0006] Reshape the profit matrix of the dynamic game process and establish a dynamic game model of satellite navigation confrontation based on the evaluation index system for the dynamic game between interference and protection, wherein the evaluation index system for the dynamic game between interference and protection is pre-established based on the evaluation index of the satellite navigation counter-interference strategy and the implementation effect of the protection measures and their technical range, sub-item evaluation model and comprehensive evaluation method;

[0007] Quantify each matrix element in the profit matrix, and establish a profit equation for both parties based on the quantified profit matrix and in accordance with the minimum-maximum and maximum-minimum principles in game theory and the use of linear programming methods, so as to solve the profit equation by maximizing the benefit gained by one's own side in dynamic game to obtain the optimal solution of the game between the two participants. The profit equation is used in different information confrontation situations and obtains the optimal mixed strategy of one's own side and its effectiveness evaluation value;

[0008] Select the corresponding protection measure combination scheme of the optimal interference strategy, solve the profit equation in each protection measure combination scheme according to the hybrid evolutionary algorithm and the joint intelligent optimization BP neural network regression algorithm, and obtain the finite profit interval corresponding to the equation. The protection measure combination scheme includes: the optimal protection measure combination scheme, the worst protection measure combination scheme and the random protection measure combination scheme. The finite profit interval is used to describe the interval range of the protection profit in the confrontation game;

[0009] According to the limited profit interval, the optimal mixed vectors corresponding to the optimal mixed interference strategies of different schemes and the optimal mixed vectors corresponding to the optimal mixed protection strategies and their convergence processes are obtained. The optimal mixed attack and defense vectors are used to determine the protection profit results of the protection system against interference threats, so as to evaluate the dynamic game effectiveness of the combination of protection measures under different information confrontation situations based on the protection profit results.

[0010] On the other hand, based on the above method, an embodiment of the present invention further provides a satellite navigation countermeasure dynamic game effectiveness evaluation system, which includes a game model construction module, a profit equation establishment module, a combined scheme solution module, and a scheme effectiveness evaluation module, and each module corresponds to the method disclosed in the embodiment.

[0011] Advantages of the present invention:

[0012] The present invention combines the strategies of both the offensive and defensive sides and different scheme combinations to construct a triple game situation where the protection system fully masters, partially obtains, and completely unknown threat party interference information during confrontation, and reshapes a dynamic game model applicable to satellite navigation countermeasures; introduces a hybrid evolutionary algorithm to solve the profit equation of linear programming, and proposes an artificial intelligence algorithm jointly optimized based on data envelopment, krill swarm, and bootstrap method to obtain the global optimal solution, determine the consistently convergent profit result, complete the optimal decision, and avoid the equation solution falling into the local optimum; finally, through case analysis, realize the dynamic game under different information confrontation situations, expand the protection benefits of the own navigation system, and ensure its safe application. And it is verified by experimental data, indicating that the solution of this case can improve the quantization accuracy of the game model, change the previous static effectiveness evaluation mode, can obtain a higher distance curve and a larger error extreme value, and is applicable to the satellite navigation countermeasure dynamic game. Description of the drawings

[0013] Figure 1 It is the effectiveness evaluation index system based on the perspective of interference and anti-interference game in the embodiment;

[0014] Figure 2 It is the technical route for solving the profit equation by the hybrid evolutionary algorithm in the embodiment;

[0015] Figure 3 It is the pseudocode of the main program of the hybrid evolutionary algorithm in the embodiment;

[0016] Figure 4 It is the specific process and improved idea diagram of the optimized BP-NN regression algorithm in the embodiment;

[0017] Figure 5 It is the schematic diagram of the dynamic game in the blind information confrontation situation in the embodiment;

[0018] Figure 6 It is the convergence process of the partial information game situation 1 in the embodiment;

[0019] Figure 7 It is the schematic diagram of the dynamic game in the partial information confrontation situation 1 in the embodiment;

[0020] Figure 8 It is the convergence process of the partial information game situation 5 in the embodiment;

[0021] Figure 9Schematic diagram of the dynamic game in case 5 of the partial information confrontation in the embodiment;

[0022] Figure 10 Convergence process of the partial information game in case 6 of the embodiment;

[0023] Figure 11 Schematic diagram of the dynamic game in case 6 of the partial information confrontation in the embodiment;

[0024] Figure 12 Convergence process of the partial information game in case 7 of the embodiment;

[0025] Figure 13 Schematic diagram of the dynamic game in case 7 of the partial information confrontation in the embodiment;

[0026] Figure 14 Schematic diagram of the dynamic game in case 1 of the complete information confrontation in the embodiment;

[0027] Figure 15 Schematic diagram of the dynamic game in case 2 of the complete information confrontation in the embodiment;

[0028] Figure 16 Schematic diagram of the dynamic game in case 3 of the complete information confrontation in the embodiment;

[0029] Figure 17 Schematic diagram of the dynamic game in case 4 of the complete information confrontation in the embodiment;

[0030] Figure 18 For the LP-PG-IBP method based on W general , W objuctive , W subjective , and W modified , and the global optimal solutions of solution combination 1 obtained by solving the LP, LP-IBP, LP-PSO and other methods based on W modified respectively;

[0031] Figure 19 For the distance degree of the profit result of solution combination 1-4 in the embodiment relative to the minimum value E L of its profit interval;

[0032] Figure 20 For the change curve graph of the evaluation results of different methods in the embodiment relative to the reference value. Detailed implementation manners

[0033] To make the purpose, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and technical solutions.

[0034] In view of the problems that the existing game models are not applicable and the core elements are not interoperable due to insufficient research on the evaluation of satellite navigation countermeasure effectiveness, the embodiments of the present invention provide a method for evaluating the dynamic game effectiveness of satellite navigation countermeasures, including:

[0035] S101. Reshape the payoff matrix of the dynamic game process according to the evaluation index system for the dynamic game between interference and protection, and establish a dynamic game model for satellite navigation countermeasures. The evaluation index system for the dynamic game between interference and protection is pre-established based on the evaluation indexes and their technical intervals, sub-evaluation models and comprehensive evaluation methods for the implementation effects of satellite navigation countermeasure interference strategies and protection measures.

[0036] Compared with the user side of GNSS, considering that the satellite navigation system side has poor dynamic performance and strong stability, as a participant in the dynamic game of satellite navigation countermeasures, the technology for the system side to counter interference threats should also be included in the protection measures. However, in the existing research, when setting protection measures, most of them focus on the anti-interference technology of the user terminal, and a few focus on the anti-interference of the system side, but none of them systematically regard the ground control part's countermeasure against interference threats and the space satellite constellation's countermeasure against threats as two complete protection measures, resulting in complex and changeable game situations, difficult quantification of game elements, and difficult solution of the payoff equation, and it is easy to obtain invalid effectiveness evaluation results. Therefore, it is necessary to comprehensively improve the existing game model to establish a dynamic game model applicable to satellite navigation countermeasures, which can be specifically designed to include the following content:

[0037] First, determine various indexes and their evaluation methods for evaluating the implementation effects of interference strategies / protection measures in satellite navigation countermeasures, establish an evaluation index system based on the dynamic game between GNSS interference and anti-interference, complete the design of the core elements of the satellite navigation countermeasure game, and reconstruct the dynamic game model of satellite navigation countermeasures;

[0038] The basic elements of the game model: participants, their pure strategy spaces, and the corresponding payoff matrix; among them, the payoff matrix is the core element of the game model, and the game model is mainly improved by reconstructing the payoff matrix to establish a dynamic game model applicable to satellite navigation countermeasures.

[0039] Participants in the game model: The threat system includes soft damage, that is, single GNSS interference source and multi-GNSS interference source collaborative interference technology and its related equipment, and the protection system includes the corresponding anti-interference technology of GNSS and its various components, etc.; these two types of systems constitute the participants in the game, namely At p and Df q .

[0040] The pure strategy space of the game model: The interference strategies included in the threat system and the protection measures adopted by the protection system respectively constitute their corresponding pure strategy spaces, which are S At= [At1, At2, …, At p and S Df = [Df1, Df2, …, Df q )。

[0041] The core element of the game model - the profit matrix: Although the goals and evaluation criteria of the participants are opposite, they share the same metric, that is, the profit matrix, as shown in Equation (1).

[0042]

[0043] As can be seen from the equation, the profit matrix is the objective function derived from the profit equation. To achieve optimal decision-making, it is not only necessary to reconstruct the profit matrix to make it applicable to satellite navigation countermeasure, but also to quantify the profit matrix.

[0044] To address the limitations of existing game methods in establishing the core element of the game (profit matrix) applicable to satellite navigation countermeasure, considering that satellite navigation countermeasure belongs to an incomplete information dynamic game, the party that obtains the information dominance can gain the initiative in the countermeasure; therefore, before the countermeasure, the protection system must first master various interference strategies that the threat system may adopt, and vice versa. In summary, in the embodiments of this case, first, determine various indicators for evaluating the implementation effects of interference strategies / protection measures and their evaluation methods, improve the existing game methods to make them applicable to satellite navigation countermeasure, and complete the design of the core elements of this type of game.

[0045] By comparing the feasibility and success rate of various interference technologies and anti-interference technologies, select 6 interference strategies At1 - At6 and 6 protection measures Df1 - Df6 with higher feasibility and success rate. Based on the established evaluation index system for the game between interference strategies and protection measures, as Figure 1 shown, relying on the developed evaluation experimental platform, using 3 testing methods (full digital simulation method, semi-physical simulation method, and field testing method), give the definitions, evaluation models, and their detection methods of various evaluation indicators for At1 - At6 and Df1 - Df6, which are used to construct the core elements of the game applicable to satellite navigation countermeasure. Using the combination weighting method, obtain the first-level and second-level evaluation results of At1 - At6 and Df1 - Df6 respectively, which are used as the elements in the matrix to construct the profit matrix, which is the key basis for quantifying the game elements and can also evaluate the implementation effects of interference strategies and protection measures.

