An Opportunity Array Radar Pattern Reconstruction Method for a Dynamic Multi-Node Platform

Abstract

The present invention provides a method for reconstructing the direction pattern of an opportunistic array radar for a dynamic multi-node platform, including: initializing task objectives and constraint condition parameters; selecting fuzzy numbers according to requirements and establishing a fuzzy chance-constrained programming model for reconstructing the direction pattern of the dynamic multi-node opportunistic array radar; and solving the model by using the matrix pencil method combined with fuzzy simulation for multi-plane array approximation. The general model and solution method constructed by the present invention can establish corresponding programming models under different task requirements, effectively solve the problem of system robustness caused by the influence of the dynamic environment involved in the direction pattern reconstruction problem in practical applications, and the node resources and position information of the opportunistic array radar can be dynamically adjusted according to the environment tasks, which is more in line with practical applications, realizes the adaptability of the opportunistic array radar, that is, the characteristic of adjusting system parameters according to different task requirements, and provides a reference for modeling and solving other problems related to the opportunistic array radar.

Description

Technical Field

[0001] The present invention belongs to the technical field of institutional radar and opportunistic array radar, and particularly relates to a method for reconfiguring the pattern of an opportunistic array radar with a dynamic multi-node platform. Background Art

[0002] Limited by institutional factors, traditional radar systems, as a means of perception, are increasingly difficult to meet current requirements. For example, the fixed array size and operating wavelength often target fixed detection targets. Radars for long-range early warning are generally huge in volume, poor in flexibility, low in battlefield adaptability, have blind areas at low elevation angles, the aperture size is limited by the carrier platform, and the combat functions are single. The opportunistic array radar is designed with the platform as the core and has the advantages of stealth, flexibility, multi-functional integration, etc. Its working state can be reorganized for opportunistic units or local modules through opportunistic decision-making according to changes in external conditions, different targets or different scenario task requirements to maximize the combat ability and survival ability of the platform.

[0003] Theoretically, in addition to the platform-centered design approach with good stealth performance, the flexibility and versatility are important manifestations of the opportunity array radar. In research, it is mainly reflected in the interpretation and application research of the opportunity concept. Since in a dynamic scenario, whether it is the environment, target, or mission requirements, they are all uncertain, and the various parameters involved are random. Using the conventional random concept cannot describe variables with unknown probability density, and a large number of repeated experiments are required for estimation, which is not desired and difficult to conduct in most scenarios. Currently, a more common approach 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 a credibility measure with self-duality has been proposed, and a complete credibility theory system has been established. Clear definitions have been given for various uncertain parameters including random, fuzzy, rough, and random rough, and the modeling mechanisms of the expected value model, chance-constrained programming, and related-chance programming have been given. The fundamental mathematical problem that the opportunity array radar needs to solve is to model, optimize, and solve the non-deterministic factors in the real-time environment according to requirements and make dynamic adjustments. The existing research on the pattern synthesis problem of the opportunity array radar mainly reflects in three aspects. First, the mathematical modeling and solution of the opportunity array radar on different platforms. Since the opportunity array radar has a platform-centered design framework, the corresponding models for different platforms are different. Second, the constraint programming models required for different mission requirements are different. In the same scenario, for a mission, according to requirements, it can be to minimize the main lobe width, minimize the number of nodes, minimize the sidelobe level, or a combination of multiple situations, etc. Finally, the selection of uncertain factors in the model. Different mission requirements and environments often correspond to different uncertain parameters, and some uncertain parameters play a decisive role in the solution of the model. Currently, for the research on the pattern synthesis problem of the opportunity array radar, Gong has given preliminary conclusions, but mainly for the optimization selection of randomly arranged array elements with fixed initial positions, and the applicable platform is more suitable for conformal arrays. Currently, there has been extensive research on the pattern synthesis problem of sparse arrays under conventional conditions, and its related solution algorithms mainly include mathematical analytical methods based on the matrix pencil and its extended algorithms based on singular value approximation, heuristic intelligent optimization solution algorithms based on genetic algorithms, differential evolution algorithms, ant colony algorithms, etc., and iterative Fourier algorithms. However, the modeling and solution of the pattern synthesis problem with uncertain parameters in the dynamic scenario of the opportunity array radar still need in-depth research, especially considering the flexible reconfiguration characteristics of the opportunity array radar itself. Therefore, the present invention mainly proposes an effective model and solution algorithm for the pattern reconstruction problem of the opportunity array radar on a 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 pattern of an opportunistic array radar on a dynamic multi-node platform, mainly solving two aspects of problems: (1) the problem that traditional sparse node pattern synthesis does not consider the influence of dynamic variables in actual applications, lacks the robustness of the overall system, and does not conform to actual applications; (2) the problem of pattern reconstruction of an opportunistic array radar when there are uncertain factors in a dynamic multi-node platform.

