Target RCS near-field measurement method based on probe compensation and phase center correction

Abstract

The present invention proposes a target RCS near-field measurement method based on probe compensation and phase center correction. The implementation steps are: obtaining echo signals from the target to be measured and a calibration object; performing phase center correction on the echo signals; performing time selection and range compensation on the corrected echo signals; obtaining spectral expansion coefficients of the target to be measured and the calibration object; performing scanning probe compensation on the spectral expansion coefficients; and obtaining target RCS near-field measurement results. In the process of obtaining target RCS near-field measurement results, the present invention performs phase center correction on the echo signals and performs scanning probe compensation on the spectral expansion coefficients. This avoids the defects of the prior art, such as delays in head sampling and the influence of the radiation characteristics of the scanning probe itself on the data obtained during the sampling process, which can lead to errors in the far-field extrapolation results. This effectively improves measurement accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic measurement technology and relates to a radar electromagnetic cross-section (RCS) measurement method, specifically to a target RCS near-field measurement method based on probe compensation and phase center correction, which can be used in the design, development and maintenance of various aircraft. Background Art

[0002] Electromagnetic scattering measurement is primarily used to measure the scattering characteristics of a target, typically measured by the radar cross section (RCS). With the advancement of radar technology, the research and design of various aircraft and electromagnetic equipment have become inseparable from RCS measurement technology. RCS measurement can generally be categorized into far-field, compact-field, and near-field methods, depending on the measurement site. For electrically large targets, far-field RCS measurement requires a very long test site and high-power test equipment, and measurement accuracy is easily affected by the test environment. Compact-field measurement can significantly shorten the test distance, but the required parabolic array is expensive, and the equipment operation and maintenance costs are high. Near-field measurement, as an emerging technology, offers advantages such as short test distance, low investment cost, indoor operation, strong confidentiality, high measurement accuracy, large information content, and all-weather operation. Near-field measurement uses a scanning probe to collect scattering data within the near-radiation zone of the target. This data is then extrapolated through specific data processing methods to determine the target's far-field RCS.

[0003] However, in the RCS near-field measurement methods currently proposed by academia, the influence of scanning probes has not been taken seriously. In test theory, scanning probes are often considered to be ideal probes, and their radiation characteristics are negligible. However, in actual tests, the radiation characteristics of the probe itself will affect the data obtained during the sampling process. Mathematically, this is reflected as a superposition of fields, that is, the directional pattern of the antenna constituting the scanning probe is superimposed on the measurement data, which will cause errors in far-field extrapolation. At the same time, when sampling, there will be a delay in probe sampling compared to the ideal situation. Converting the delayed data into a continuous signal will cause the phase center of the obtained echo signal to shift, thereby affecting the accuracy of subsequent data processing. For example, He Xinyi, Tong Guangde, Xu Xiuli, and Liao Yi disclosed a near-field to far-field conversion method for near-field local illumination target scattering in their patent application number 202111020081.8 filed on November 2, 2021, titled "A near-field to far-field conversion method for near-field local illumination target scattering". The method first divides the target into P scattering areas, performs 2D plane sampling on each scattering area in sequence, obtains the 2D near-field scattering data of each sampling point, and then obtains the 2D near-field test antenna received echo signal expression, performs far-field extrapolation on the 2D near-field scattering data of the scattering area, obtains the 2D far-field scattering characteristic quantity of the scattering area, performs total field synthesis on the 2D far-field scattering characteristic quantities of each scattering area, and calculates the overall RCS of the target based on the RCS relationship. This method can integrate target segmentation and near-field conversion, and can perform dimensionality reduction from three-dimensional to two-dimensional, so as to quickly and conveniently obtain the target RCS. However, its shortcomings are: after obtaining the near-field data, the delay problem is not considered, and the sampled data is directly processed, which will cause a phase offset in the echo signal expression. Before performing far-field extrapolation, the radiation characteristics of the probe itself are not considered, which will affect the data obtained during the sampling process, resulting in errors in the final target RCS near-field measurement. Summary of the Invention

[0004] The purpose of the present invention is to address the shortcomings of the above-mentioned prior art and propose a target RCS near-field measurement method based on probe compensation and phase center correction, so as to solve the technical problems existing in the prior art that the measurement accuracy is reduced due to ignoring the influence of the scanning probe and the delay of the probe sampling.

