Opportunistic array radar directional diagram reconstruction method of dynamic multi-node platform

Abstract

The invention provides an opportunistic array radar directional diagram reconstruction method for a dynamic multi-node platform. The opportunistic array radar directional diagram reconstruction method comprises the steps of initializing a task target and constraint condition parameters; a fuzzy number is selected according to requirements, and a fuzzy opportunity constraint programming model for dynamic multi-node opportunity array radar directional diagram reconstruction is established; and solving the model by adopting a multi-area-array approximation matrix pencil method in combination with fuzzy simulation. According to the method, corresponding planning models can be established under different task requirements by utilizing the constructed general model and the solving method, so that the problem of system robustness caused by dynamic environment influence involved in practical application of a directional diagram reconstruction problem is effectively solved; node resources, position information and the like of the opportunity array radar can be dynamically adjusted along with environment tasks, practical application is better met, change of the opportunity array radar along with encountering is achieved, namely, the characteristic of opportunity adjustment of system parameters is achieved according to different task requirements, and reference is provided for modeling and solving of other problems related to the opportunity array radar.

Description

Technical Field

[0001] The invention belongs to the technical field of opportunity array radars, and in particular relates to a method for reconstructing a directional pattern of an opportunity array radar on a dynamic multi-node platform. Background Art

[0002] Limited by institutional factors, traditional radar systems as a means of perception are increasingly difficult to adapt to current needs. For example, fixed array size and working wavelength are often aimed at fixed detection targets. Long-range early warning radars are generally huge in size, poor in flexibility, low in battlefield adaptability, blind spots at low elevation angles, and aperture size is limited by the carrier platform. The combat function is single and has other shortcomings. The opportunity array radar is designed with the platform as the core, and has the advantages of stealth, flexibility, and multi-functional integration. Its working state can be reorganized through opportunity decision-making to reorganize the opportunity unit or local module according to changes in external conditions, different targets or different scenario mission requirements to maximize the combat capability and survivability of the platform.

[0003] In theory, the typical characteristics of opportunity array radar include good stealth performance in addition to the platform-centered design method. Its flexibility and versatility are its important manifestations. In the research, it is mainly reflected in the interpretation and application research of the concept of opportunity. Since the environment, target and task requirements are uncertain in dynamic scenes, the parameters involved are random. Conventional random concepts cannot describe variables with unknown probability density. A large number of repeated experiments are required for estimation, which is undesirable and difficult to carry out in most scenarios. At present, the more general practice is to introduce the concept of fuzzy sets to characterize uncertain parameters. Some researchers have proposed a possibility measure for the measurement of fuzzy events, and then proposed a credibility measure with self-duality, and established a complete credibility theory system. It has given clear definitions of various uncertain parameters including random, fuzzy, rough, random rough, etc., and given the modeling mechanism of expected value model, opportunity constraint programming, and related opportunity programming. The fundamental mathematical problem that opportunity array radar needs to solve is to optimize and solve the modeling of non-deterministic factors in the real-time environment according to the needs, and make dynamic adjustments. Existing research on the problem of pattern synthesis of opportunity array radar mainly reflects three aspects. First, the mathematical modeling and solution of opportunity array radars of different platforms. Since the opportunity array radar is a design framework with the platform as the core, the corresponding models of different platforms are different; second, the constraint programming models required to be established for different task requirements are different. In the same scenario, the task can be to minimize the main lobe width, minimize the number of nodes, minimize the side lobe level, or a combination of multiple situations according to the requirements; finally, the selection of uncertain factors in the model. Different task requirements and environments often correspond to different uncertain parameters, and some uncertain parameters play a decisive role in the solution of the model. At present, Gong has given preliminary conclusions on the research on the problem of pattern synthesis of opportunity array radar, but it is mainly for the optimization of random array elements with fixed initial positions, and the platform used is more suitable for conformal arrays. At present, there has been extensive research on the problem of pattern synthesis of sparse arrays under conventional conditions. The relevant solution algorithms mainly include mathematical analytical methods based on singular value approximation matrix bundles and their expansion algorithms, intelligent optimization solution algorithms based on genetic, differential evolution, ant colony and other heuristics, iterative Fourier algorithms, etc. However, the modeling and solution of the pattern synthesis problem with uncertain parameters in the dynamic scene of opportunity array radar still need in-depth research, especially for the flexible reconstruction characteristics of opportunity array radar itself. Therefore, the present invention mainly proposes an effective model and solution algorithm for the problem of pattern reconstruction of opportunity array radar on dynamic multi-node platform. Summary of the invention