[0005] Technical solution:

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

[0007] S1. According to actual requirements, combining the characteristics of the opportunistic array radar itself to optimize the target, set one or more task requirements; regard the error influences including the maximum reconstruction error δ0, the maximum error of the main lobe width δ1, and the maximum error of the sidelobe level δ2 as constraint errors;

[0008] S2. Obtain the minimum approximable planar array size M×N according to the task requirements;

[0009] S3. Use the minimum approximable planar array to establish a Hankel augmented matrix;

[0010] S4. Obtain error parameters according to the constructed Hankel augmented matrix;

[0011] S5. Obtain the range of the approximable planar array and the range of the number of reconstructed nodes;

[0012] S6. Establish a dynamic multi-node pattern synthesis model based on fuzzy chance-constrained programming;

[0013] S7. Use the matrix pencil algorithm and fuzzy simulation technology of multi-planar array approximation to solve the dynamic multi-node pattern synthesis model.

[0014] In step S1, the task requirements include one or more of minimizing the main lobe width, minimizing the sidelobe level, and minimizing the number of node resources.

[0015] Step S3 further includes:

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

[0017]

[0018] Among them, and represent the abscissa and ordinate of the nth array element on the coordinate axis, λ is the wavelength, and w n is the excitation of the n array elements during the reconstruction of the target pattern;

[0019] Construct the augmented matrix X e :

[0020]

[0021] Step S4 further includes:

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

[0023]

[0024] where U s and V s represent the main lobe direction, V n and U n represent the side lobe direction. The superscript H represents the conjugate transpose, and:

[0025] Σ s = diag(σ1 σ2...σ Q )

[0026] Σ n = diag(σ Q+1 σ Q+2 ...σ S )

[0027] where diag is the function to construct a diagonal matrix, and σ S is the non-zero singular value of X e , and σ1 ≥ σ2 ≥ … ≥ σ s ≥ 0. Use the matrix singular value property to define the pattern approximation error ε:

[0028]

[0029] where q is the intermediate parameter of the approximation error parameter.

[0030] Step S5 further includes:

[0031] Reconstruct the pattern approximation error ε ≤ ε0 according to the task requirements to obtain the theoretical minimum reconstruction node number Q1:

[0032]

[0033] Define the maximum reconstruction node number using the pattern sparse reconstruction sparsity. If 90% of the smallest planar array that meets the requirements is taken, the maximum reconstruction node number Q2 is obtained:

[0034]

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

[0036]

[0037] Step S6 further includes:

[0038] Define 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 represented as:

[0041]

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

[0043] In the formula, N p is the maximum number of nodes that can be allocated for the pth task pattern reconstruction;

[0044] Define fuzzy variables:

[0045]

[0046] In the formula, ξ p is the minimum number of units required for the pth task pattern reconstruction, and NS is the total number of all available nodes;

[0047] The constraint conditions of the uncertain environment are represented by the following inequality group:

[0048]

[0049] In the formula, the superscript (p) represents the pth task, δ is the error requirement of each constraint condition, δ0, δ1, and δ2 are the maximum reconstruction error, the maximum main lobe width error, and the maximum sidelobe level error 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, 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) respectively represent the constraints encountered in actual applications; ξ1 is the minimum number of units required for the first task pattern reconstruction;​

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

[0051]

[0052] where is the optimistic value of the maximized objective function, f(X,ξ) is the objective function, f1(X,ξ)...f I (X,ξ) are the various requirements encountered in the actual situation, are the optimistic values of the maximized objective functions corresponding to the various requirements, I is the total number of requirements; β is the credibility requirement of the objective function; α is the confidence level such that the constraint conditions 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 pattern synthesis models are given according to different tasks: the simultaneous decision-making and the hierarchical decision-making models; among them, the simultaneous decision-making model is:

[0054]

[0055] where err represents the reconstruction error, B(X) and SL(X) respectively represent the main lobe width and the reconstruction level after actual reconstruction; is the optimistic value of the maximized 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, NS2 is the total number of all available nodes on the Y-axis; y n is the node working state, y n = 0 or 1, and ξ2 is the minimum number of cells required for the reconstruction of the second task pattern;

[0056] The hierarchical decision-making model is:

[0057]

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

[0059] Step S7 further includes:

[0060] S71, using the eigen-solution space of the Hankel matrix X e to transform the model events and environmental parameters, preprocess the model data, and obtain the reconstruction nodes of the model and the dynamic range of the approximated planar array;

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

[0062] S73. Use fuzzy simulation to generate input data for different planar array approximations for the model, and obtain a feasible planar array and the number of nodes whose credibility meets the given requirements;

[0063] S74. Substitute the data that meets the requirements into the model, and use the constraint conditions and related MPM methods to check the feasibility of the input data; if it is feasible, store the generated data of the fuzzy simulation, and further calculate and store the current event objective 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. The obtained f is the optimistic value of the objective function that meets the given confidence level, and the fuzzy simulation generated data corresponding to f is the solution that meets the constraint conditions of the requirements.

[0065] Beneficial effects:

[0066] The method for reconstructing the pattern of an opportunity array radar for a dynamic multi-node platform according to the present invention can use the constructed general model and solution method to establish a corresponding planning model under different task requirements, effectively solve the problem of system robustness caused by the influence of the dynamic environment involved in the pattern reconstruction problem in practical applications. The node resources and position information of the opportunity array radar can be dynamically adjusted according to the environment and tasks, which is more in line with practical applications, realizes the adaptability of the opportunity array radar, that is, the characteristic of adjusting system parameters according to different task requirements, and provides a certain reference for modeling and solving other problems related to opportunity array radars in the future. Description of the drawings

[0067] Figure 1 It is the basic flowchart of using fuzzy simulation in the process of solving the model according to the present invention;

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

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

[0070] Figure 4 They are the pattern diagrams of four planar arrays that can be used for overall approximation;

[0071] Figure 5 It is the pattern reconstructed under the simultaneous decision-making model;

[0072] Figure 6 It is a schematic diagram of the node position distribution of the pattern reconstructed under the simultaneous decision-making model;

[0073] Figure 7Reconstruct the direction diagram under a hierarchical decision-making model with minimizing the number of nodes as the primary goal;

[0074] Figure 8 Schematic diagram of the node position distribution of the reconstructed direction diagram under a hierarchical decision-making model with minimizing the number of nodes as the primary goal;

[0075] Figure 9 Reconstruct the direction diagram under a hierarchical decision-making model with minimizing the main lobe width as the primary goal;

[0076] Figure 10 Schematic diagram of the node position distribution of the reconstructed direction diagram under a hierarchical decision-making model with minimizing the main lobe width as the primary goal. Detailed implementation manners

[0077] The following embodiments can enable those skilled in the art to understand the present invention more comprehensively, but do not limit the present invention in any way.

[0078] Refer to Figure 2 , the present invention discloses an opportunity array radar direction diagram reconstruction method for a dynamic multi-node platform, and the opportunity array radar direction diagram reconstruction method includes the following steps:

[0079] S1. According to actual requirements, comprehensively optimize the target in combination with the characteristics of the opportunity array radar itself, and set one or more task requirements; take the error influences including the maximum reconstruction error δ0, the maximum sidelobe level error δ2, and the maximum main lobe width error δ2 as the constraint errors;

[0080] S2. Obtain the minimum approximable planar array size M×N according to the task requirements;

[0081] S3. Establish a Hankel augmented matrix using the minimum approximable planar array;

[0082] S4. Obtain the error parameters according to the constructed Hankel augmented matrix;

[0083] S5. Obtain the range of the approximable planar array and the range of the number of reconstructed nodes;

[0084] S6. Establish a dynamic multi-node direction diagram synthesis model based on fuzzy chance-constrained programming;

[0085] S7. Solve the dynamic multi-node direction diagram synthesis model by using the matrix pencil algorithm and fuzzy simulation technology of multi-planar array approximation.