[0046] According to the satellite navigation countermeasure performance evaluation index system, to address the limitations of existing game methods in establishing the core element of the game (profit matrix) applicable to satellite navigation countermeasure, it is also necessary to establish an evaluation index system for the game between interference and anti-interference.

[0047] Specifically, first, combine Figure 1As shown in the GNSS interference performance evaluation index system diagram in (a), it is determined that the evaluation indexes of At1 are D1 - D10, the evaluation indexes of At3 are D11 - D29, the evaluation indexes of At2 are D30 - D49, the evaluation indexes of At4 are D11 - D30 (the same as At3), the evaluation indexes of At5 are D11 - D30 (the same as At3), and the evaluation indexes of At6 are D50 - D59. Subsequently, combined with Figure 1 the GNSS user - side and system - side anti - interference performance evaluation index system diagrams in (b - c), the evaluation indexes corresponding to Df4, Df2, Df3, and Df1 are D1 - D9 and D15 - D21, D1 - D9 and D15 - D21, D6 - D21, D6 - D9 and D15 - D27 in sequence, the evaluation index of Df6 is D1 - D15, and the evaluation index of Df5 is D12 - D24. On this basis, the effectiveness evaluation index system from the perspective of interference - anti - interference game can be as Figure 1 shown in (d).

[0048] The dynamic game of the protection system against the threat system can be simplified into the dynamic games of the GNSS with complete knowledge, partial knowledge, and complete ignorance of the interference strategy. In these cases, from Figure 1 it can be seen that Df1, Df2, and Df3 can all cope with the interference threats of the strategies from At1 to At6, while Df4 mainly copes with the interference threats of At2, At3, and At5, Df5 mainly copes with the interference threats of At1 and At4, and Df6 mainly copes with the interference threats of At2, At4, and At5; among them, the evaluation indexes included in the interference strategy and protection measures are represented by numbers. Therefore, the core element of the reconstructed complete and applicable dynamic game model for satellite navigation countermeasure, that is, the pay - off matrix, can be as shown in Equation (2):

[0049]

[0050] In the formula, E is the pay - off matrix of the satellite navigation countermeasure dynamic game model.

[0051] S102. Quantify each matrix element in the pay - off matrix. Based on the quantified pay - off matrix and according to the min - max and max - min principles in game theory and using the linear programming method, establish the pay - off equations for both sides of the confrontation, and solve the pay - off equations by maximizing the benefit during the dynamic game of one's own side to obtain the optimal solution of the game between the two participants. The pay - off equations are used for different information confrontation situations and to obtain the optimal mixed strategy and its effectiveness evaluation value of one's own side.

[0052] (1) Considering that the technical requirements of the indicators in the profit matrix are in the form of intervals, in the embodiments of this case, the existing weighted average type FCA comprehensive evaluation method can be improved by using interval theory first to complete the quantification of the measurable performance in the profit matrix; then, a grey expert system method is proposed to complete the quantification of the unmeasurable performance in the profit matrix by using this method, improve the quantification accuracy of the unmeasurable performance in the profit matrix, and complete the quantification of the game model.

[0053] Use the expert system to determine the horizontal score and vertical score of each interference strategy and protection measure in the blind information game situation respectively. Among them, Table 1 lists the scoring rules of 10 experts.

[0054] Table 1 Standard interval numbers of scoring rules

[0055]

[0056] Among the 10 experts in Table 1, 4 can be set to be in the field of navigation and positioning, marked in red in Table 2, 3 can be set to be in the field of satellite communication, marked in blue in Table 2, and 3 can be set to be in the field of systems engineering, marked in yellow in Table 2. Using the peer evaluation method, the normalized confidence weight w of the scoring results given by each expert can be determined in terms of the peer's professional ability, familiarity with the research field, confidence level of the scoring results, etc. c (g), and the results are shown in Table 2.

[0057] Table 2 Confidence weight assignment of scoring results

[0058]

[0059] First, create the attack ability estimate J qp (g) of the g-th expert against the p-th strategy when facing the q-th measure for anti-interference and its corresponding preset reference value J qp 0 (g), and the corresponding models are shown in Formulas (3) and (4); similarly, the protection ability estimate J pq (g) of the g-th expert against the q-th measure when facing the attack of the p-th strategy and its corresponding preset reference value J pq 0 (g) can be determined:

[0060]

[0061] Among them, g is set to 1, 2,..., 10; p and q respectively represent an interference strategy and a protection measure; b qp and b pq are respectively the score results of the p-th interference strategy when facing the protection of the q-th measure and the score of the q-th protection measure when facing the threat of the p-th strategy.

[0062] Subsequently, the scoring matrices established by 10 experts J(1), …, J(g), …, J(10) and their reference sequences [J 0 (1), …, J 0 (g)] are normalized and initialized to obtain the absolute degree and relative degree of grey correlation. The models are as shown in Equations (5) and (6):

[0063] l qp 0 (g) = J qp 0 (g) - J 11 0 (g), l qp (g) = J qp (g) - J 11 (g) (5)

[0064] l qp 0 (g)' = J qp 0 (g) / [J 11 0 (g) + λ], l qp (g)' = J qp (g) / [J 11 (g) + λ]

[0065] Based on this, a normalized image matrix, L 0 (g) and L(g), and an initial image matrix, L 0 (g)' and L(g)', can be established. The model is as shown in Equation (7):

[0066]

[0067] Where l qp (g) and l qp 0 (g), l qp (g)' and l qp 0 (g)' are the normalization points of J qp (g) and J qp 0 (g) and the initialization points of the two; λ is a very small constant that makes the denominator non - zero.

[0068] Next, based on the obtained L 0 (g) and L(g), the grey - correlation absolute quantity corresponding to the g - th expert, |s 0 (g)|, |s(g)|, and |s(g) - s 0 (g)|, can be further determined. The corresponding model is as shown in Equation (8):

[0069]

[0070] Finally, based on the absolute and relative grey relational quantities obtained above, the absolute degree and relative degree of grey relation, ε(g) and γ(g), can be modeled as in Equation (9).

[0071]

[0072] Furthermore, the grey comprehensive value ρ(g) of the g-th expert can be determined by the evaluation model given in Equation (10):

[0073] ρ(g) = θε(g) + (1 - θ)γ(g) (10)

[0074] where θ ∈ [0, 1] and it has a greater impact on ρ(g); therefore, the value of θ in the evaluation model is taken as 0.5, indicating that the absolute quantity and relative quantity contribute equally to the grey comprehensive value of the g-th expert.

[0075] (2) By using the linear programming method, based on the quantified profit matrix and following the min-max principle and max-min principle of game theory, a profit equation was established.

[0076] When the protection system is in a blind information game situation where it cannot grasp any attack measures taken by the threat system and can only rely on relevant theoretical knowledge of game theory for decision-making, at this time, if each element in its corresponding profit matrix can satisfy the equality equation in the following formula, based on the profit matrix (see Equation (2)) and using the min-max principle and max-min principle of game theory, as in Equation (11), a profit equation can be established for the protection system, and this equation can obtain the optimal pure strategy and effectiveness evaluation value of the system under blind information conditions;

[0077]

[0078] However, the equality equation in Equation (11) is an ideal condition; in fact, most elements of the quantified profit matrix can only satisfy the inequality equation in Equation (12).

[0079] X * = (x1 * , …, x p * …, x6 * ), Y * = (y1 * , …, y q * , …, y6 * ) (12)

[0080] Therefore, in actual satellite navigation countermeasures, it is almost impossible for the protection system to obtain the optimal pure strategy, but it can always obtain the optimal mixed anti-jamming strategy, which is called the optimal solution. At the same time, according to this mixed strategy, within the scope of the rules of zero-sum game, the selected optimal solution can ensure that the profit of the threat system is not less than E(X*, Y*), and the loss of the protection system is not higher than E(X*, Y*), so that the game can reach an equilibrium.

[0081] To obtain the optimal mixed strategy, a profit equation can be constructed based on the quantified profit matrix. Relevant methods include the mathematical programming algorithm (MP) and the iterative-Brown algorithm, etc. The mathematical programming algorithm is more convenient and faster than the iterative method. Therefore, in the embodiments of this case, this method can be selected to construct the following profit equation:

[0082] ① For the threat system, X* satisfies: j = 1, 2,..., q and x i * ≥0. Let v*>0, and let x i / v* = x i *. The profit of the threat system implementing interference is not less than v*, which can be expressed in the form of linear programming as:

[0083]

[0084] Solve the linear programming function given by formula (13) to obtain the optimal solution x i of the threat system and its optimal mixed interference strategy x i * = x i / v*.

[0085] ② For the protection system, Y* satisfies: i = 1, 2,..., p and y j * ≥0. Let ω*>0, and let y j / ω* = y j *. The loss of the protection system suffering damage is at most not more than ω*, which can be expressed in the form of linear programming as:

[0086]

[0087] Solve the linear programming function given by formula (14) to obtain the optimal solution y j of the protection system and its optimal mixed measure y j * = y j / ω*.

[0088] (3) To solve the profit equation, considering that GA and PSO are more suitable for solving the profit equation and they are complementary, a hybrid evolutionary algorithm PSO-GA with short convergence time and easier to achieve global optimality is proposed to solve the profit equation to obtain the global optimal solution.

[0089] The main idea of the hybrid evolutionary algorithm (PSO-GA, abbreviated as GP) jointly improved based on the particle swarm optimization algorithm PSO and the genetic algorithm GA is as follows Figure 2 shown, which is listed in the following three points in sequence:

[0090] Step 1: Utilize the fast convergence of PSO, and according to the models given by Equations (15) and (16), track the individual optimal p best M and the group optimal g best M to update the speed and position of the individual, so that the initial population can achieve a certain degree of evolution in the previous stage;

[0091]

[0092] where b and d respectively represent the dimension of the search space and the population size; r n1 and r n2 are random numbers in [0, 1]; W0 represents the constant inertia weight; C1 and C2 respectively represent the self-learning ability and the learning ability of other individuals; M represents the generation number of the existing population; x bd M and v bd M respectively represent the current position and its speed of the individual.