[0004] Technical problems to be solved: The purpose of the present invention is to provide a method for reconstructing the radiation pattern of an opportunity array radar on a dynamic multi-node platform, which mainly solves two problems: (1) the problem that traditional sparse node radiation pattern synthesis does not take into account the influence of dynamic changes in actual application, lacks the robustness of the overall system and is not suitable for practical application; (2) the problem of radiation pattern reconstruction of the opportunity array radar when the dynamic multi-node platform contains uncertain factors.

[0005] Technical solution:

[0006] A method for reconstructing a radar pattern of an opportunity array of a dynamic multi-node platform, the method comprising the following steps:

[0007] S1, according to actual needs, combined with the characteristics of the opportunity array radar itself, the comprehensive optimization target can be set to set one or more task requirements; the error effects including the maximum reconstruction error δ0, the maximum error of the main lobe width δ1, and the maximum error of the side lobe level δ2 are used as constraint errors;

[0008] S2, obtain the minimum approximate array size M×N according to the task requirements;

[0009] S3, using the minimum approximable surface array to establish the Hank augmented matrix;

[0010] S4, obtain error parameters according to the constructed Hank augmented matrix;

[0011] S5, obtaining the range of the approximate surface array and the range of the number of reconstruction nodes;

[0012] S6, establish a dynamic multi-node directional graph synthesis model based on fuzzy chance constrained programming;

[0013] S7, uses a matrix beam algorithm of multi-surface array approximation and fuzzy simulation technology to solve the dynamic multi-node directional pattern synthesis model.

[0014] In step S1, the task requirement includes one or more of minimizing the main lobe width, minimizing the side lobe level, and minimizing the number of node resources.

[0015] Step S3 further comprises:

[0016] Construct the target sampling pattern, and uniformly sample all target patterns in the (u, v) plane, with the sampling interval being (-1, 1); if the number of sampling points on the u and v axes is 2M+1 and 2N+1 respectively, the sampling point of the p-th target pattern is expressed as:

[0017]

[0018] in, and represents the horizontal and vertical coordinates of the nth array element on the coordinate axis, λ is the wavelength, w n The excitation of n array elements when reconstructing the target pattern;

[0019] Construct the augmented matrix X e :

[0020]

[0021] Step S4 further comprises:

[0022] For the augmented matrix X e Perform singular value decomposition to obtain:

[0023]

[0024] Where U s and V s Indicates the main lobe direction, V n and U n represents the sidelobe direction, the superscript H represents the conjugate transpose, and:

[0025] Σ s =diag(σ1σ2...σ Q )

[0026] Σ n =diag(σ Q+1 σ Q+2 ... S )

[0027] Where diag is the function for constructing a diagonal matrix, σ S For X e non-zero singular values ​​of , and σ1≥σ2≥…≥σ s ≥0, the singular value characteristics of the matrix are used to define the pattern approximation error ε:

[0028]

[0029] Where q is the intermediate parameter when approximating the error parameter.