[0086] In step S1, for the variability of the target, due to the characteristics of the opportunistic array radar itself (or the pattern of the opportunistic array radar), the conditional constraints in the dynamic scenario vary within a certain range. Therefore, the model task objectives can be to minimize the main lobe width, minimize the sidelobe level, minimize the number of node resources, etc., or a combination of them. For the multi-objective nature, the number p of tasks or objectives in the pattern reconstruction of the present invention can be greater than or equal to 1. The constraint conditions include given demand constraint errors such as the maximum reconstruction error δ0, the maximum sidelobe level error δ2, and the maximum main lobe width error δ2. Then, the credibility α, β that satisfy the task objectives and constraint conditions and the expected maximum main lobe B w are solved, and the expected minimum sidelobe level SL is obtained. According to the required minimum main lobe width B w the size of the uniform planar array for approximation can be obtained as M×N.

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

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

[0089]

[0090] where:

[0091]

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

[0093]

[0094] In step S4, performing singular value decomposition on X e can obtain:

[0095]

[0096] The superscript H represents the conjugate transpose, and:

[0097] Σ s = diag(σ1 σ2... σ Q )

[0098] Σ n = diag(σ Q+1 σ Q+2 ... σ S )

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

[0100]

[0101] In step S5, first, when reconstructing the directivity pattern approximation error ε≤ε0 according to the task requirements, 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 the directivity pattern sparse reconstruction. If 90% of the minimum face array that meets the requirements is taken, the maximum number of reconstruction nodes can be obtained:

[0104]

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

[0106]

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

[0108] 1) Define the decision variable:

[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 is the maximum number of nodes that can be allocated for the pth task directivity pattern reconstruction.

[0114] 2) Fuzzy quantity representation

[0115] ​Affected by the uncertainty of factors such as task objective requirements in a dynamic environment, the number of nodes ξ required to synthesize the expected radiation pattern is uncertain, and it is also impossible to obtain the random distribution of variables through a large number of actual repeated experiments in a timely manner. Therefore, fuzzy variables need to be used to describe it, as follows:

[0116]

[0117] In the above formula, ξ p is the minimum number of units required for the reconstruction of the p-th task radiation pattern, and NS is the total number of all available nodes.

[0118] 3) Constraint condition representation

[0119] The constraint conditions can include multiple factors such as the number of nodes used for each radiation pattern synthesis, synthesis error, minimum reconstruction time, etc. Then the constraint conditions in the uncertain environment can be represented by the following inequality group:

[0120]

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

[0122]

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

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

[0125]

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

[0127]

[0128] The solution of step (7) mainly uses the method of polyhedron array approximation combined with fuzzy simulation for solution, and the specific steps are as follows

[0129] Step 1): Use the eigen-solution space of the Hankel matrix X e to transform the model events and environmental parameters, preprocess the model data, and obtain the reconstruction nodes of the model and the dynamic range of the approximation array

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

[0131] Step 3): Use fuzzy simulation to generate input data for different array approximations of the model, and obtain feasible arrays and the number of nodes whose credibility meets the given requirements;

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

[0133] Step 5): If it is feasible, store the generated data of the fuzzy simulation, and further calculate and store the current event objective 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. The obtained f is the optimistic value of the objective function that meets the given confidence level, and the fuzzy simulation generated data corresponding to f is the solution that meets the constraint conditions of the demand.