[0093] Step 2: Use the genetic algorithm to encode the problem parameters into chromosomes, and then continue to perform selection operations, crossover operations, and mutation operations iteratively according to the models given by Equations (17) and (18) to exchange the information of the chromosomes in the population and optimize the evolved population so that it will not fall into local optimality in the later stage;

[0094] Step 3: Stop after meeting the conditions of fast convergence speed and strong global search ability, and there will be corresponding results output that meet the conditions, which can be used as a sign of the completion of the solution of the profit equation.

[0095]

[0096] z mj = z ij (1 - s) + z nj s, z nj = z ij (1 - s) + z mj s. (18)

[0097] where, z ij is the mutation operation mode of the i-th individual for the j-th gene; z max and z min are the upper and lower bounds of z ij respectively; u is the number of iterations; s represents survival of the fittest, i.e., an optimal solution; U max is the maximum number of generations of evolution, i.e., the maximum number of iterations; z mj and z nj are the crossover operation modes of the m-th chromosome and the n-th chromosome of the j-th gene respectively.

[0098] According to the method flow and improvement idea of PSO-GA, the pseudo-code of the main program of the hybrid evolutionary algorithm GP adopted by the present invention running on Matlab R2017b is further sorted out as shown. According to the relationship between the biological inheritance concept and the concept of parameters included in the hybrid evolutionary algorithm, as shown in Table 3, after multiple experiments, the parameter design table of the hybrid evolutionary algorithm is formulated, as shown in Table 4, and its rationality has a great influence on the function of the hybrid evolutionary algorithm.

[0099] Table 3 Corresponding relationship between biological genetics concepts and evolutionary algorithm concepts

[0100]

[0101] Table 4 Detailed parameter design table of the hybrid evolutionary algorithm

[0102]

[0103] (4) Considering that the convergence results obtained by each run of the hybrid evolutionary algorithm are different, an improved BP-NN regression algorithm based on DEA-KHA-Bootstrap is introduced to reduce the randomness of the generated model parameters in the optimization problem, weaken the adverse effects brought by the unstable convergence results on the credibility of the performance evaluation results, etc., make up for the three deficiencies of BP-NN regression, and achieve optimal decision-making.

[0104] Considering that the convergence results obtained by the hybrid evolutionary algorithm are different each time it runs, the present invention combines intelligent algorithms such as data envelopment analysis (DEA), krill herd algorithm (KHA), and classical bootstrap method (FB) to jointly improve the commonly used BP-NN regression algorithm, and proposes a BP-NN optimization algorithm to train the optimal solution to determine the profit result. However, there are three deficiencies in the existing BP neural network. First, the present invention combines the heuristic algorithm KHA with excellent performance in the global optimal algorithm to optimize and fix the thresholds, weights, and other optimization parameters of the existing BP-NN regression model, and establishes a new regression model as the basic model of the BP-NN regression algorithm to solve the second deficiency that its model parameters are prone to fall into local optimum. Subsequently, in view of the fact that DEA adopts the idea of optimal linear programming and has strong objectivity, and combined with the simple and effective FB, it can complete the pre-training and sample expansion of the new regression model, and solve the other two deficiencies of the BP-NN regression, namely, it cannot be explicitly expressed, cannot be directly used, and has small sample problems. According to the importance of overcoming the three deficiencies of the BP-NN regression algorithm, as Figure 4 shown.

[0105] ① The krill herd algorithm (KHA) is a new type of intelligent optimization algorithm that simulates the foraging activities of krill herds in the Antarctic Ocean. Since the krill individuals in the krill herd move towards food under the combined influence of food and nearby krill during foraging activities, the position change of each krill individual i krill is mainly affected by three factors, as shown in Equation (19), namely, the movement caused by other krill individuals (the involved index is the induced velocity N ikrill ), the foraging action (the index is the foraging velocity F ikrill ), and the random diffusion (the index is the diffusion velocity D ikrill ).

[0106]

[0107] KHA can improve the second deficiency of the BP-NN regression algorithm, that is, the model parameters are prone to fall into local optimum. The key definitions are as follows:

[0108] Three behaviors that affect the position change of krill individuals. Taking a krill individual as an example, the first factor is the latest position change N ikrill,old generated by the relative position N ikrill,new of this krill individual caused by other krill individuals in the previous unit time, as shown in Equation (20); the second factor is the position change F ikrill,new generated by the latest foraging of the krill individual, as shown in Equation (21);

[0109]

[0110] The third factor is that the krill swarm gradually approaches the optimal position over time. Therefore, as the number of iterations increases, the random diffusion part of the krill swarm decreases linearly. Accordingly, let the current iteration number and the maximum iteration number be \(I\) current and \(I\) max , then Equation (23) can be improved according to Equation (22) to obtain a mathematical model that satisfies the gradual disappearance of the random diffusion behavior of the krill swarm:

[0111]

[0112] Assume that after the above three behaviors are completed by the krill swarm in the time period \([t, t + \Delta t]\), the updated position of the krill individual can be obtained as Equation (24):

[0113]

[0114] In the formula, \(N\) max is the maximum induced velocity; \(\alpha\) ikrill,local , \(\alpha\) ikrill,target is the direction vector provided by the neighboring individuals' induction and the optimal individuals; \(F\) f is the foraging velocity; \(\beta\) ikrill,food , \(\beta\) ikrill,best is the vector of the attraction of the food source to the individual and the optimal target vector of the \(i\) krill -th individual; \(X\) ikrill (t + \Delta t), X ikrill (t) are the positions of the individual at times \((t + \Delta t)\) and \(t\); \(U\) j , \(L\) j are the upper and lower limits of \(j\); \(w\) n , \(w\) f are the weights of \(N\) ikrill,old and \(F\) ikrill,new respectively.

[0115] Genetic operations based on the above three behaviors. According to the principle of the genetic algorithm, the genetic operations of KHA are divided into crossover and mutation operations.

[0116] Among them, the crossover operation is defined as an operation to generate a new krill individual through replacement and recombination as Equation (25):

[0117]

[0118] In the formula, \(x\) ikrill,mkrill is the \(m\) ikrill -th parameter of \(x\) krill ; \(x\) rkrill,mkrill is the \(m\) ikrill,mkrill -th parameter of an individual \(x\) rkrill different from \(x\) krill ; \(r\) krill \(\in [1, 2, \ldots, N\) p and \(r\)krill ≠i krill ; rand is a uniformly distributed random number in the range of [0, 1]; C r is the crossover probability. Based on the crossover operation, the mutation operation is defined as an operation to make changes and adjustments to the newly generated krill individuals, as shown in Equation (26):

[0119]

[0120] In the formula, x gbest,mkrill is the m gbest -th parameter of the current global optimal individual x krill ; x pkrill≠ikrill,mkrill and x qkrill≠ikrill,mkrill are the m pkrill -th parameters of individuals x qkrill and x krill , and both p krill and q krill belong to [1, …, i krill -1, i krill +1, i krill +2, …, N p ; M u is the mutation probability.

[0121] ②Data Envelopment Analysis (DEA) is a method based on the concept of relative efficiency, which evaluates the relative effectiveness or efficiency of the same type of targets according to multiple input indicators and multiple output indicators. There are two types of DEA models. One is the DEA-CCR model, which is used to analyze the situation where the profit value remains unchanged and is mainly used to measure technical efficiency. The other is the DEA-BCC model, which is used to analyze the situation where the profit value is variable and is mainly used to measure the ratio of technical efficiency to scale efficiency. In the embodiments of this case, the DEA-CCR model can be selected, and its result is used as the expected output of the regression model.

[0122] According to the index attributes, for a certain interference strategy / anti-interference measure, define the input parameter X' as an evaluation index whose corresponding performance evaluation result is inversely proportional to the comprehensive ability evaluation result, and define the output parameter Y' as an evaluation index whose corresponding evaluation result is directly proportional. Let the weight vectors of the input and output parameters be W X' , W Y' . By solving the following equations, as shown in Equation (27), the optimal weight vectors W i , W X' best , W Y' best of the i-th decision-making unit DMU

[0123]

[0124] Subsequently, the cross-efficiency $E$ of the $i$-th decision-making unit (DMU) relative to the $j$-th decision-making unit (DMU) can be obtained by using Equation (28). i relative to the $j$-th decision-making unit (DMU) j is $E$ ij .

[0125]

[0126] Finally, the evaluation ranking can be carried out according to the cross-efficiency $E$ of each decision-making unit. However, it is not excluded that there may be a situation where the indicators are equal and cannot be evaluated. At this time, the cross-efficiency only represents the relative efficiency of multiple evaluation samples. ij To improve its deficiencies, the minimum cross-efficiency $E$, the average cross-efficiency, and the maximum cross-efficiency $E$ are used to determine the cross-efficiency for evaluating the GNSS protection effectiveness against satellite navigation countermeasures, and the data envelopment analysis is completed as shown in Equation (29):

[0127] i min and the maximum cross-efficiency $E$ i max n In summary, by introducing the improved DEA, the average cross-efficiency of all interference strategies / anti-interference measures is used as the expected output of the regression model, fully mining the internal relationship between data, completing the model training and parameter determination of the KHA-BP-NN algorithm; then, by using simulation and test data, the number of iterations and the amount of operations are reduced, and the deficiencies of the existing BP-NN regression algorithm are improved.

[0128]

[0129]

[0130]

[0131] ③ The classical bootstrap method FB is a type of non-parametric Monte Carlo method. Its essence is to resample the observed information and then make statistical inferences about the distribution characteristics of the population. First, through resampling, the problem of sample reduction caused by cross-validation can be avoided. Second, FB can also be used to create data randomness. According to the basic model of the BP neural network, after completing the preprocessing of the training samples and the initialization of the model, for each group of training samples, the input parameter vector ($X1', X2', \ldots, X$ n ') is determined according to the performance ranking, and the empirical distribution $X1' \sim F$ n (x') is constructed, and the corresponding expression is as shown in Equation (30):

[0131]

[0132] Using the FB method, non-parametric sampling is used to sample from $F$ nRandomly extract 100 groups of samples from (x'), which is the maximum likelihood estimation of the sample data. Based on this, after completing the training sample augmentation through the classical bootstrap method, the BP-NN is used to train the samples; the test samples are evaluated through the trained model to solve the third deficiency of the existing BP-NN regression algorithm.

