Plasma sheath multi-order dispersion effect error compensation method, system and equipment based on two-step self-focusing processing, medium and program product

Abstract

The invention belongs to the technical field of radar signal processing, discloses a plasma sheath multi-order dispersion effect error compensation method, system, equipment, medium and program product based on two-step self-focusing processing, and aims to solve the problem of plasma sheath multi-order dispersion effect error influence of radar in the hypersonic flight vehicle imaging detection process. Obtaining a strong scattering point target in the image through strong point target search, and constructing a dispersion effect error compensation image matrix; based on a maximum contrast self-focusing processing principle and an image focusing theory, iteratively processing and compensating second-order and third-order phase errors of a dispersion effect; outputting an image after the multi-order dispersion effect error compensation, and realizing the accurate compensation of the multi-order dispersion effect error of the target wrapped by the plasma sheath; systems, devices, media for implementing the method, program products including computer programs implementing the method; the method has the characteristics of high dispersion effect error compensation precision, high compensation efficiency, strong adaptability and simple compensation processing steps.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and in particular relates to a plasma sheath multi-order dispersion effect error compensation method, system, equipment, medium, and program product based on two-step self-focusing processing. Background Art

[0002] When hypersonic vehicles fly through the atmosphere at extremely high speeds, they experience intense friction with gas molecules, ionizing the surrounding air and forming a plasma sheath on the vehicle's surface, which interferes with electromagnetic wave transmission. Synthetic aperture radar (SAR), as a high-resolution radar system, offers advantages such as strong penetration, real-time performance, and a wide range of applications. Using SAR to detect moving aerial targets, particularly hypersonic targets, is a current research hotspot. However, unlike traditional low-speed targets, hypersonic targets fly at extremely high speeds. After intense friction with the air, a plasma sheath forms on their surface. The dispersion effect of this plasma sheath causes the radar range signal to become broadened and asymmetric, resulting in defocusing of the SAR image in the range direction, significantly interfering with the tracking and identification of hypersonic targets.

[0003] Similar to the ionosphere, the plasma sheath is essentially a dispersive plasma medium. The phase perturbations caused by this dispersive medium on electromagnetic waves can distort the range signal, and this phase perturbation is known as the dispersion effect. Because the phase perturbations caused by the dispersion effect are related to the radar signal frequency, Taylor analysis shows that each order of this phase component will cause different types of effects on the radar signal: the first-order phase term causes signal offset, the second-order phase term causes imaging defocus, the third-order phase term causes signal sidelobe asymmetry, and the fourth-order and higher phase terms are generally negligible due to their small values. Furthermore, as the resolution of radar detection systems improves and the electron density of the plasma sheath increases, the impact of the various orders of phase errors caused by the dispersion effect will become increasingly severe.

[0004] The patent application with publication number CN116859388A, entitled "A Method for Suppressing Dispersion Effects in ISAR Imaging of Plasma Sheath-Coated Targets," proposes a dispersion effect error compensation method based on image maximum contrast self-focusing. Based on the principle of image maximum contrast self-focusing and prior knowledge, a dispersion compensation factor is constructed in the frequency domain and a compensation function is constructed in combination with a dispersion error model. An iterative cyclic compensation process is used to achieve compensation for the dispersion effect phase error. However, this method only considers the imaging defocusing problem caused by the second-order phase error in the dispersion effect during high-resolution radar detection of hypersonic targets covered by a plasma sheath, and ignores the influence of third-order and higher-order phase errors.