[0030] Step S5 further comprises:

[0031] According to the task requirements, the reconstructed directional graph approximation error ε≤ε0 is obtained, and the theoretical minimum number of reconstruction nodes Q1 is obtained:

[0032]

[0033] The sparse reconstruction sparsity of the directional graph is used to define the maximum number of reconstruction nodes. If 90% of the minimum array that meets the requirements is taken, the maximum number of reconstruction nodes Q2 is obtained:

[0034]

[0035] In the formula, Indicates rounding down; the upper limit of the approximate array size M1×N1 is obtained:

[0036]

[0037] Step S6 further comprises:

[0038] Define the decision variables:

[0039] X=[X1 X2...X N-1 X N ]

[0040] In the formula, X n represents the nth decision variable. If the first decision variable is the node working state, the decision variable X1 is expressed as:

[0041]

[0042] x n =0 or 1, n=1,2,...,N p -1,N p

[0043] Where N p Reconstruct the maximum number of nodes that can be assigned to the p-th task direction graph;

[0044] Define fuzzy variables:

[0045]

[0046] In the formula, ξ p The minimum number of units required to reconstruct the p-th task direction graph, NS is the total number of all available nodes;

[0047] The constraints of the uncertain environment are expressed by the following set of inequalities:

[0048]

[0049] Wherein, the superscript (p) represents the pth task, δ is the error requirement of each constraint, δ0, δ1 and δ2 are the maximum reconstruction error, the maximum error of the main lobe width and the maximum error of the side lobe level, respectively, err is the error between the reconstructed pattern and the expected pattern, B(X1) is the main lobe width of the reconstructed pattern under the decision variable X1, and B w is the expected main lobe width, SL(X1) is the maximum sidelobe level under the decision variable X1, SL is the expected maximum sidelobe level, g0(X,ξ)…g J (X,ξ) represent the constraints encountered in practical applications; ξ1 is the minimum number of units required for the reconstruction of the first task direction graph;

[0050] The general form of fuzzy chance constraint programming for dynamic multi-node opportunity array radar is obtained as follows:

[0051]

[0052] in is the optimistic value of maximizing the objective function, f(X,ξ) is the objective function, f1(X,ξ)...f I (X,ξ) are the various requirements encountered in actual situations, is the optimistic value of the maximization objective function corresponding to each demand, I is the total number of demands; β is the credibility requirement of the objective function; α is the confidence level that makes the constraint condition hold; G(X,ξ) is the fuzzy constraint, X is the decision vector, and ξ is the fuzzy vector.

[0053] In step S6, two different dynamic multi-node directional diagram comprehensive models are given according to different tasks: a simultaneous decision model and a hierarchical decision model; wherein the simultaneous decision model is:

[0054]

[0055] Where err represents the reconstruction error, B(X) and SL(X) represent the actual main lobe width and reconstruction level after reconstruction, respectively; is the optimistic value of maximizing the objective function; F(X,Y,ξ1,ξ2) is the objective function, which contains two decision variables X and Y; NS1 is the total number of all available nodes on the X axis, and NS2 is the total number of all available nodes on the Y axis; y n is the node working status, y n =0 or 1, ξ2 is the minimum number of units required for reconstructing the second task direction graph;

[0056] The hierarchical decision model is:

[0057]

[0058] Where G(x,y,ξ) is the fuzzy constraint under the decision variables x and y.

[0059] Step S7 further comprises:

[0060] S71, using Hank matrix X e The model events and environmental parameters are transformed in the characteristic solution space, the model data is preprocessed, and the reconstruction nodes of the model and the dynamic range of the approximate surface array are obtained;

[0061] S72, set the initial task target value to f = -∞;

[0062] S73, using fuzzy simulation to generate input data of different surface array approximations for the model, and obtaining feasible surface arrays and node numbers that meet given requirements for credibility;

[0063] S74, substitute the data that meets the requirements into the model, and use the constraints and MPM related methods to check the feasibility of the input data; if feasible, store the generated data of the fuzzy simulation, and further calculate and store the current event target value f n , if f <f n , set f = f n , otherwise return to step S72;

[0064] S75, repeat steps S72 to S74 for a given number of times, and the obtained f is the optimistic value of the objective function that satisfies the given confidence level, and the fuzzy simulation generated data corresponding to f is the solution that satisfies the constraint conditions.