[0133] In the embodiments of this case, taking the protection system and the threat system participating in the dynamic game of satellite navigation countermeasure as the research objects, the KHA-BP neural network regression model as the basic model, on this basis, the data envelopment analysis DEA is respectively introduced as the expected output of the regression model, and then the classical bootstrap method FB is used to expand the training samples and complete the model training to complete the BP-NN optimization. The specific steps can be summarized as follows:

[0134] Step 1: Use the newff function in Matlab to construct a BP neural network model, set the number of neurons in the hidden layer, and use KHA to optimize the parameters of the BP neural network model such as the learning efficiency, the number of training times, and the error upper limit.

[0135] Step 2: According to the polarization attribute of the evaluation index, divide the ability-type indicators in the performance evaluation index system into the input and output of DEA; use the linprog function in Matlab to solve the system of equations (27) to obtain the optimized weight vectors of each decision-making unit.

[0136] Step 3: For the confrontation game situation faced by the decision maker, use the optimized weight vector and formula (28), and calculate the E of the current 5 interference strategies / 5 anti-interference measures according to formula (29). i min , and E i max , which is used to determine the expected output as the regression model.

[0137] Step 4: Divide the test data and the simulation theoretical values of the performance indicators into training samples and samples to be tested according to the ratio of 3:7, determine the number of neurons in each layer. Among them, the input layer has 7 - 14 neurons, the output layer has 1, and the hidden layer has 8; use the mapminmax function in Matlab to preprocess the training and test samples to the interval [0, 1], and initialize the connection weight and threshold matrix as random numbers in [-1, 1].

[0138] Step 5: According to formula (30), use the Randint function in Matlab to perform Bootstrap resampling on the training samples, randomly extract 100 groups of training samples, construct new training samples, and complete the training of the BP-NN regression model based on KHA.

[0139] Step 6: Set the initial parameters of KHA according to formula (19), including determining Imax , N max , F f and D max etc.; and initialize a group of populations within the search space, where each krill individual represents a feasible solution to the optimization problem.

[0140] Step 7: Input the training samples to train the neural network and use the test samples for prediction to obtain the expected output Y expect =(y iexpect ) 1×n and the predicted output Y forecast =(y iforecast ) 1×n . Then calculate the individual fitness F according to Equation (31) individaul .

[0141] F individaul =||y iexpect -y iforecast || (31)

[0142] Calculate the change in krill position caused by 3 influencing factors according to Equations (20 - 24). After adding the genetic operation, recalculate the position of the krill individual according to Equations (25) and (26). Return to Equation (31) to calculate the individual fitness until the termination condition is met.

[0143] Step 8: Assign the obtained individual positions (connection weights and thresholds) to the improved regression model; for the training samples, calculate the output errors of each layer of neurons according to the sample input, expected output, connection weights and thresholds, and adjust the individual positions to reach the optimal position.

[0144] Step 9: When the output error of the output layer neurons meets the requirements, the model training is completed, and return to Step 7 again.

[0145] S103. Select the optimal interference strategy to form the corresponding protection measure combination plan, solve the profit equation in each protection measure combination plan according to the hybrid evolutionary algorithm and the combined intelligent BP neural network regression algorithm, and obtain the corresponding finite profit interval of the equation. The protection measure combination plan includes: the optimal protection measure combination plan, the worst protection measure combination plan and the random protection measure combination plan. The finite profit interval is used to describe the interval range where the protection profit is located during the confrontation game.

[0146] To achieve optimal decision-making and dynamic game, it is assumed that the known combination of solutions for the threat system is its optimal combination of solutions, such as Solution 2, Solution IV, Solution IV, Solution 6, Solution 6, Solution IV. The combination of solutions 1 - 4 for the protection system can be selected, which are respectively the optimal combination of solutions, the worst combination of solutions, the random combination of solutions 1, and the random combination of solutions 2 for the protection system to counter the threat system. As an example, the specific scenario settings of the example are shown in Table 5. Conduct the effectiveness evaluation of the satellite navigation countermeasure dynamic game to obtain the optimal decision result, and then realize the dynamic game under different information countermeasure situations.

[0147] Table 5 Specific parameter settings of countermeasure solutions

[0148]

[0149] (1) Realize the quantification of the profit matrix for various evaluation indicators and different countermeasure solutions. Around the comprehensive evaluation method of weighted average type FCA, considering that the technical requirements of the indicators in the profit matrix in Equation (2) are in interval form, first, use interval theory to improve the existing comprehensive evaluation method, propose a quantification method for interval-improved fuzzy comprehensive evaluation (FCA), complete the quantification of the measurable performance in the profit matrix, and then use the grey expert system to improve the quantification accuracy of the non-measurable performance in the profit matrix. Therefore, obtain the interval quantification matrix [E L , E U as shown in Equations (32) and (33).

[0150]

[0151] On this basis, in order to reasonably integrate the interval matrix, the comprehensive evaluation matrix for the optimal combination of solutions for both sides of the confrontation, and the comprehensive evaluation matrices F At 最优方案 , F At 最差方案 , F At 随机组合1 , F At 随机组合2 , etc. for the worst solution and other random solution combinations can be determined first. As shown in Equation (34):

[0152]

[0153] Then, using the determined comprehensive evaluation matrix as shown in Equation (34), combined with the ability scoring matrix J(4) selected by the grey expert system method given in Equation (35), where, since the normalized grey comprehensive value ρ(4)′ of J(4) is the largest, J(4) should be selected;

[0154] [ρ(1)′,ρ(2)′,ρ(3)′,ρ(4)′,ρ(5)′,ρ(6)′,ρ(7)′,ρ(8)′,ρ(9)′,ρ(10)′]

[0155] =[0.136, 0.073, 0.127, 0.147, 0.107, 0.141, 0.083, 0.015, 0.110, 0.060]

[0156]

[0157] Finally, through the multiplication and addition operations of the final-level weight set (w 1 ), the quantification of the profit matrix for different combination schemes of the two adversarial parties can be realized, and the percentage results obtained are as shown in Eqs. (36) to (39):

[0158]

[0159]

[0160] To sum up, the profit matrix realizes the quantification of the profit matrix for different combination schemes of the offensive and defensive parties, and obtains the quantification matrices E 最优方案 、E 最差方案 、E 随机组合1 、E 随机组合2 .

[0161] (2) Establish a profit equation based on the quantified profit matrix. According to the min-max principle and max-min principle in game theory, using the linear programming method, the profit matrices E L =(e qp L ) 6×6 and E U =(e qp U ) 6×6 obtained from Eqs. (32) and (33) are converted into two mutually dual linear programming problems, and the profit equations of the two adversarial parties can be established, as shown in Eq. (40).

[0162]

[0163] In the formula, v* and ω* are the profit expected values of the two adversarial parties. When the above equations are solved, during the confrontation process, the threat system can grasp its most unfavorable result under the optimal conditions, while the protection system can obtain its best result under the worst conditions.

[0164] (3) Determine the finite profit interval of the solution of the profit equation. Use the PSO-GA hybrid evolutionary algorithm to solve the profit equations of both sides of the confrontation, and then determine the finite profit interval of the equation solution through the improved BP-NN algorithm based on DEA-KHA-Bootstrap. In the case of confrontation, the anti-interference protection profit implemented by the protection system should fall within this interval.

[0165] Specifically, the program of the hybrid evolutionary algorithm can be run 100 times. Use the PSO-GA hybrid evolutionary algorithm to solve the profit equations of both sides of the confrontation in formula (40), and then determine the profit results through the improved BP-NN algorithm based on DEA-KHA-Bootstrap. The optimal hybrid vector X corresponding to the optimal hybrid interference strategy can be obtained and normalized * (E L ) and X * (E U ), and the optimal hybrid vector Y corresponding to the optimal hybrid anti-interference measure * (E L ) and Y * (E U ) are respectively as shown in formula (41).

[0166]

[0167] Using the optimal hybrid vectors obtained from formula (41), during satellite navigation confrontation, the protection profit result E of the GNSS against interference threats can be further obtained result =[E L result ,E U result and its result matrix E L result and E U result , as shown in formula (42):

[0168]

[0169] In the case of confrontation, the protection profit implemented by the protection system should fall within this interval. If E result ∈[1.3637, 29.9722], then as E increases, the protection profit of the protection system is greater, and then the anti-interference ability of GNSS will be stronger. If E result > 29.9722, then compared with the threat system with weaker interference ability, at this time, the anti-interference ability of the protection system is very strong, resulting in the threat system being unable to implement continuous interference. If E result<1.3637, the threat system has a strong interference capability due to high-power interference signals and other reasons. Therefore, the anti-interference capability of the protection system is very weak at this time; but the attack is easily detected by the protection system, and the threat system cannot continue to interfere at this time. In summary, when the threat system performs the interference task, its interference capability is too small, which will cause the task to fail. It will also fail because its interference capability is too large and is detected by the protection system, which will cause the task to fail.

[0170] S104. Obtain the optimal mixed vectors corresponding to the optimal mixed interference strategies of different schemes and the optimal mixed vectors corresponding to the optimal mixed protection strategies and their convergence processes based on the limited profit interval, and use the optimal mixed attack and defense vectors to determine the protection profit results of the protection system against interference threats, so as to evaluate the dynamic game effectiveness of the combination of protection measures under different information confrontation situations based on the protection profit results.

