A measurement matrix construction method suitable for moment method based on compressed sensing

Abstract

The present invention discloses a measurement matrix construction method suitable for the moment method based on compressed sensing, which relates to the field of electromagnetic numerical calculation and enables the moment method based on compressed sensing to obtain deterministic calculation results. First, the number of rows of the extracted impedance matrix is ​​determined based on the number of characteristic basis functions serving as a sparse basis. Then, the extraction interval step size is determined based on the number of rows to be extracted. Finally, the impedance matrix and excitation vector are uniformly extracted according to a fixed step size to construct a deterministic measurement matrix and measurement values. The present invention provides a new measurement matrix construction method for the moment method based on compressed sensing, which solves the problem of unstable calculation results caused by the traditional random construction of the measurement matrix.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic numerical calculation, and in particular to a measurement matrix construction method suitable for a moment method based on compressed sensing. Background Art

[0002] As an effective electromagnetic numerical algorithm, the method of moments (MoM) is often used to analyze the electromagnetic scattering characteristics of targets. However, the matrix equations in the MoM are complex to solve, consuming significant time and memory when solving scattering problems involving electrically large targets. The compressed sensing-based method of moments (CS-MoM) introduces compressed sensing technology into the MoM, effectively reducing the complexity of solving the matrix equations. Its key concept is to treat the induced current as the raw signal and then efficiently solve it through sparse, measurement, and reconstruction techniques. Existing techniques typically construct the measurement matrix by randomly extracting a few rows from the impedance matrix or by left-multiplying it with a low-dimensional random Gaussian matrix. Because the measurement matrix constructed by this method is random, uncertainty in the calculation results is unavoidable. Summary of the Invention

[0003] The present invention aims to provide a method for constructing a measurement matrix for the compressed sensing-based method of moments (CS-MoM) to address the uncertainty in the calculation results. This method constructs the measurement matrix by uniformly extracting a small number of rows from the impedance matrix at a fixed step size. This deterministic measurement matrix can produce deterministic calculation results.

[0004] To achieve the above objectives, the basic steps of implementing the technical solution of the present invention are as follows:

[0005] Step 1: Use characteristic basis functions to perform sparse transformation on the induced current, and determine the number of rows of the impedance matrix to be extracted according to the number of characteristic basis functions.

[0006] Step 2: The number of rows to be extracted determines the extraction step size, and the impedance matrix and excitation vector are uniformly extracted row by row, starting from the first row. The rows of the extracted impedance matrix are combined to construct the measurement matrix, and the corresponding excitation vector values ​​are combined as the measurement values.

[0007] Step 3: Construct a compressed sensing model from the measurement matrix and measurement values ​​and solve for the induced current.

[0008] Compared with the prior art, the present invention has the advantage that the measurement matrix constructed by the fixed-step uniform extraction method is a deterministic measurement matrix. Once the number of characteristic basis functions is determined, the constructed measurement matrix is ​​unique, thereby obtaining a unique and deterministic calculation result. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 The basic flow chart of the method of the present invention is shown in FIG.

[0010] Figure 2 Schematic diagram of the calculation results of the method of the present invention. DETAILED DESCRIPTION

[0011] The basic flow diagram of the method of the present invention is as follows Figure 1 As shown, the implementation of the technical solution is further described in detail below with reference to the accompanying drawings:

[0012] Step 1: Divide the conductor target surface into m smaller subdomains, calculate the main characteristic basis function and secondary characteristic basis function of each subdomain respectively, and perform sparse transformation on the induced current:

[0013]

[0014] Where, I is the induced current, J CBF represents the characteristic basis function, and α is the weight coefficient of the basis function. If the total number of characteristic basis functions is P, the number of rows of the impedance matrix to be extracted is determined as M = kP. Generally, k is 3-5.

[0015] Step 2: Determine the extraction interval s based on the number of rows to be extracted M, and s is close to An integer where N is the number of unknowns. Starting from the first row of the impedance matrix Z, extract every s rows and extract the corresponding elements in the excitation vector V. The measurement matrix is ​​constructed from the rows in the extracted impedance matrix The corresponding excitation vector elements constitute the measurement value

[0016] Step 3: Convert the matrix equation ZI=V in the moment method into a compressed sensing calculation model:

[0017]

[0018] Then, the coefficient vector α is reconstructed using a reconstruction algorithm, and the induced current I is obtained.

[0019] The method of the present invention is further illustrated below using a specific example. Obviously, the described embodiment is only a portion of the embodiments of the present invention, not all of the embodiments. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0020] The present invention takes the calculation of the bistatic radar cross section (RCS) of a conducting cube with a side length of 1m as an example. The incident excitation is a plane wave with an angle of The frequency is 800MHz. The cube surface is divided at a spacing of 0.1λ (λ is the wavelength of the incident plane wave), resulting in a total of 24,309 unknowns. The target is divided into 26 subdomains. The method of the present invention and the traditional CS-MoM are used to solve the problem respectively. Among them, the number of characteristic basis functions obtained is 676. k is set to 4. In the traditional CS-MoM, a random row-by-row extraction method is used to construct the measurement matrix. In this method, the uniform extraction step size s is 8. 5,000 simulation experiments were carried out using these two methods, and the RCS errors of the experimental results were sorted in ascending order, as shown below. Figure 2 As shown. Figure 2 It can be seen that the RCS error obtained by the traditional CS-MoM is unstable, while the RCS error obtained by the method of the present invention is stable and approximately the average value of the traditional CS-MoM. This example verifies the effectiveness of the method of the present invention.

[0021] In summary, the present invention adopts a method of uniformly extracting an impedance matrix at a fixed step size to construct a deterministic measurement matrix, thereby improving the stability of the results of the compressed sensing-based moment method.

Claims

1. A method for constructing a measurement matrix suitable for the moment method based on compressed sensing, characterized in that: Here are the steps: Step 1: Use characteristic basis functions to perform sparse transformation on the induced current. Where, I is the induced current, J CBF represents the characteristic basis function, α is the weight coefficient of the basis function, if the number of all characteristic basis functions is P, the number of rows of the impedance matrix to be extracted is determined according to the number of characteristic basis functions, M = kP, where k is 3; Step 2: The extraction step size is determined by the number of rows to be extracted, and the impedance matrix and excitation vector are uniformly extracted row by row starting from the first row. The rows of the extracted impedance matrix are combined to construct the measurement matrix, and the corresponding excitation vector values ​​are combined as the measurement values. The measurement matrix constructed by uniform extraction at a fixed step size is a deterministic measurement matrix. In step 2, the number of rows to be extracted M determines the extraction interval s, and s is close to An integer where N is the number of unknowns. Starting from the first row of the impedance matrix Z, extract one row every s rows and extract the corresponding elements in the excitation vector V. The measurement matrix is ​​constructed from the rows in the extracted impedance matrix. The corresponding excitation vector elements constitute the measurement value Step 3: Construct a compressed sensing model based on the measurement matrix and measurement values ​​and solve for the induced current; The matrix equation ZI=V in the moment method is transformed into a compressed sensing calculation model: Then, the coefficient vector α is reconstructed using a reconstruction algorithm, and the induced current I is obtained.

Images