[0065] Beneficial effects:

[0066] The method for reconstructing the radiation pattern of an opportunity array radar of a dynamic multi-node platform of the present invention can utilize the constructed general model and solution method to establish corresponding planning models under different task requirements, effectively solve the system robustness problem caused by the dynamic environmental influence involved in the radiation pattern reconstruction problem in practical applications, and the node resources and location information of the opportunity array radar can be dynamically adjusted with the environmental tasks, which is more in line with practical applications, and realizes the characteristic of the opportunity array radar changing with circumstances, that is, adjusting system parameters according to different task requirements, which provides a certain reference for modeling and solving other problems involved in the opportunity array radar in the future. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 The basic flow chart of the present invention using fuzzy simulation to solve the model process;

[0068] Figure 2 It is a flow chart of the method for reconstructing the radar pattern of an opportunity array of a dynamic multi-node platform of the present invention;

[0069] Figure 3 It is a schematic diagram of the reconstruction error curve of the 12×12 uniform array;

[0070] Figure 4 are four array patterns that can be used for overall approximation;

[0071] Figure 5 It is the direction map reconstructed under the simultaneous decision model;

[0072] Figure 6 This is a schematic diagram of the node position distribution of the reconstructed directional graph under the simultaneous decision model;

[0073] Figure 7To reconstruct the directional graph under the hierarchical decision model with minimizing the number of nodes as the primary goal;

[0074] Figure 8 This is a schematic diagram of the node position distribution of the reconstruction direction graph under the hierarchical decision model with minimizing the number of nodes as the primary goal;

[0075] Fig. 9 To reconstruct the radiation pattern under the hierarchical decision model with the minimum main lobe width as the primary goal;

[0076] Fig.10 Schematic diagram of the node position distribution of the reconstructed pattern under the hierarchical decision model with the minimum main lobe width as the primary goal. DETAILED DESCRIPTION

[0077] The following examples will enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any way.

[0078] See also Figure 2 The present invention discloses a method for reconstructing a radar pattern of an opportunity array on a dynamic multi-node platform. The method comprises the following steps:

[0079] S1, according to actual needs, combined with the characteristics of the opportunity array radar itself, the comprehensive optimization target can be set to set one or more task requirements; the error effects including the maximum reconstruction error δ0, the maximum error of the sidelobe level δ2, and the maximum error of the main lobe width δ2 are used as constraint errors;

[0080] S2, obtain the minimum approximate array size M×N according to the task requirements;

[0081] S3, using the minimum approximable surface array to establish the Hank augmented matrix;

[0082] S4, obtain error parameters according to the constructed Hank augmented matrix;

[0083] S5, obtaining the range of the approximate surface array and the range of the number of reconstruction nodes;

[0084] S6, establish a dynamic multi-node directional graph synthesis model based on fuzzy chance constrained programming;

[0085] S7, uses a matrix beam algorithm of multi-surface array approximation and fuzzy simulation technology to solve the dynamic multi-node directional pattern synthesis model.

[0086] In step S1, for the variability of the target, due to the characteristics of the opportunity array radar itself (or the opportunity array radar pattern), the conditional constraints in the dynamic scene vary within a certain range, so the model task goal can be to minimize the main lobe width, minimize the side lobe level, or minimize the number of node resources, etc., or both; for multi-objective, the number of tasks or targets p in the present invention when reconstructing the pattern can be greater than or equal to 1. The constraints include: given demand constraint errors including the maximum reconstruction error δ0, the maximum side lobe level error δ2, the maximum main lobe width error δ2, etc. Then solve the credibility α, β that satisfies the task objectives and constraints, and the expected maximum main lobe B w , the expected minimum sidelobe level SL. According to the required minimum main lobe width B w It can be concluded that the size of the uniform array used for approximation is M×N.