[0005] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0006] (1) Obtain the echo signals of the target to be measured and the calibration object:

[0007] (1a) Initialize the scanning probe to The distance from the origin of the polar coordinate system to the polar coordinate axis angle coordinate is R mea The working frequency of the scanning probe is f, and the far-field cross-sectional patterns of its transmitting and receiving ends are ET 、E R ; The radius of the spherical calibration body required for measurement is r sph , its far-field radar cross-section at frequency f is The object to be measured and the calibration body are located at the origin of the polar coordinate system during measurement;

[0008] (1b) The scanning probe takes the origin of the polar coordinate system as the center and R mea The radius of the target to be measured, the calibration object and the empty background are sampled uniformly L times, and the S of the target to be measured, the calibration object and the empty background are obtained. 21 Data U0={U 01 ,U 02 ,...,U 0l ,...,U 0L}、U1={U 11 ,U 12 ,...,U 1l ,...,U 1L} and U2={U 21 ,U 22 ,...,U 2l ,...,U 2L}, where l∈{1,2,...,L}, L≥100;

[0009] (1c) Calculate S for each target to be measured 21 Data U 0l , S of each calibration body 21 Data U 1l The corresponding empty background S 21 Data U 2l The difference between the two is used to obtain the discrete echo data of the target to be measured U'0={U' 01 ,U' 02 ,...,U' 0l ,...,U' 0L}、Discrete echo data of calibration body U'1={U' 11 ,U' 12 ,...,U' 1l ,...,U' 1L}, and transform U'0 and U'1 into continuous echo signals of the target to be measured respectively through the Nyquist theorem Echo signal of the calibration body

[0010] (2) Perform phase center correction on the echo signal:

[0011] Calculate the phase offset R between the echo signal of the target to be measured and the calibration object del and through R del Echo signal of the target to be measured Echo signal of the calibration body Perform phase center correction respectively to obtain the corrected echo signal of the target to be measured Calibration body echo signal

[0012]

[0013]

[0014] Where p∈{0,1}, c is the speed of light in vacuum, e is the natural logarithm, j is an imaginary number, t peak It is the time length from the issuance of the sampling instruction to the receipt of the echo data;

[0015] (3) Perform time selection and range compensation on the corrected echo signal:

[0016] (3a) The Hamming window function Ham(·) is used to correct the target echo signal. Calibration body echo signal Perform time selection to obtain the echo signal of the target to be measured after time selection Calibration body echo signal

[0017]

[0018] Where R0 represents the distance from the geometric center of the smallest cube with a side length of D that can enclose the object to be measured to the scanning probe;

[0019] (3b) Use the gate function G(R0) to correct the target echo signal Calibration body echo signal Perform range compensation to obtain the echo signal of the target to be measured after distance compensation Calibration body echo signal

[0020]

[0021]

[0022] where R gate is the range threshold, a is the compensation coefficient, a∈[0,2];

[0023] (4) Obtain the spectrum expansion coefficients of the target to be measured and the calibration object:

[0024] Echo signal of the target to be measured after distance compensation Calibration body echo signal Perform inverse Fourier transform respectively to obtain the spectrum expansion coefficients B0 of the target to be measured and the calibration body.0-N ,...,B 0n ,...,B 0N}、B1={B 1-N ,...,B 1n ,...,B 1N}, where n represents the spectral expansion order of the target to be measured and the calibration body, N represents the truncation order of the target to be measured and the calibration body, and

[0025] (5) Scanning probe compensation for spectral expansion coefficient:

[0026] (5a) Far-field cross-sectional pattern E of the transmitting and receiving ends of the scanning probe T and E R Perform integral transformation and calculate the spectrum expansion coefficient under local coordinates obtained by integral transformation Perform transfer transformation to obtain the probe spectrum expansion coefficient in global coordinates Where m represents the spectral expansion order of the scanning probe, M represents the truncation order of the scanning probe, and

[0027] (5b) The spectral expansion coefficient P of the scanning probe in the global coordinate TR Perform probe compensation on the spectral expansion coefficients B0 and B1 of the target to be measured and the calibration body respectively, and obtain the spectral expansion coefficients of the target to be measured and the calibration body after compensation. The calculation formula for each spectrum expansion coefficient is:

[0028]

[0029] (6) Obtain target RCS near-field measurement results:

[0030] Spectral expansion coefficient of the target to be measured and the calibration body after compensation Perform far-field extrapolation respectively to obtain the far-field radar cross-sectional area of ​​the target to be measured and the calibration body and through right Perform calibration to obtain the far-field radar cross-sectional area of ​​the target to be measured This is the RCS near-field measurement result of the target to be measured:

[0031]

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] 1. The present invention performs phase center correction on the echo signals of the target to be measured and the calibration object respectively by using the phase offset of the echo signals of the target to be measured and the calibration object, and uses a Hamming window function to perform time selection on the correction results. Then, a gate function is used to perform range compensation on the time selection results to obtain the spectral expansion coefficients of the target to be measured and the calibration object. This avoids the influence of the phase offset in the echo signal expression on the accuracy of the spectral expansion coefficient caused by directly processing the sampled data in the prior art, and effectively improves the measurement accuracy.

[0034] 2. The present invention performs scanning probe compensation on the spectral expansion coefficients obtained by performing phase center correction on the echo signals of the target echo and the calibration object, and then performs far-field extrapolation on the compensation results to obtain the target RCS near-field measurement results. This avoids the influence of the radiation characteristics of the scanning probe itself on the data obtained during the sampling process when directly using the spectral expansion coefficients for far-field extrapolation, ensures the accuracy of the far-field extrapolation results, and further improves the measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is an implementation flow chart of the present invention;

[0036] Figure 2 This is a comparison chart of the RCS near-field measurement results and simulation results obtained by the present invention. DETAILED DESCRIPTION

[0037] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] Reference Figure 1 , the present invention comprises the following steps:

[0039] Step 1) Obtain the echo signals of the target to be measured and the calibration object:

[0040] (1a) Initialize the scanning probe to The distance from the origin of the polar coordinate system to the polar coordinate axis angle coordinate is R mea The working frequency of the scanning probe is f, and the far-field cross-sectional patterns of its transmitting and receiving ends are E T 、E R ; The radius of the spherical calibration body required for measurement is r sph , its far-field radar cross-section at frequency f is The object to be measured and the calibration body are located at the origin of the polar coordinate system during measurement. In this embodiment, the object to be measured is a conical sphere, f = 10 GHz, r sph =200.7mm, R mea =2.5m;

[0041] (1b) The scanning probe takes the origin of the polar coordinate system as the center and R mea The radius of the target to be measured, the calibration object and the empty background are sampled uniformly L times, and the S of the target to be measured, the calibration object and the empty background are obtained. 21 Data U0={U 01 ,U 02 ,...,U 0l ,...,U 0L}、U1={U 11 ,U 12 ,...,U 1l ,...,U 1L} and U2={U 21 ,U 22 ,...,U 2l ,...,U 2L}, where l∈{1,2,...,L}, and in this embodiment, L=180;

[0042] (1c) Calculate S for each target to be measured 21 Data U 0l , S of each calibration body 21 Data U 1l The corresponding empty background S 21 Data U 2l The difference between the two is used to obtain the discrete echo data of the target to be measured U'0={U' 01 ,U' 02 ,...,U' 0l ,...,U' 0L}、Discrete echo data of calibration body U'1={U' 11 ,U' 12 ,...,U' 1l ,...,U' 1L}, and transform U'0 and U'1 into continuous echo signals of the target to be measured respectively through the Nyquist theorem Echo signal of the calibration body The transformation formula is:

[0043]

[0044] Among them, π is the ratio of the circumference of a circle, is the scanning probe sampling spacing, and In this embodiment

[0045] Step 2) Perform phase center correction on the echo signal:

[0046] Calculate the phase offset R between the echo signal of the target to be measured and the calibration object del and through R delEcho signal of the target to be measured Echo signal of the calibration body Perform phase center correction respectively to obtain the corrected echo signal of the target to be measured Calibration body echo signal Compared to the ideal situation, there will be a delay in probe sampling. Converting the delayed data into a continuous signal will cause the phase center of the obtained echo signal to shift, thus affecting the accuracy of subsequent data processing. However, the delay is difficult to measure directly. Therefore, the phase offset corresponding to the delay is obtained by calculating the propagation length of light corresponding to the entire sampling time and then subtracting the actual sampling distance:

[0047]

[0048]

[0049] Where p∈{0,1}, c is the speed of light in vacuum, e is the natural logarithm, j is an imaginary number, t peak It is the time length from the issuance of the sampling instruction to the receipt of the echo data;

[0050] Step 3) Perform time selection and range compensation on the corrected echo signal:

[0051] (3a) The Hamming window function Ham(·) is used to correct the target echo signal. Calibration body echo signal Perform time selection to obtain the echo signal of the target to be measured after time selection Calibration body echo signal

[0052]

[0053] Where R0 represents the distance from the geometric center of the smallest cube with a side length of D that can enclose the object to be measured to the scanning probe. In this embodiment, D = 0.5m;

[0054] (3b) Use the gate function G(R0) to correct the target echo signal Calibration body echo signal Perform range compensation to obtain the echo signal of the target to be measured after distance compensation Calibration body echo signal

[0055]

[0056]

[0057] where R gate is the range threshold, a is the compensation coefficient, a∈[0,2], in this embodiment, Rgate =0.45m, a=2;

[0058] Step 4) Obtain the spectrum expansion coefficients of the target to be measured and the calibration object:

[0059] Correcting the phase center of the echo signal can avoid the influence of the probe sampling delay when calculating the spectrum expansion coefficient in this step; correct ... Calibration body echo signal Perform inverse Fourier transform respectively to obtain the spectrum expansion coefficients B0 of the target to be measured and the calibration body. 0-N ,...,B 0n ,...,B 0N}、B1={B 1-N ,...,B 1n ,...,B 1N}, the calculation formula for each spectrum expansion coefficient is:

[0060]

[0061] in represents the n-order second-kind Hankel function, where n represents the order of spectrum expansion of the target and calibration body, N represents the truncation order of the target and calibration body, and B 0-N Indicates the -Nth spectral expansion coefficient of B0. In spectral expansion theory, the expansion order of the spectrum extends to positive and negative infinity. However, in engineering practice, it is impossible to calculate infinite expansion coefficients. Therefore, the truncation order is used to limit the positive and negative orders to ensure practicability.

[0062] Step 5) Perform scanning probe compensation on the spectrum expansion coefficient:

[0063] (5a) Far-field cross-sectional pattern E of the transmitting and receiving ends of the scanning probe T and E R Perform integral transformation and calculate the spectrum expansion coefficient under local coordinates obtained by integral transformation Perform transfer transformation to obtain the probe spectrum expansion coefficient in global coordinates The transformation formulas are:

[0064]

[0065]

[0066] Where m represents the spectral expansion order of the scanning probe, M represents the truncation order of the scanning probe, and represents the n+m-order second-kind Hankel function, and in this embodiment, M=50;

[0067] (5b) The radiation characteristics of the probe itself will affect the data obtained during the sampling process. In mathematical expression, it is reflected as the superposition of fields and in the spectrum expansion coefficient, it is reflected as multiplication. Therefore, the spectrum expansion coefficient P of the scanning probe in the global coordinate is TR Perform probe compensation on the spectral expansion coefficients B0 and B1 of the target to be measured and the calibration body respectively, and more accurate spectral expansion coefficients of the target to be measured and the calibration body can be obtained after compensation. The calculation formula for each spectrum expansion coefficient is:

[0068]

[0069] Step 6) Obtain target RCS near-field measurement results:

[0070] Spectral expansion coefficient of the target to be measured and the calibration body after compensation Perform far-field extrapolation respectively to obtain the far-field radar cross-sectional area of ​​the target to be measured and the calibration body The calculation formula is:

[0071]

[0072] pass right Perform calibration to obtain the far-field radar cross-sectional area of ​​the target to be measured This is the RCS near-field measurement result of the target to be measured:

[0073]

[0074] The technical effects of the present invention are described below in conjunction with simulation experiments.

[0075] 1. Simulation conditions and content:

[0076] The simulation was completed using the commercial electromagnetic simulation software FEKO, and the actual measurement was completed in a standard microwave anechoic chamber.

[0077] The far-field radar cross-sectional area of ​​the target to be measured obtained by simulating the target to be measured according to the embodiment of the present invention is compared with the far-field radar cross-sectional area obtained by the actual measurement result of the present invention. The comparison results are as follows: Figure 2 shown.

[0078] 2. Analysis of simulation results:

[0079] Reference Figure 2The horizontal axis represents the angle of the far-field RCS of the target to be measured, and the vertical axis represents the gain value of the far-field RCS of the target to be measured. The solid line in the figure represents the theoretical value obtained by simulation, and the dotted line represents the RCS near-field measurement result obtained by this method. The lower right corner is the conical sphere of the target to be measured used in this embodiment. It can be seen that the theoretical value is basically consistent with the measurement result. The error between the front and side of the conical sphere is within 0.5dB. The RCS gain value of the tapered tail is very low, but the theoretical value is also basically consistent with the measurement result.

[0080] The above description is only a specific example of the present invention, which is only used to illustrate the technical solution of the present invention and does not constitute any limitation to the present invention. Obviously, ordinary technicians in this field can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents; and these modifications or replacements based on the concept of the present invention are within the scope of protection of the present invention.