[0005] The prior art has a comprehensive influence on the imaging results of the radar signal when the high-resolution radar system detects and the plasma sheath electron density is high, and the traditional method cannot solve the radar signal imaging distortion problem caused by the multi-order dispersion effect. SUMMARY

[0006] In order to overcome the above-mentioned defects of the prior art, the purpose of the present application is to provide a plasma sheath multi-order dispersion effect error compensation method, system, device, medium and program product based on two-step self-focusing processing, which is used for the image affected by the plasma sheath multi-order dispersion effect error in the radar imaging process of a hypersonic target, adopts an image peak value search to obtain a strong point target in the image, adopts a maximum contrast self-focusing to compensate for the second-order phase error of the dispersion effect based on the image focusing theory (Carrara W, Goodman R S, Majewski R M. Spotlight Synthetic Aperture Radar: Signal Processing Algorithms [J]. 1995.), further adopts a maximum contrast self-focusing to compensate for the third-order phase error of the dispersion effect, and realizes accurate compensation of the multi-order dispersion effect error in the radar detection process of the plasma sheath coated target, which has the characteristics of high error compensation precision, high compensation efficiency, strong scalability and simple processing steps.

[0007] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is:

[0008] A plasma sheath multi-order dispersion effect error compensation method based on two-step self-focusing processing, comprising the following steps:

[0009] Step 1, strong point target search: adopting a peak value search method to search for a strong scattering point P in a SAR image A, and constructing a SAR two-dimensional image matrix I with P as a center element;

[0010] Step 2, second-order phase error compensation of dispersion effect: setting an initial dispersion compensation factor γ1, an iteration step length Δγ1, and constructing a second-order phase error compensation function Δψ of dispersion effect According to the image focusing theory, a dispersion effect error detection threshold γ is calculated g1 , the dispersion compensation factor is adjusted according to the contrast of the image matrix before and after compensation, and the second-order phase error compensation of dispersion effect on the SAR two-dimensional image matrix I is realized through cyclic iteration;

[0011] Step 3, third-order phase error compensation of dispersion effect: setting an initial dispersion compensation factor γ2, an iteration step length Δγ2, and constructing a third-order phase error compensation function Δψ of dispersion effect, according to the image focusing theory, a dispersion effect error detection threshold γ is calculated g2, adjusting the dispersion compensation factor according to the contrast of the image matrix before and after compensation, and realizing the third-order phase error compensation of the dispersion effect on the SAR two-dimensional image matrix I2 after the second-order phase error compensation of the dispersion effect through cyclic iteration;

[0012] Step 4, outputting the compensated image: outputting the plasma sheath multi-order dispersion effect error compensated image based on the SAR two-dimensional image matrix after second-order and third-order phase error compensation.

[0013] The step 1 is specifically as follows:

[0014] Search for the strong scattering point P in the SAR image, whose coordinates are (L a , L r ), with P as the central element, construct the SAR two-dimensional image matrix I=A[L a -N+1:L a +N,L r -N+1:L r +N], where N is the number of points.

[0015] The step 2 is specifically as follows:

[0016] Step 2.1: Set the dispersion compensation factor γ1 and the iteration step size Δγ1, and calculate the second-order phase error detection threshold γ of the dispersion effect according to the image focusing theory. g1 , the calculation formula is:

[0017]

[0018] Where B w is bandwidth;

[0019] Step 2.2: Construct the second-order phase error compensation function for dispersion effect. The calculation formula is:

[0020]

[0021] Where j is the imaginary unit and f is the frequency;

[0022] Step 2.3: Perform a range-direction Fast Fourier Transform (FFT) on the original SAR two-dimensional image matrix I according to formula (3) to obtain the SAR two-dimensional range spectrum matrix I f , according to formula (4) multiplied by the dispersion effect second-order phase error compensation function After compensation, the inverse fast Fourier transform (IFFT) is performed according to formula (5) to obtain the SAR two-dimensional time domain matrix I after the second-order phase error compensation of the dispersion effect. c , the calculation formula is:

[0023] I f = FFT(I) (3)

[0024]

[0025] I c = IFFT(I f_c ) (5)

[0026] In the formula, I f_c is the SAR two-dimensional range spectrum matrix after the dispersion effect second-order phase error compensation, FFT(·) is the fast Fourier transform operation, and IFFT(·) is the inverse fast Fourier transform operation;

[0027] Step 2.4, according to formula (6) and formula (7), the contrast C1 and C2 of the SAR image before and after the dispersion effect second-order phase error compensation are calculated respectively, and the calculation formula is:

[0028]

[0029]