[0087] In step S3, the method for constructing the Hank augmented matrix of the minimum array is as follows:

[0088] 1) Construct the target sampling pattern and uniformly sample all target patterns in the (u,v) plane, with the sampling interval being (-1,1). If the number of sampling points on the u and v axes are 2M+1 and 2N+1 respectively, then the sampling point of the p-th target pattern can be expressed as:

[0089]

[0090] in:

[0091]

[0092] 2) Construct the augmented matrix X e :

[0093]

[0094] In step S4, e Performing singular value decomposition yields:

[0095]

[0096] The superscript H stands for conjugate transpose, and:

[0097] Σ s =diag(σ1σ2...σ Q )

[0098] Σ n =diag(σ Q+1 σ Q+2 ... S )

[0099] diag is the function for constructing diagonal matrices, σS For X e non-zero singular values ​​of , and σ1≥σ2≥…≥σ s ≥0, the pattern approximation error is defined using the matrix singular value characteristics:

[0100]

[0101] In step S5, firstly, when the direction graph is reconstructed according to the task requirements and the approximation error ε≤ε0, the theoretical minimum number of reconstruction nodes can be obtained:

[0102]

[0103] The maximum number of reconstruction nodes is defined by using another parameter sparsity of directional pattern sparse reconstruction. If 90% of the minimum array that meets the requirements is taken, the maximum number of reconstruction nodes can be obtained:

[0104]

[0105] Based on this, the upper limit of the approximate array size M1×N1 is obtained:

[0106]

[0107] Step S6 can be divided into the following three steps:

[0108] 1) Define decision variables:

[0109] X=[X1 X2...X N-1 X N ];

[0110] X n represents the nth decision variable. If the first decision variable is the node working state, the decision variable X1 can be expressed as:

[0111] X1=[x1x2...x Np-1 x Np ]

[0112] x n =0 or 1, n=1,2,...,N p -1,N p

[0113] N p The maximum number of nodes that can be allocated for reconstructing the p-th task direction graph.

[0114] 2) Fuzzy quantity representation

[0115] Affected by the uncertainty of factors such as task target requirements in a dynamic environment, the number of nodes ξ required to synthesize the desired directional graph is uncertain, and it is impossible to obtain the random distribution of variables through a large number of repeated experiments in time. Therefore, fuzzy variables need to be used to describe it, as follows:

[0116]

[0117] In the above formula, p is the minimum number of units required to reconstruct the p-th task direction graph, and NS is the total number of all available nodes.

[0118] 3) Constraints expression

[0119] The constraints can include the number of nodes used in each directional graph, synthesis error, minimum reconstruction time and other factors. The constraints of the uncertain environment can be expressed by the following inequality group:

[0120]

[0121] 4) The general form of fuzzy chance-constrained programming for dynamic multi-node opportunity array radar:

[0122]

[0123] Two use case models are given according to different tasks - simultaneous decision-making and hierarchical decision-making models as follows:

[0124] (1) The simultaneous decision model is:

[0125]

[0126] Where err represents the reconstruction error, B(X) and SL(X) represent the actual main lobe width and reconstruction level after reconstruction; (2) The hierarchical decision model is:

[0127]

[0128] The solution of step (7) is mainly solved by the method of multi-faceted array approximation combined with fuzzy simulation. The specific steps are as follows:

[0129] Step 1): Use the Hank matrix X e The characteristic solution space of the model is used to transform the model events and environmental parameters, preprocess the model data, and obtain the dynamic range of the model reconstruction nodes and approximation array.

[0130] Step 2): Set the initial task target value to f = -∞;

[0131] Step 3): Use fuzzy simulation to generate input data of different array approximations for the model, and obtain feasible arrays and node numbers that meet given requirements;

[0132] Step 4): Substitute the data that meets the requirements into the model and use the constraints and MPM related methods to check the feasibility of the input data;

[0133] Step 5): If feasible, store the generated data of the fuzzy simulation, and further calculate and store the current event target value f n , if f <f n , set f = f n , otherwise return to step 2;

[0134] Step 6): Repeat steps 2 to 5 for a given number of times, and the resulting f is the optimistic value of the objective function that satisfies a given confidence level. The fuzzy simulation generated data corresponding to f is the solution that satisfies the constraint conditions.