Claims

1. A method for measuring target radar cross-section (RCS) near-field based on probe compensation and phase center correction, characterized in that: The following steps are involved: (1) Obtain the echo signals of the target to be measured and the calibration object: (1a) Initialize the scanning probe to The distance from the origin of the polar coordinate system to the polar coordinate axis angle coordinate is R mea The working frequency of the scanning probe is f, and the far-field cross-sectional patterns of its transmitting and receiving ends are E T 、E R ; The radius of the spherical calibration body required for measurement is r sph , its far-field radar cross-section at frequency f is The object to be measured and the calibration body are located at the origin of the polar coordinate system during measurement; (1b) The scanning probe takes the origin of the polar coordinate system as the center and R mea The radius of the target to be measured, the calibration object and the empty background are sampled uniformly L times, and the S of the target to be measured, the calibration object and the empty background are obtained. 21 Data U0={U 01 ,U 02 ,...,U 0l ,...,U 0L }、U1={U 11 ,U 12 ,...,U 1l ,...,U 1L } and U2={U 21 ,U 22 ,...,U 2l ,...,U 2L }, where l∈{1,2,...,L}, L≥100; (1c) Calculate S for each target to be measured 21 Data U 0l , S of each calibration body 21 Data U 1l The corresponding empty background S 21 Data U 2l The difference between the two is used to obtain the discrete echo data of the target to be measured U'0={U' 01 ,U′ 02 ,...,U' 0l ,...,U' 0L }、Discrete echo data of calibration body U'1={U' 11 ,U′ 12 ,...,U′ 1l ,...,U′ 1L }, and transform U'0 and U'1 into continuous echo signals of the target to be measured respectively through the Nyquist theorem Echo signal of the calibration body (2) Perform phase center correction on the echo signal: Calculate the phase offset R between the echo signal of the target to be measured and the calibration object del and through R del Echo signal of the target to be measured Echo signal of the calibration body Perform phase center correction respectively to obtain the corrected echo signal of the target to be measured Calibration body echo signal Where p∈{0,1}, c is the speed of light in vacuum, e is the natural logarithm, j is an imaginary number, t peak It is the time length from the issuance of the sampling instruction to the receipt of the echo data; (3) Perform time selection and range compensation on the corrected echo signal: (3a) The Hamming window function Ham(·) is used to correct the target echo signal. Calibration body echo signal Perform time selection to obtain the echo signal of the target to be measured after time selection Calibration body echo signal Where R0 represents the distance from the geometric center of the smallest cube with a side length of D that can enclose the object to be measured to the scanning probe; (3b) Use the gate function G(R0) to correct the target echo signal Calibration body echo signal Perform range compensation to obtain the echo signal of the target to be measured after distance compensation Calibration body echo signal where R gate is the range threshold, a is the compensation coefficient, a∈[0,2]; (4) Obtain the spectrum expansion coefficients of the target to be measured and the calibration object: Echo signal of the target to be measured after distance compensation Calibration body echo signal Perform inverse Fourier transform respectively to obtain the spectrum expansion coefficients B0 of the target to be measured and the calibration body. 0-N ,...,B 0n ,...,B 0N }、B1={B 1-N ,...,B 1n ,...,B 1N }, where n represents the spectral expansion order of the target to be measured and the calibration body, N represents the truncation order of the target to be measured and the calibration body, and (5) Scanning probe compensation for spectral expansion coefficient: (5a) Far-field cross-sectional pattern E of the transmitting and receiving ends of the scanning probe T and E R Perform integral transformation and calculate the spectrum expansion coefficient under local coordinates obtained by integral transformation Perform transfer transformation to obtain the probe spectrum expansion coefficient in global coordinates Where m represents the spectral expansion order of the scanning probe, M represents the truncation order of the scanning probe, and (5b) The spectral expansion coefficient P of the scanning probe in the global coordinate TR Perform probe compensation on the spectral expansion coefficients B0 and B1 of the target to be measured and the calibration body respectively, and obtain the spectral expansion coefficients of the target to be measured and the calibration body after compensation. The calculation formula for each spectrum expansion coefficient is: (6) Obtain target RCS near-field measurement results: Spectral expansion coefficient of the target to be measured and the calibration body after compensation Perform far-field extrapolation respectively to obtain the far-field radar cross-sectional area of ​​the target to be measured and the calibration body and through right Perform calibration to obtain the far-field radar cross-sectional area of ​​the target to be measured This is the RCS near-field measurement result of the target to be measured:

2. The target RCS near-field measurement method based on probe compensation and phase center correction according to claim 1 is characterized in that: In step (1c), U'0 and U'1 are transformed into continuous target echo signals by Nyquist theorem. Echo signal of the calibration body The transformation formula is: Among them, π is the ratio of the circumference of a circle, is the scanning probe sampling spacing, and 3. The target RCS near-field measurement method based on probe compensation and phase center correction according to claim 1 is characterized in that: The echo signal of the target to be measured after distance compensation described in step (4) Calibration body echo signal Perform inverse Fourier transform respectively to obtain the spectrum expansion coefficients B0 of the target to be measured and the calibration body. 0-N ,...,B 0n ,...,B 0N }、B1={B 1-N ,...,B 1n ,...,B 1N }, where the calculation formula for each spectral expansion coefficient is: in represents the nth-order Hankel function of the second kind.

4. The target RCS near-field measurement method based on probe compensation and phase center correction according to claim 1 is characterized in that: The far-field cross-sectional pattern E of the transmitting and receiving ends of the scanning probe described in step (5a) T and E R Perform integral transformation and calculate the spectrum expansion coefficient under local coordinates obtained by integral transformation Perform transfer transformation, the transformation formulas are: in represents the n+m-order Hankel function of the second kind.

5. The target RCS near-field measurement method based on probe compensation and phase center correction according to claim 1 is characterized in that: The spectrum expansion coefficients of the compensated target and calibration body described in step (6) Perform far-field extrapolation separately, and the calculation formula is:

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