[0171] Specifically, the optimal hybrid vector X corresponding to the optimal hybrid interference strategy facing different scheme combinations can be obtained and normalized by running the hybrid evolutionary algorithm PSO-GA program 100 times, using PSO-GA to solve the profit equation of the adversaries in equation (40), and then determining the profit result by using the BP-NN regression algorithm improved based on DEA-KHA-Bootstrap. * (E 最优方案 ),X * (E 最差方案 ),X * (E 随机组合1 ) and X * (E 随机组合2 ), and the optimal hybrid anti-interference measures corresponding to the optimal hybrid vector Y for different scheme combinations * (E 最优方案 ), Y * (E 最差方案 ), Y * (E 随机组合1 ) and Y * (E 随机组合2 ) are shown in formula (43) respectively.

[0172]

[0173] Based on the optimal mixed vector obtained by formula (43), in the case of satellite navigation confrontation, the anti-interference profit result E facing the interference threat can be further obtained: 最优方案 result 、E 最差方案 result 、E 随机组合1 result and E 随机组合2 result , and its resulting matrix E 最优方案 result 、E最差方案 result , E 随机组合1 result and E 随机组合2 result , as shown in Equation (44).

[0174]

[0175] As can be seen from the above formula, in the confrontation situation, the anti-interference protection profit of the protection system is not less than 4.5174, and the obtained result will be used to realize the dynamic game of blind information confrontation for different scheme combinations.

[0176] Furthermore, based on the above method, an embodiment of the present invention further provides a satellite navigation confrontation dynamic game effectiveness evaluation system, including: a game model construction module, a profit equation establishment module, a combined scheme solution module, and a scheme effectiveness evaluation module, where,

[0177] The game model construction module is used to reshape the profit matrix of the dynamic game process according to the evaluation index system for the dynamic game between interference and protection and establish a dynamic game model for satellite navigation confrontation. The evaluation index system for the dynamic game between interference and protection is pre-established according to the evaluation indexes of satellite navigation confrontation interference strategies and the implementation effects of protection measures, their technical intervals, sub-item evaluation models, and comprehensive evaluation methods;

[0178] The profit equation establishment module is used to quantify each element in the profit matrix, and based on the quantified profit matrix, according to the min-max and max-min principles in game theory and using the linear programming method, establish the profit equations of both sides of the confrontation, so as to solve the profit equations by maximizing the benefits obtained during the dynamic game of one's own side to obtain the optimal solutions of the game between the two participants. The profit equations are used for different information confrontation situations and are used to obtain the optimal mixed strategies of one's own side and the effectiveness evaluation values of the mixed strategies;

[0179] The combined scheme solution module is used to select the optimal interference strategy to form the corresponding protection measure combination scheme, solve the profit equations in each protection measure combination scheme according to the hybrid evolutionary algorithm and the combined intelligent optimization BP neural network regression algorithm, and obtain the finite profit interval corresponding to the equation. The protection measure combination scheme includes: the optimal protection measure combination scheme, the worst protection measure combination scheme, and the random protection measure combination scheme. The finite profit interval is used to describe the interval range where the protection profit is located during the confrontation game;

[0180] The solution effectiveness evaluation module is used to obtain the optimal mixed vectors corresponding to the optimal mixed interference strategies and the optimal mixed vectors corresponding to the optimal mixed protection strategies and their convergence processes of different solutions based on the limited profit interval, and determine the protection profit results of the protection system against interference threats by using the optimal mixed attack and defense vectors, so as to evaluate the dynamic game effectiveness of the protection measure combination solutions in different information confrontation scenarios according to the protection profit results.

[0181] Finally, to verify the effectiveness of the solution in this case, the following combines measured cases such as GNSS distributed jamming and suppression-assisted deception jamming to further explain and visually deduce the dynamic games in 15 different information confrontation scenarios.

[0182] In a game, the anti-jamming measures of the protection system change with the change of the interference strategies of the threat system. However, due to the different reconnaissance capabilities of the threat system and the interference / target recognition capabilities of the protection system, the completeness of the effective information mastered by both sides of the confrontation is different. Therefore, aiming at the strength of the protection system's ability to obtain effective information about the threat system, combined with confrontation cases, 15 typical dynamic games are realized, and the specific content is described as follows:

[0183] (1) Realize 4 kinds of blind information games for different solution combinations. Specifically, for different solution combinations, the threat system can use the optimal decision-making method proposed in the solution of this case to determine the anti-jamming profit when the navigation system confronts interference threats.

[0184] At this time, for different solution combinations, the threat system first uses the hybrid evolutionary algorithm PSO-GA in the solution of this case to obtain the optimal mixed vectors corresponding to the optimal mixed strategies, as shown in formulas (43) and (44); then uses the improved BP-NN regression algorithm based on DEA-KHA-Bootstrap to determine the corresponding anti-jamming profit E 最优方案 result 、E 最差方案 result 、E 随机组合1 result and E 随机组合2 result , which do not exceed 10.0150, 4.5174, 6.3127, and 6.5892 respectively. Therefore, in this game scenario, as Figure 5 shown, the threat system is more inclined to adopt the strategy of implementing interference by joint / synergistic deployment of multiple jamming sources (At6); at this time, to reduce the interference threat suffered by the protection system, the system will choose to integrate the space constellation protection measures with high spatial signal quality - strong service performance - stable state estimation (Df6) or the anti-jamming measures of the navigation equipment combined with the multi-source sensor system (Df1 or Df3) to cope with the interference threat.

[0185] (2) Implement 7 types of dynamic games of partial information confrontation for different scenario combinations, specifically including 4 scenarios, namely, the threat system knows that the protection system will not adopt Df4, the threat system knows that the protection system will not adopt Df1, the threat system knows that the protection system will not adopt Df2, and the threat system knows that the protection system will not adopt Df3. The following is an introduction to these 4 scenarios respectively:

[0186] ① The threat system knows that the protection system will not adopt Df4

[0187] Implement the partial information game for the optimal scenario combination (scenario combination 1). Assume that the threat system knows that the protection system will not use the navigation device equipped with a high-precision clock and an array antenna (Df4). Then the attack system can choose interference strategies such as At1, At2, At3, At5, and At6. Subsequently, it enters the state of partial information selection. Therefore, at this time, the optimal decision-making problem of the six-dimensional profit equation will be transformed into the optimal decision-making problem of the five-dimensional profit equation; and use the hybrid evolutionary algorithm PSO-GA to first obtain the optimal hybrid vector corresponding to the optimal hybrid strategy, and then use the DEA-KHA-Bootstrap improved BP-NN regression algorithm to determine its result matrix, as shown in equation (45). Therefore, the simulation results corresponding to the optimal hybrid vector are as Figure 6 shown.

[0188] From equation (45) and Figure 6 it can be seen that the threat system is more inclined to adopt GNSS generative deception interference strategies (At3), repeater deception interference strategies (At2), and multi-jammer joint / synergistic interference strategies (At6); at this time, in order to reduce the intentional interference threat suffered by the protection system, the system can adopt multi-frequency navigation devices combined with multi-satellite navigation systems (Df2), navigation devices combined with vision / inertial systems (Df3), and navigation devices combined with other multi-source sensor systems (Df1) to cope with the interference.

[0189]

[0190] Therefore, in the case of the partial information game for the optimal scenario combination, the anti-interference profit E of the protection system 组合1 resul is 9.9954, which is less than the anti-interference profit (10.0150) in the case of blind information game for the same combination. Then, the interference ability of the threat system is stronger during the partial game, and its damage effect is proportional to the reconnaissance ability of the system. In addition, the process of the partial information game for the optimal scenario combination is shown in Figure 7 .

[0191] ② The threat system knows that the protection system will not adopt Df1

[0192] Implement the partial information game for the optimal solution (hereinafter referred to as combination 1). Assume that the threat system knows that the protection system will not use the anti-jamming measures (Df1) of the navigation equipment combined with the multi-source sensor fusion system. Then the attack system can select interference strategies such as At1, At2, At3, At4, At5, At6, etc. Subsequently, it enters the state of partial information selection. Therefore, at this time, the optimal decision-making problem of the six-by-six profit equation will be transformed into the optimal decision-making problem of the six-by-five profit equation; and the hybrid evolutionary algorithm PSO-GA is used to first obtain the optimal hybrid vector corresponding to the optimal hybrid strategy, and then the improved BP-NN regression algorithm is used to determine its result matrix, as shown in Equation (46). Therefore, the simulation results corresponding to the optimal hybrid vector are respectively as Figure 8 shown.

[0193]

[0194] From Equation (46) and Figure 8 it can be seen that the threat system is more inclined to adopt the strategies of implementing interference attacks in the signal acquisition stage (At4), implementing spoofing attacks in the signal tracking stage (At5), and multi-jammer joint / synergistic interference strategies (At6); at this time, the protection system can adopt the anti-jamming measures (Df2) of the multi-frequency navigation equipment combined with the multi-satellite navigation system, the anti-jamming measures (Df3) of the navigation equipment combined with the vision / inertial system, and the anti-jamming measures (Df4) of the navigation equipment equipped with a high-precision clock and an array antenna to cope with the interference. Therefore, for the optimal solution combination, in such a partial information game situation, the anti-jamming profit of the protection system is not greater than 9.7609, less than the anti-jamming profit (10.0150) in the blind information game for the same combination, and also less than the anti-jamming profit (9.9954) in the partial information game when it is known that the protection system will not adopt Df4; then in the set game situation, the interference ability of the threat system is stronger, and the anti-jamming ability of the protection system in the confrontation process is weaker. In addition, the process of the partial information (known not to adopt Df1) game is shown in Figure 9 , and it can be viewed and analyzed according to the instructions of the serial number and the arrow.

[0195] ③ The threat system knows that the protection system will not adopt Df2

[0196] Partial information game for solution combination 1 is realized. Suppose the threat system knows that the protection system will not use the anti-jamming measure (Df2) of the multi-frequency navigation device with the multi-satellite navigation system combination. Then the attack system can choose interference strategies such as At1, At2, At3, At4, At5, At6, etc. Subsequently, it enters the selection state of partial information. Therefore, at this time, the optimal decision-making problem of the six-by-six profit equation will be transformed into the optimal decision-making problem of the six-by-five profit equation; and the hybrid evolutionary algorithm PSO-GA is used to first obtain the optimal hybrid vector corresponding to the optimal hybrid strategy, and then the improved BP-NN regression algorithm based on DEA-KHA-Bootstrap is used to determine its result matrix, as shown in Equation (47). Therefore, the simulation result of the optimal hybrid vector is as Figure 10 shown.