[0135] Examples

[0136] The example mainly considers the single-target task, and takes the number of targets p as 1. If there are 200 dynamic nodes in the initial space, it is necessary to form a main-to-sub ratio of 20dB and a zero-to-zero main lobe width of less than 23° with as few nodes as possible. According to the requirements, the approximate uniform array is at least 12x12 after preliminary calculation. The reconstruction error represented by the singular value of the Hankel matrix constructed by the array is as follows Figure 3 As shown in the figure, it can be seen that the more nodes are used for single-plane array approximation, the smaller the error. Assume that the error requirement is at least less than 10 -2 , the sparsity cannot exceed 90%, so according to the calculation node number, the minimum number cannot be less than 58 and the maximum number cannot exceed 129. In order to ensure the robustness of the entire system, the actual task may require a larger array or a number of nodes higher than the theoretical minimum number of reconstruction units to approximate the reconstructed pattern to obtain a lower main lobe width or approximation error. Using formula (10), it is further concluded that the array size range is 12x12 to 19x19, Figure 4 There are several approximate arrays that meet the requirements within the range. It can be seen intuitively that the size of the array directly affects the main lobe width of the radiation pattern. The specific parameters of each array are shown in Table 1.

[0137] Table 1: Some uniform array pattern information that meets the requirements

[0138]

[0139]

[0140] According to expert experience and some experimental data, the number of reconstruction units is set to the trapezoidal fuzzy number ξ1 (57, 71, 97, 130), and the number of rows and columns of the approximation array unit is set to the trapezoidal fuzzy number ξ2 (11, 15, 17, 20). The above preprocessed data is substituted into the general model of fuzzy opportunity constraint programming of dynamic multi-node opportunity array radar, where ΔB is 23°, δ0 represents the maximum acceptable reconstruction error, which is -20dB, δ1 represents the acceptable error size between the maximum side lobe and -20dB, which is 3dB, and the minimum main lobe width B w Take 23°. Next, two models are further established according to different task requirements. The overall process of the fuzzy simulator in model solution is as follows: Figure 1 and Figure 2 shown.

[0141] Model 1: Simultaneous decision-making model. The task requirement is to ensure the smallest possible main lobe width and the number of reconstruction nodes. The following model can be obtained:

[0142]

[0143] λ determines the conditional weight of the task objective. If λ is 1, the task is to minimize the number of reconstruction elements as the only optimization objective. If λ is 0, the task is to minimize the main lobe width as the only optimization objective. Here, λ is taken as 0.5, that is, the credibility is maximized while ensuring that the number of reconstruction elements and the main lobe width are as small as possible. By solving, it can be concluded that the optimistic value of the objective function is 0.3615 under the condition of satisfying the given credibility of 0.9. At this time, a 15x15 array is selected for approximation, and the number of sparse elements is 87. Specifically, Figure 5 As shown. At this time, the corresponding maximum sidelobe is -17.39dB, the first zero point main lobe width is 18°, and the minimum spacing between positions is 0.0501 wavelength. That is, when the credibility is greater than 0.9, when the approximation array is 15x15 and the number of sparse nodes is 87, the established objective function value can be maximized.

[0144] Model 2: Hierarchical decision model. The task requires that the number of reconstruction nodes should be kept as small as possible, and the following two-level chance-constrained programming model can be obtained.

[0145]

[0146] Since the two objective functions are in an opposing relationship, if a larger β is directly given, it is easy to have no solution. For the solution of the above formula, first set the credibility of the minimum node number function objective value α = 0.8, and the corresponding optimistic value is 70. Then determine the confidence range of the minimum main lobe width β that can meet the requirements at this time, that is, the range of β that meets the constraints when the minimum number of nodes takes the optimistic value of α. Using the model solution, it can be concluded that β is less than or equal to 0.5, and the corresponding objective function value is 13. The approximation results and reconstructed coordinate positions are as follows: Figure 7 and Figure 8 shown.

[0147] At this time, the corresponding maximum sidelobe is -17.27dB, the first zero point main lobe width is 21.2°, and the minimum spacing between positions is 0.3636 wavelengths. That is, when the minimum number of nodes is 70 for the optimistic value of the confidence level of 0.9, the minimum width of the main lobe zero point can reach 21.2°.