[0135] Example

[0136] The example mainly considers a single-objective task. Take the number of objectives p as 1. If there are 200 dynamic nodes in the initial space, it is required to form a main-to-secondary ratio of 20 dB with as few nodes as possible, and the null main lobe width is less than 23°. According to the requirements, after preliminary calculation, the approximate uniform planar array is at least 12x12. The reconstruction error represented by the singular value of the Hankel matrix constructed by this planar array is as Figure 3 shown. It can be seen that the more nodes are used for the approximation of the single-sided planar array, the smaller the error. Assume that the error requirement is at least less than 10 -2 , and the sparsity cannot exceed 90%. Then, according to the calculation, the minimum number of nodes cannot be less than 58 and the maximum cannot exceed 129. In actual tasks, in order to ensure the robustness of the entire system, it may be necessary to use a larger planar array or a number of nodes higher than the theoretical minimum reconstruction unit number to approximate the reconstructed pattern in order to obtain a lower main lobe width or approximate error, etc. Using Equation (10), the range of the planar array size is further obtained as 12x12 to 19x19. Figure 4 are several approximate planar arrays that meet the requirements within the range. It can be directly seen that the size of the planar array directly affects the main lobe width of the pattern. The specific parameters of each planar array are shown in Table 1.

[0137] Table 1 Information on the patterns of some uniform planar arrays that meet the requirements

[0138]

[0139]

[0140] Set the number of reconstruction units as the trapezoidal fuzzy number ξ1(57, 71, 97, 130) according to expert experience and some experimental data, and the number of rows and columns of the approximation plane array units as the trapezoidal fuzzy number ξ2(11, 15, 17, 20). Substitute the above preprocessed data into the general model of the dynamic multi-node opportunistic array radar fuzzy chance-constrained programming, where ΔB is taken as 23°, δ0 represents the maximum acceptable reconstruction error, with a value of -20 dB, δ1 represents the acceptable error size between the maximum sidelobe and -20 dB, taken as 3 dB, and the minimum main lobe width B w is taken as 23°. Next, two models are further established according to different task requirements. The overall process of the fuzzy simulator in model solving is as Figure 1 and Figure 2 shown.

[0141] Model 1: Simultaneous decision-making model. The task requirement is to simultaneously ensure as small a main lobe width and as few reconstruction nodes as possible. The following model can be obtained:

[0142]

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

[0144] Model 2: Hierarchical decision-making model. The task requirement is to first ensure as few reconstruction nodes as possible, and the following two-layer chance-constrained programming model can be obtained.

[0145]

[0146] Since the two objective functions are in an adversarial relationship, if a relatively large β is directly given, it is likely to result in no solution. For the solution of the above equation, first set the confidence level α of the objective value of the minimum node number function to 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 satisfies the constraint conditions under the premise of taking the α optimistic value of the minimum node number. Using the model to solve, it can be obtained that β is less than or equal to 0.5, and the corresponding objective function value at this time is 13. The approximation result and the reconstructed coordinate positions are as Figure 7 and Figure 8 shown.

[0147] The corresponding maximum sidelobe at this time is -17.27 dB, the main lobe width at the first null is 21.2°, and the minimum spacing between positions is 0.3636 wavelengths. That is, when the optimistic value of the confidence level 0.9 can take the minimum number of nodes as 70, the minimum main lobe null width 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 value of the confidence level 0.9 approaches the phased array size of 17x17, and the corresponding minimum number of nodes with a confidence level of 0.67 is 108. The obtained simulation results are as Figure 9 and Figure 10 shown.

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

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

[0151]

[0152] It can be seen from Table 2 that for different task objective requirements, the optimization results obtained under the same conditions are different. First, if both minimizing the number of nodes and minimizing the sidelobe level are considered, then it is necessary to ensure that the objective function is solved under the condition that the confidence levels are simultaneously satisfied; if priorities are assigned to the two objectives, although the optimization performance of the objective with higher priority can be further improved, due to the mutually restrictive relationship between these two objectives, the confidence level and optimization result of the other objective will be reduced, which is in line with the actual situation. Combining the simulation results and corresponding analyses of each independent task above, it is further verified that each result meets the constraint conditions and task requirements, which verifies the effectiveness of the present model and solution algorithm. That is, for the problem of opportunity array pattern reconstruction under uncertain conditions, the present model and solution algorithm can achieve different desired optimization results when the objectives reach the required confidence levels.

[0153] The above are only the preferred embodiments of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should be regarded as within 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, using matrix beam algorithm of multi-surface array approximation and fuzzy simulation technology to solve the dynamic multi-node pattern synthesis model; 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.

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: ∑ 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: Reconstruct the direction map according to the task requirements. Approximation error ε≤ε 0， Get the theoretical minimum number of reconstruction nodes Q1: 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 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.

Images