[0197]

[0198] From Equation (47) and Figure 10 it can be seen that the threat system is more inclined to adopt the strategies of GNSS suppression jamming attack (At1), interference attack during the signal acquisition stage (At4), and multi-jammer joint / synergistic jamming strategy (At6); at this time, the protection system can adopt the anti-jamming measures (Df1) of the navigation device combined with other multi-source sensor fusion systems, the anti-jamming measures (Df3) of the navigation device combined with the vision / inertial system, and the anti-jamming measures (Df4) of the navigation device equipped with a high-precision clock and an array antenna to cope with the interference. Therefore, for the optimal solution combination, in such a partial information game scenario, the anti-jamming profit of the protection system is not greater than 10.3431, which is greater than the anti-jamming profit (10.0150) in the blind information game for the same combination, and also greater than the anti-jamming profits (9.9954 and 9.7609) of other partial information games; then in the set game scenario, the interference ability of the threat system is weaker, so the anti-jamming ability of the protection system is stronger in the confrontation process. In addition, the process of the partial information (known not to adopt Df2) game is shown in Figure 11 , and the process can be viewed and analyzed according to the instructions of the serial number and its arrow.

[0199] ④ The threat system knows that the protection system will not adopt Df3

[0200] Partial information game for solution combination 1 is realized. Suppose the threat system knows that the protection system will not use the anti-jamming measures (Df3) of the navigation device combined with the vision / inertial system, then the attack system can select interference strategies such as At1, At2, At3, At4, At5, At6, etc. Subsequently, it enters the selection state of partial information. Therefore, at this time, the optimal decision-making problem of the six-by-six profit equation will be transformed into the optimal decision-making problem of the six-by-five profit equation; and the hybrid evolutionary algorithm PSO-GA is used to first obtain the optimal hybrid vector corresponding to the optimal hybrid strategy, and then the improved BP-NN regression algorithm based on DEA-KHA-Bootstrap is used to determine its result matrix, as shown in Equation (48). Therefore, the simulation results of the optimal hybrid vector are as Figure 12 shown.

[0201]

[0202] From Equation (48) and Figure 12 it can be seen that the threat system is more inclined to adopt the strategies of GNSS retransmission spoofing interference attack (At2), GNSS generation spoofing interference attack (At3), and multi-jammer joint / synergistic interference strategy (At6); at this time, the protection system can adopt the anti-jamming measures (Df2) of the multi-frequency navigation device combined with multiple satellite navigation systems, the anti-jamming measures (Df4) of the navigation device equipped with a high-precision clock and an array antenna, and the space constellation protection measures (Df6) integrating high spatial signal quality - strong service performance - stable state estimation to cope with the interference. Therefore, for the optimal solution combination, in such a partial information game situation, the anti-jamming profit of the protection system is not greater than 6.5795, less than the anti-jamming profit (10.0150) in the blind information game for the same combination, and also less than the anti-jamming profits (9.9954, 9.7609, and 10.3431) of the above other partial information games; then in the set game situation, the interference ability of the threat system is stronger, and the anti-jamming ability of the protection system is the weakest in the confrontation process. In addition, the process of the partial information (known not to use Df3) game is as Figure 13 shown.

[0203] (3) Complete information game for solution combinations 1-4 is realized. Specifically, both sides of the confrontation only need to use the weighted average type FCA and grey expert system method improved based on the improved index weight determination method and interval theory to quantify the profit matrices corresponding to solutions 1-4; there is no need to further derive the profit equations and solve them to obtain the global optimal solution.

[0204] At this time, based on a full understanding of existing anti-jamming measures, the threat system will select the threat strategy with the best damage effect; similarly, the protection system will do the same. Specifically, both sides of the confrontation only need to use the weighted average type FCA and grey expert system methods improved based on the improved index weight determination method and interval theory to quantify the profit matrices corresponding to different established solution combinations 1-4; there is no need to further derive the profit equations and solve them to obtain the global optimal solution. The quantified profit matrices obtained are shown in Equations (49) to (52).

[0205] ① Full information game for solution combination 1

[0206] If the threat system directly selects the strategy of multi-jammer joint / synergistic deployment to implement jamming attacks (At6), and the protection system selects the anti-jamming measure of the navigation device combined with the vision / inertial system (Df3), then the protection profit at this time is 15.9914. Subsequently, the threat system immediately changes its original strategy and selects the strategy of GNSS repeater spoofing jamming (At2), then the protection profit of the protection system immediately drops to the minimum of this series, that is, 8.5113.

[0207]

[0208] Therefore, in order to improve the GNSS security protection ability, the protection system will immediately change its original measure (Df3) and switch to selecting the space constellation protection measure that integrates high spatial signal quality - strong service performance - stable state estimation (Df6), and its protection profit immediately increases to 11.6838. At this time, in order to further reduce the jamming threat suffered by the protection system, the system can also select another measure (Df2) on the basis of the original anti-jamming measure (Df6) to jointly respond to the current attack. In addition, the full information game process for solution combination 1 is shown in Figure 14 as follows.

[0209] ② Full information game for solution combination 2

[0210] If the threat system directly selects the strategy At6, and the protection system selects the anti-jamming measure of the navigation device combined with the multi-source sensor fusion system (Df1), then the protection profit at this time is 12.5407. Subsequently, the threat system immediately changes its original strategy and selects the strategy of GNSS generative spoofing jamming (At3), then the protection profit of the protection system immediately drops to the minimum of this series, that is, 2.3273.

[0211]

[0212] Therefore, to improve the anti-interference ability, the protection system will immediately change the original measure (Df1) and switch to the anti-interference measure Df4, and its protection profit will immediately increase to 2.3415. At this time, to further reduce the interference threat suffered by the protection system, the system can select another anti-interference measure (Df2) on the basis of the original anti-interference measure (Df4) to jointly respond to the current attack. In addition, the complete information game process for scenario combination 2 is shown in Figure 15 , which can be viewed and analyzed according to the sequence number and the indication of the arrow.

[0213] ③ Complete information game for scenario combination 3

[0214] If the threat system directly selects the strategy of implementing interference by jointly / synergistically deploying multiple interference sources (At6), and the protection system selects the anti-interference measure (Df2) of a multi-frequency navigation device with a multi-satellite navigation system combination, then the protection profit at this time is 10.0487. Subsequently, the threat system immediately changes the original strategy and selects the strategy of implementing interference during the signal acquisition stage (At4), then the protection profit of the protection system immediately drops to 5.9411. Therefore, to improve the anti-interference ability, the protection system will immediately change the original measure (Df2) and switch to the measure (Df1) of a navigation device combined with a multi-source sensor fusion system, and its protection profit will immediately increase to 7.9377.

[0215]

[0216] At this time, to further reduce the interference threat suffered by the protection system, the system can select another anti-interference measure (Df5 or Df4) on the basis of the original anti-interference measure (Df1) to jointly respond to the current attack. In addition, the complete information game process for scenario combination 3 is shown in Figure 16 , and the process can be viewed and analyzed according to the sequence number and the indication of its arrow.

[0217] ④ Complete information game for scenario combination 4

[0218] If the threat system directly selects At6 and the protection system selects the anti-interference measure (Df4) of a navigation device equipped with a high-precision clock and an array antenna, then the protection profit at this time is 9.7376. Subsequently, the threat system immediately changes the original strategy and selects the strategy of GNSS jamming (At1), then the protection profit of the protection system immediately drops to the minimum of this series, that is, 3.2702.

[0219]

[0220] Therefore, in order to improve the anti-interference ability, the protection system will immediately change the original measure (Df4) and switch to the ground operation and control protection measure (Df5) that integrates strong service performance and station functions. Its protection profit will then increase to 4.8915. At this time, to further reduce the interference threat suffered by the protection system, the system can select another measure (Df1) on the basis of the original anti-interference measure (Df5), and the two jointly respond to the current attack. Then, the complete information game process for scenario combination 4 is as Figure 17 .

[0221] Based on scenario combinations 1 - 4, 5 evaluation rules are designed in the experiment, 7 typical optimal decision-making methods are selected, and around the two aspects of evaluation indicators and evaluation results, a comparison is made with the optimal decision-making method proposed in the solution of this case, and the optimal solutions and optimal strategies corresponding to scenario combinations 1 - 4 are obtained to verify the correctness of the obtained results and the superiority of the proposed method.

[0222] First, from the level of evaluation results, based on scenario combinations 1 - 4, 8 typical optimal decision-making methods are selected to obtain the profit results corresponding to each scenario, their corresponding profit intervals, as well as their optimal solutions and optimal strategies, and the verification and feedback work of the method proposed in the solution of this case and the results obtained are completed.

[0223] Based on scenario combinations 1 - 4, it aims to verify the results obtained and the method proposed in the solution of this case. Assuming that the solution of this case uses the fuzzy grey expert-guided system method to quantify the profit matrix, the following different solution methods are selected to obtain the profit results corresponding to each scenario [E 1 , E 2 , E 3 , E 4 and E 1 , E 2 , E 3 , E 4 corresponding profit intervals [E L , E U , as well as their optimal solutions and optimal strategies, as shown in Tables 6 and 7. Among them, taking E 1 as an example, the convergence process of E 1 corresponding to 8 solution methods is as Figure 18 : After the profit equation is constructed based on LP, the solution methods for comparison include ① the proposed methods using the general combined weighting method (LP - PG - IBP with W general ), objective weighting method (LP - PG - IBP with W objective ), subjective weighting method (LP - PG - IBP withW subjective ) and improved combined weighting method (LP - PG - IBP with W modified ) respectively to solve the profit equation; ② using the method based on Wmodified The PSO (LP-PSO with W modified ), is used to solve the profit equation; ③ The GA (LP-GA with W modified ) based on W modified is used to solve the profit equation; ④ The LP and improved BP-NN regression algorithm (LP-IBP with W modified ) based on W modified is used to solve the profit equation; and ⑤ The LP method (LP withW modified ) based on W modified ) is adopted.