[0148] Similarly, if minimizing the main lobe width is the priority optimization goal and minimizing the number of nodes is the secondary goal, the optimistic approximation array size with a confidence level of 0.9 can be obtained to be 17x17. At this time, the minimum number of nodes corresponding to a confidence level of 0.67 is 108. The simulation results are shown in the figure below. Fig. 9 and Fig.10 shown.

[0149] The item data obtained from the three types of tasks are shown in Table 2.

[0150] Table 2 Target simulation data results under three tasks

[0151]

[0152] It can be seen from Table 2 that the optimization results obtained under the same conditions are different for different task objectives. First, if the two objectives of minimizing the number of nodes and minimizing the sidelobe level are considered at the same time, it is necessary to ensure that the formulated objective function is solved under the condition that the credibility is met at the same time; if the two objectives are prioritized, although the result can further improve the optimization performance of the high-priority objective, due to the mutual constraints between the two objectives, the credibility and optimization results of the other objective will be reduced, which is consistent with the actual situation. Combining the simulation results and corresponding analysis of the above independent tasks, it is concluded that each result meets the constraints and task requirements, which further verifies the effectiveness of this model and solution algorithm. That is, for the reconstruction of the opportunity array pattern under uncertain conditions, this model and solution algorithm can achieve different expected optimization results when the target reaches the required credibility.

[0153] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A method for reconstructing the radar pattern of an opportunity array of a dynamic multi-node platform, characterized in that: The opportunity array radar pattern reconstruction method comprises the following steps: S1, according to actual needs, combined with the characteristics of the opportunity array radar itself, the comprehensive optimization target can be set to set one or more task requirements; the error effects including the maximum reconstruction error δ0, the maximum error of the main lobe width δ1, and the maximum error of the side lobe level δ2 are used as constraint errors; S2, obtain the minimum approximate array size M×N according to the task requirements; S3, using the minimum approximable surface array to establish the Hank augmented matrix; S4, obtain error parameters according to the constructed Hank augmented matrix; S5, obtaining the range of the approximate surface array and the range of the number of reconstruction nodes; S6, establish a dynamic multi-node directional graph synthesis model based on fuzzy chance constrained programming; S7, uses a matrix beam algorithm of multi-surface array approximation and fuzzy simulation technology to solve the dynamic multi-node directional pattern synthesis model.

2. The method for reconstructing the radar pattern of an opportunity array of a dynamic multi-node platform according to claim 1 is characterized in that: In step S1, the task requirement includes one or more of minimizing the main lobe width, minimizing the side lobe level, and minimizing the number of node resources.

3. The method for reconstructing the radar pattern of an opportunity array of a dynamic multi-node platform according to claim 1, characterized in that: Step S3 further comprises: Construct the target sampling pattern, and uniformly sample all target patterns in the (u, v) plane, with the sampling interval being (-1, 1); if the number of sampling points on the u and v axes is 2M+1 and 2N+1 respectively, the sampling point of the p-th target pattern is expressed as: in, and represents the horizontal and vertical coordinates of the nth array element on the coordinate axis, λ is the wavelength, w n The excitation of n array elements when reconstructing the target pattern; Construct the augmented matrix X e :

4. The method for reconstructing the radar pattern of an opportunity array of a dynamic multi-node platform according to claim 2, characterized in that: Step S4 further comprises: For the augmented matrix X e Perform singular value decomposition to obtain: Where U s and V s Indicates the main lobe direction, V n and U n represents the sidelobe direction, the superscript H represents the conjugate transpose, and: S s =diag(σ1σ2...σ Q ) S n =diag(σ Q+1 s Q+2 ...s S ) Where diag is the function for constructing a diagonal matrix, σ S For X e non-zero singular values ​​of , and σ1≥σ2≥…≥σ s ≥0, the singular value characteristics of the matrix are used to define the pattern approximation error ε: Where q is the intermediate parameter when approximating the error parameter.