[0224] Table 6 Optimal solutions and selected optimal strategies (measures) obtained by different methods (a) Minimum value E L of v* and ω*

[0225]

[0226] (b) Maximum value E U of v* and ω*

[0227]

[0228] (c) v* and ω* of E 1 corresponding to solution combination 1

[0229]

[0230] (d) v* and ω* of E 2 corresponding to solution combination 2

[0231]

[0232] (e) v* and ω* of E 3 corresponding to solution combination 3

[0233]

[0234] (f) v* and ω* of E 4 corresponding to solution combination 4

[0235]

[0236] Table 7 Profit results of different solution combinations and their minimum and maximum values

[0237]

[0238] Table 6 shows that no matter which solution method is adopted and no matter what kind of confrontation scenario is faced, the solution method proposed in the solution of this case (LP-PG-IBP with Wmodified ) The globally optimal solutions obtained are all the same as the pre-set ideal interference strategy (i.e., the strategy of joint / cooperative deployment of multiple interference sources for interference, x6 * ), and the profit results obtained are also the largest within their extreme value ranges, which further illustrates the superiority of the method proposed in the present invention. In addition, from Figure 18 the convergence process, it can also be seen that for the solution method after adding the improved BP-NN regression algorithm, its convergence effect and convergence speed are better than the corresponding convergence process of the planning solution method based on the heuristic algorithm; taking LP-PG-IBP as an example, if this solution method uses the improved combined weighting method to fix the weights, its convergence effect is better than that when it uses other weighting methods to fix the weights.

[0239] As can be seen from Table 7, compared with other confrontation scenarios (i.e., solution combinations 1-4), regardless of the solution method used, the profit result corresponding to combination 1 is the largest, indicating that the optimal confrontation scenario obtained is combination 1. This result is consistent with the result after multi-attribute decision-making and comprehensive evaluation and then verification in the early stage. Therefore, it further verifies the effectiveness of the method proposed in the present invention and the rationality of the obtained results. In summary, through the comparison and analysis of the results listed in Table 6 and Table 7 and Figure 18 the verification is completed.

[0240] Secondly, from the level of evaluation results, calculation models of 5 evaluation rules are designed, and based on the 5 evaluation rules, the evaluation results obtained by the j-th (j = 1, 2,..., 7) decision-making method are compared and analyzed with the evaluation results corresponding to the solution of this case to complete the verification and feedback work of the method proposed and the results obtained.

[0241] (1) Calculation models of evaluation rules

[0242] Based on this, first of all, references need to be given, including: ① the reference extreme value of the profit result, ② the reference profit results of each confrontation scenario 1-4 (solution combinations 1-4), and ③ the ideal interference strategy under one confrontation scenario. For the first two points, for the sake of fairness, the reference is set to 1; for the third point, the conclusion consistently given by the expert system is the strategy of joint / cooperative interference of multiple interference sources (At6).

[0243] On this basis, in order to complete the verification under the i-th (i = 1, 2, 3, 4) confrontation scenario, based on the following 5 evaluation rules, the results obtained by the j-th (j = 1, 2,..., 7) solution method can be compared with the results obtained by the solution method proposed in the present invention (LP-PG-IBP with W modified ). These evaluation rules include ① the distance degree between the profit result and its corresponding minimum value. The calculation model of the first evaluation rule is shown in Equation (53):

[0244]

[0245] ② The normalized distance degree between the reference distance degree (the distance degree between the reference profit result and its corresponding minimum value) and the distance degree; ③ The normalized range between the maximum profit result and the reference result. The calculation models of the second and third rules are as shown in Equations (54) and (55):

[0246]

[0247] ④ The extreme difference of the normalized distance degree; ⑤ The coefficient of variation between the normalized distance degree and its maximum value. The calculation models of the fourth and fifth rules are as shown in Equations (56) and (57) respectively:

[0248]

[0249]

[0250] The above evaluation indexes can all reflect the absolute value of the dispersion degree of the data relative to the given reference. As the distance degree (or normalized distance degree) and the normalized range (or extreme difference) increase and the coefficient of variation decreases, the larger the profit result, the better the corresponding solution method. On this basis, according to the calculation models of the five evaluation rules, the relevant calculation results are obtained, and their comparison relationships are determined, such as Figure 19 and Figure 20 and Table 8 to complete the verification and feedback work on the method proposed in the present invention and the results obtained thereby.

[0251] (2) Verification based on the evaluation results

[0252] From Figure 19 it can be seen that the distance degree result curve corresponding to the solution method (LP-PG-IBP with W modified ) proposed in the present invention is higher than the distance degree results corresponding to any other solution method, that is, the proposed solution method is superior to other solution methods, which also indirectly shows the superiority of the improved combined weighting method.

[0253] From Figure 20 and Table 8, it can be seen that: ① From the normalized distance degree, normalized range, and extreme difference of the four confrontation scenarios 1-4 (scheme combinations 1-4), by comparing the relevant evaluation results corresponding to different solution methods, the larger these evaluation results are, the better the performance of the corresponding solution method; and the evaluation results corresponding to the solution method LP-PG-IBP with W modified proposed in the present invention are the largest, so it is superior to other solution methods. ② From the coefficient of variation, LP-PG-IBP with W subjective and LP-PG-IBP with W modifiedand LP-PG-IBP with W objective The corresponding coefficient of variation is relatively large, while LP with W modified and LP-IBP with W modified The corresponding coefficient of variation is relatively small, indicating that the latter has a smaller degree of dispersion relative to the given reference. This shows that the profit equation constructed using the linear programming method, the profit results determined by improving the BP-NN regression algorithm, and the weight determination results obtained using the improved combined weighting method are all more reliable. In addition, using the improved combined weighting method W modified The method for solving the weight determination, such as LP with W modified 、LP-IBP with W modified 、LP-PSO with W modified 、LP-GA with W modified and LP-PG-IBP with W modified , the corresponding coefficients of variation are all smaller than those of the solution methods based on other weight determination methods. Therefore, the improved combined weighting method makes a more significant contribution to obtaining the global optimal solution and expanding the profit results.

[0254] Table 8 Summary table of evaluation results corresponding to different methods

[0255]

[0256] In summary, the verification of the result rationality and method superiority has been completed.

[0257] The experimental results show that: ① Under any test scenario, the minimum profit during the confrontation of the tested equipment (system) should fall within the interval [1.364, 29.972]. The closer the profit is to the maximum value of the interval, the stronger the anti-interference threat ability of the equipment (system). ② During partial information game, the protection profit is less than the profit value during blind information game, and as the threat party's information recognition integrity increases, the anti-interference threat ability of the tested equipment (system) weakens. ③ During complete information game, the protection system will, in accordance with the principle of maximizing the profit value, dynamically adjust the anti-interference measures according to the interference strategy, expanding the benefits while enhancing its protection ability. ④ Compared with the existing evaluation methods, the solution in this case improves the quantization accuracy of the game model, changes the previous static effectiveness evaluation mode, the obtained distance curve is higher, and the maximum error value is larger, which is more suitable for the dynamic game of satellite navigation countermeasure.

[0258] Unless otherwise specifically stated, the relative steps, numerical expressions, and numerical values of the components and steps described in these embodiments do not limit the scope of the present invention.

Claims

1. A method for evaluating the effectiveness of satellite navigation countermeasure dynamic game, characterized in that, Including: Remodeling the profit matrix of the dynamic game process according to the evaluation index system for the dynamic game between interference and protection, and establishing a dynamic game model for satellite navigation countermeasure. The evaluation index system for the dynamic game between interference and protection is pre-established based on the evaluation indexes, their technical intervals, sub-evaluation models and comprehensive evaluation methods for satellite navigation countermeasure interference strategies and protection measures implementation effects; Quantifying each matrix element in the profit matrix, establishing the profit equations for both sides of the confrontation based on the quantified profit matrix, according to the min-max and max-min principles in game theory and using the linear programming method, and solving the profit equations by maximizing the benefits during the dynamic game of one's own side to obtain the optimal solutions for the game of both participants. The profit equations are used for different information confrontation situations and to obtain the optimal mixed strategies and their effectiveness evaluation values of one's own side; Selecting the optimal interference strategies to form corresponding protection measure combination schemes, solving the profit equations in each protection measure combination scheme according to the hybrid evolutionary algorithm and the combined intelligent optimization BP neural network regression algorithm, and obtaining the corresponding finite profit intervals of the equations. The protection measure combination schemes include: the optimal protection measure combination scheme, the worst protection measure combination scheme and the random protection measure combination scheme. The finite profit intervals are used to describe the interval range where the protection profit is located during the confrontation game; Obtaining the optimal mixed vectors corresponding to the optimal mixed interference strategies of different schemes, and the optimal mixed vectors corresponding to the optimal mixed protection strategies and their convergence processes according to the finite profit intervals, and determining the protection profit results of the protection system against interference threats using the optimal mixed attack and defense vectors, so as to evaluate the dynamic game effectiveness of the protection measure combination schemes in different information confrontation situations based on the protection profit results; 2. The satellite navigation countermeasure dynamic game effectiveness evaluation method according to claim 1, wherein The evaluation index system for the dynamic game between interference and protection is an index system for GNSS safety protection pre-established according to GNSS interference and anti-interference technologies and based on the evaluation principles of game theory. The evaluation principles are determined according to the requirements and capabilities of different application levels in satellite navigation countermeasure tasks; 3. The satellite navigation countermeasure dynamic game effectiveness evaluation method according to claim 1 or 2, characterized in that, Remodeling the profit matrix of the dynamic game process according to the evaluation index system for the dynamic game between interference and protection, and establishing a dynamic game model for satellite navigation countermeasure, including: Regarding the threat system composed of single GNSS interference source and multi-GNSS interference source cooperative interference technologies and their related equipment, and the protection system composed of GNSS and its corresponding anti-interference technologies for each component in satellite navigation countermeasure as the participants of the game model, and selecting the interference strategies and protection measures with high feasibility and success rate in the threat system and the protection system to construct the pure strategy space of the game model participants; According to the established evaluation index system for the game between interference strategies and protection measures, using the evaluation indexes, their sub-evaluation models and comprehensive evaluation methods respectively included in the interference strategies and protection measures in the pure strategy space, and obtaining each element in the profit matrix through the evaluation experimental platform, and establishing the profit matrix based on each element; Constructing a dynamic game model for satellite navigation countermeasure based on the participants, pure strategy space and profit matrix; 4. The satellite navigation countermeasure dynamic game effectiveness evaluation method according to claim 1, characterized in that Quantifying each element in the profit matrix based on the dynamic game model, including: Divide each element in the profit matrix into measurable elements and non-measurable elements; Quantify the measurable elements in the profit matrix using the fuzzy comprehensive evaluation method improved based on interval theory, and quantify the non-measurable elements in the profit matrix using the proposed grey expert system method. The grey expert system forms a knowledge base using the historical experience and expert knowledge of the expert system and completes the quantification of non-measurable elements after improvement based on the grey theory system.

5. The satellite navigation countermeasure dynamic game effectiveness evaluation method according to claim 4, characterized in that Quantify the non-measurable elements in the profit matrix using the grey expert system, including: Set the scoring levels for scoring each interference strategy and protection measure in the blind information game scenario and the corresponding scoring intervals for the levels, and determine the confidence weights of the scoring results of each domain expert according to the professional ability, domain familiarity and scoring result confidence of the experts in the field; Create an ability scoring matrix given by each domain expert and the corresponding preset reference values according to the scoring intervals and the confidence weights of the scoring results. The ability scoring matrix is used to describe the ability estimation of the expert for the attack ability of the corresponding interference strategy / anti-interference ability of the protection measure when facing the anti-interference of the protection measure / interference of the interference strategy. The preset reference value represents the reference value calculated using the scoring results and the confidence weights of the scoring results; Establish a zeroed image matrix and an initial image matrix by zeroing and initializing the established scoring matrix, and obtain the grey correlation absolute quantity and relative quantity of each domain expert using the image matrix, so as to determine the grey comprehensive value of the corresponding domain expert according to the grey correlation absolute quantity and relative quantity; Quantify the non-measurable elements by normalizing the grey comprehensive value of the expert and selecting the ability scoring matrix with the largest normalized grey comprehensive value, so as to realize the quantification of the profit matrix for various evaluation indicators.

6. The satellite navigation countermeasure dynamic game effectiveness evaluation method according to claim 1, wherein Solve the profit equation by maximizing the protection benefit during the dynamic game of both sides to obtain the global optimal solution for the game of both participating sides, including: Solve the profit equation and generate the solution result. The solution result includes the optimal mixed attack and defense strategies adopted in the game of the participants and the effectiveness evaluation value of the optimal mixed attack and defense strategies; Input the solution result into a pre-trained evaluation model, and use the evaluation model to obtain the stable global optimal solution for the game of both sides in satellite navigation countermeasure. The evaluation model is based on a hybrid evolutionary algorithm jointly improved by the particle swarm optimization algorithm PSO and the genetic algorithm GA, and uses three intelligent algorithms, namely the data envelopment analysis method, the krill swarm algorithm and the classical bootstrap method, to jointly train and optimize the regression model.

7. The satellite navigation countermeasure dynamic game effectiveness evaluation method according to claim 6, wherein The project of joint training and optimization of the evaluation model includes: Construct a BP neural network and initialize the weights and thresholds of the network, and use the krill swarm algorithm and the data envelopment analysis method to optimize the network parameters. The network parameters include learning efficiency, number of training times, error upper limit, optimal weights and thresholds. Among them, use the mixed strategy evaluation index as the input of the data envelopment analysis method, and use the data envelopment analysis method to obtain the crossover probability, average crossover probability and maximum crossover probability of the mixed strategy, so as to use the crossover probability, average crossover probability and maximum crossover probability of the mixed strategy as the expected output of the neural network; Construct training samples and test samples based on the performance index evaluation data of the hybrid strategy. Use the classical bootstrap method to perform Bootstrap resampling on the training samples, and expand the training samples by random sampling to generate new training samples, so as to train the neural network with the new training samples; Use the trained neural network to predict the output of the test samples. Calculate the fitness of krill individuals based on the expected output and the prediction of the test samples, and update the positions of krill individuals based on the fitness of krill individuals. Assign the updated positions of krill individuals that meet the termination conditions of the krill swarm to the neural network to obtain the initial evaluation model; Use the test samples to evaluate the initial evaluation model. Judge whether the initial evaluation model meets the expectations according to the error coefficient and the coefficient of determination. If it meets the expectations, use the initial evaluation model as the pre-trained evaluation model and output the final global optimal solution. If it does not meet the expectations, return to the step of training the neural network with the training samples and execute it again. The error coefficient and the coefficient of determination are used to describe the change range of the model output error, the change trend of the mean value of the model output optimal solution, and comprehensively measure the reliability of the model.

8. The satellite navigation countermeasure dynamic game effectiveness evaluation method according to claim 1, characterized in that Solve the profit equation in each combination plan of protection measures and obtain the corresponding finite profit interval of the equation to realize the dynamic game of different information confrontation situations, including: Obtain the profit matrix in each combination plan of protection measures, and use the fuzzy comprehensive evaluation method based on interval theory and the grey expert system to quantify the measurable elements and unmeasurable elements in the profit matrix respectively. According to the percentile interval comprehensive evaluation matrix for all strategy / measure evaluation index technical intervals, the comprehensive evaluation matrix for the optimal plan combination, the worst plan combination and the random plan combination of both sides of the confrontation, as well as the first- and second-level weight sets and the selected ability scoring matrix, perform multiplication and addition operations to obtain the interval quantization profit matrix for each type of evaluation index technical interval and the quantization profit matrix for different plan combinations of both sides of the confrontation respectively; Use the linear programming method and according to the maximin and minimax principles of game theory, convert the two types of quantization profit matrices into dual linear programming problems respectively, and establish the profit equations of both sides of the confrontation; Solve the profit equations for each type of evaluation index technical interval through the hybrid evolutionary algorithm and the combined intelligent optimization BP-NN regression algorithm to obtain the finite profit interval of the profit equation solution, which is used as the judgment standard for the level of the protection ability of the protection system against interference threats and the size of the effectiveness evaluation result obtained by implementing anti-interference; Solve the profit equations for different plan combinations of both sides of the confrontation through the hybrid evolutionary algorithm and the combined intelligent optimization BP-NN regression algorithm to obtain the optimal hybrid vectors and their protection profit results of different plan combinations, and realize the dynamic game of blind information confrontation, partial information confrontation and complete information confrontation according to the effective profit interval.

9. A satellite navigation countermeasure dynamic game effectiveness evaluation system, characterized in that Including: game model construction module, profit equation establishment module, combination plan solution module and plan effectiveness evaluation module, where, A game model construction module, which is used to reshape the profit matrix of the dynamic game process and establish a dynamic game model for satellite navigation countermeasure according to the evaluation index system for the dynamic game between interference and protection. The evaluation index system for the dynamic game between interference and protection is pre-established according to the evaluation indexes and their technical intervals, sub-item evaluation models and comprehensive evaluation methods for the implementation effects of satellite navigation countermeasure interference strategies and protection measures; A profit equation establishment module, which is used to quantify each element in the profit matrix. Based on the quantified profit matrix, according to the min-max and max-min principles in game theory and using the linear programming method, establish the profit equations of both sides of the confrontation, and solve the profit equations by maximizing the benefit during the dynamic game of one's own side to obtain the optimal solution of the game between the two participants. The profit equations are used for different information confrontation situations and are used to obtain the optimal mixed strategy of one's own side and the effectiveness evaluation value of the mixed strategy; A combined solution module, which is used to select the optimal interference strategy to form the corresponding protection measure combination plan, solve the profit equations in each protection measure combination plan according to the hybrid evolutionary algorithm and the combined intelligent optimization BP neural network regression algorithm, and obtain the finite profit interval corresponding to the equation. The protection measure combination plan includes: the optimal protection measure combination plan, the worst protection measure combination plan and the random protection measure combination plan. The finite profit interval is used to describe the interval range where the protection profit is located during the confrontation game; A plan effectiveness evaluation module, which is used to obtain the optimal mixed vector corresponding to the optimal mixed interference strategy of different plans, and the optimal mixed vector corresponding to the optimal mixed protection strategy and its convergence process according to the finite profit interval, and determine the protection profit result of the protection system against interference threats by using the optimal mixed attack and defense vectors, so as to evaluate the dynamic game effectiveness of the protection measure combination plan in different information confrontation situations.

10. A satellite navigation countermeasure evaluation experimental platform, characterized in that, An evaluation experiment platform for satellite navigation countermeasure is set up relying on an automatic measuring robot and dynamic evaluation software. The dynamic evaluation software is used for dynamic game, and uses specified test methods to carry out simulation tests to evaluate the GNSS interference and anti-interference capabilities for different interference scenarios and in the face of multiple user terminals. The evaluation experiment platform includes interference signal generation, GNSS signal reception, interference signal acquisition, storage and playback, signal analysis, automatic measurement and comprehensive evaluation units. The specified test methods include broadcasting specific instructions, theoretical formula modeling, hardware-in-the-loop simulation test, full-physical static test, full-physical dynamic test and 1-9 scale method. And the experiment platform uses multiple processors and multiple memories coupled to a single processor to evaluate the effectiveness of the satellite navigation countermeasure dynamic game. The memories store computer programs, and the computer programs can be executed by at least one processor to implement the method according to any one of claims 1-8.

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