5. The method for reconstructing the radar pattern of an opportunity array of a dynamic multi-node platform according to claim 1, characterized in that: Step S5 further comprises: According to the task requirements, the reconstructed directional graph approximation error ε≤ε0 is obtained, and the theoretical minimum number of reconstruction nodes Q1 is obtained: The sparse reconstruction sparsity of the directional graph is used to define the maximum number of reconstruction nodes. If 90% of the minimum array that meets the requirements is taken, the maximum number of reconstruction nodes Q2 is obtained: In the formula, Indicates rounding down; the upper limit of the approximate array size M1×N1 is obtained:

6. The method for reconstructing the radar pattern of an opportunity array of a dynamic multi-node platform according to claim 1, characterized in that: Step S6 further comprises: Define the decision variables: X=[X1 X2...X N-1 X N ] In the formula, X n represents the nth decision variable. If the first decision variable is the node working state, the decision variable X1 is expressed as: x n =0 or 1, n=1,2,...,N p -1,N p Where N p Reconstruct the maximum number of nodes that can be allocated for the p-th task direction graph; Define fuzzy variables: In the formula, ξ p The minimum number of units required to reconstruct the p-th task direction graph, NS is the total number of all available nodes; The constraints of the uncertain environment are expressed by the following set of inequalities: Wherein, the superscript (p) represents the pth task, δ is the error requirement of each constraint, δ0, δ1 and δ2 are the maximum reconstruction error, the maximum error of the main lobe width and the maximum error of the side lobe level, respectively, err is the error between the reconstructed pattern and the expected pattern, B(X1) is the main lobe width of the reconstructed pattern under the decision variable X1, and B w is the expected main lobe width, SL(X1) is the maximum sidelobe level under the decision variable X1, SL is the expected maximum sidelobe level, g0(X,ξ)…g J (X,ξ) represent the constraints encountered in practical applications; ξ1 is the minimum number of units required for the reconstruction of the first task direction graph; The general form of fuzzy chance constraint programming for dynamic multi-node opportunity array radar is obtained as follows: in is the optimistic value of maximizing the objective function, f(X,ξ) is the objective function, f1(X,ξ)...f I (X,ξ) are the various requirements encountered in actual situations, is the optimistic value of the maximization objective function corresponding to each demand, I is the total number of demands; β is the credibility requirement of the objective function; α is the confidence level that makes the constraint condition hold; G(X,ξ) is the fuzzy constraint, X is the decision vector, and ξ is the fuzzy vector.

7. The method for reconstructing the radar pattern of an opportunity array of a dynamic multi-node platform according to claim 6, characterized in that: In step S6, two different dynamic multi-node directional diagram comprehensive models are given according to different tasks: a simultaneous decision model and a hierarchical decision model; wherein the simultaneous decision model is: Where err represents the reconstruction error, B(X) and SL(X) represent the actual main lobe width and reconstruction level after reconstruction, respectively; is the optimistic value of maximizing the objective function; F(X,Y,ξ1,ξ2) is the objective function, which contains two decision variables X and Y; NS1 is the total number of all available nodes on the X axis, and NS2 is the total number of all available nodes on the Y axis; y n is the node working status, y n =0 or 1, ξ2 is the minimum number of units required for reconstructing the second task direction graph; The hierarchical decision model is: Where G(x,y,ξ) is the fuzzy constraint under the decision variables x and y.

8. The method for reconstructing the radar pattern of an opportunity array of a dynamic multi-node platform according to claim 1, characterized in that: Step S7 further comprises: S71, using Hank matrix X e The model events and environmental parameters are transformed in the characteristic solution space, the model data is preprocessed, and the reconstruction nodes of the model and the dynamic range of the approximate surface array are obtained; S72, set the initial task target value to f = -∞; S73, using fuzzy simulation to generate input data of different surface array approximations for the model, and obtaining feasible surface arrays and node numbers that meet given requirements for credibility; S74, substitute the data that meets the requirements into the model, and use the constraints and MPM related methods to check the feasibility of the input data; if feasible, store the generated data of the fuzzy simulation, and further calculate and store the current event target value f n , if f <f n , set f = f n , otherwise return to step S72; S75, repeat steps S72 to S74 for a given number of times, and the obtained f is the optimistic value of the objective function that satisfies the given confidence level, and the fuzzy simulation generated data corresponding to f is the solution that satisfies the constraint conditions.

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