[0030] In the formula, I1(x,y) is the modulus value of each element in the SAR two-dimensional image matrix before the dispersion effect second-order phase error compensation, I2(x,y) is the modulus value of each element in the SAR two-dimensional time domain matrix after the dispersion effect second-order phase error compensation, x is the number of azimuth sampling points, and y is the number of range sampling points;

[0031] Step 2.5, the size relationship of the contrasts C1 and C2 before and after the compensation is compared: if C1>C2, then Δγ1 takes-Δγ1 / 2; if C1<C2, then Δγ1 takes Δγ1. A new dispersion effect second-order phase error compensation function is constructed and the dispersion effect second-order phase error compensation processing is performed. Through continuous loop iteration, when the iteration step Δγ1 is less than the dispersion error detection threshold γ g1 , the loop ends, and the dispersion effect second-order phase error compensation processing is completed.

[0032] The step 3 is specifically:

[0033] Step 3.1, set the dispersion compensation factor γ2 and the iteration step Δγ2, calculate the dispersion error detection threshold γ g2 according to the image focusing theory, and the calculation formula is:

[0034]

[0035] Step 3.2, construct a dispersion effect third-order phase error compensation function, and the calculation formula is:

[0036] Δψ = exp(-j(γ2+ Δγ2) x f 3 ) (9)

[0037] Step 3.3, according to formula (10) to the dispersion effect of the second order phase error compensation after SAR two-dimensional image matrix I c performing distance direction Fast Fourier Transform (FFT) to obtain the dispersion effect of the second order phase error compensation after SAR two-dimensional distance spectrum matrix I f_c , according to formula (11) multiplied by dispersion effect of the third order phase error compensation function Δψ for compensation processing, after compensation according to formula (12) to obtain the dispersion effect of the third order phase error compensation after SAR two-dimensional time domain matrix I ct , the calculation formula is:

[0038] I f_c = FFT(I c ) (10)

[0039] I f_ct = I f_c x Δψ (11)

[0040] I ct = IFFT(I f_ct ) (12)

[0041] In the formula, I f_ct is the dispersion effect of the third order phase error compensation after SAR two-dimensional distance spectrum matrix;

[0042] Step 3.4, according to formula (13) and formula (14) respectively calculate the dispersion effect of the third order phase error compensation before and after SAR image contrast C3 and C4, the calculation formula is:

[0043]

[0044] In the formula, I3(x,y) is the dispersion effect of the third order phase error compensation before SAR two-dimensional image matrix each element modulus, I4(x,y) is the dispersion effect of the third order phase error compensation after SAR two-dimensional time domain matrix each element modulus;

[0045] Step 3.5, compare the size relationship of contrast C3 and C4 before and after compensation: adjust the iteration step, if C3>C4, Δγ2 takes-Δγ2 / 2; if C3<C4, Δγ2 takes Δγ2. With this to construct the new dispersion effect of the third order phase error compensation function Δψ, and carry out the dispersion effect of the third order phase error compensation processing. Through the continuous loop iteration, when the iteration step Δγ2 is less than the dispersion error detection threshold γ g2When the cycle ends, the dispersion effect third-order phase error compensation processing is completed.

[0046] A two-step self-focusing processing-based plasma sheath multi-order dispersion effect error compensation system comprises:

[0047] A strong point target search module: a peak search method is adopted to search for a strong scattering point P in a SAR image A, and a SAR two-dimensional image matrix I is constructed with P as a central element;

[0048] A dispersion effect second-order phase error compensation module: an initial dispersion compensation factor γ1, an iteration step Δγ1, and a dispersion effect second-order phase error compensation function Δψ1 are set A dispersion effect error detection threshold γ is calculated according to an image focusing theory g1 , the dispersion compensation factor is adjusted according to the contrast of the image matrix before and after compensation, and through cyclic iteration, the dispersion effect second-order phase error compensation of the SAR two-dimensional image matrix I is realized;

[0049] A dispersion effect third-order phase error compensation module: an initial dispersion compensation factor γ2, an iteration step Δγ2, and a dispersion effect third-order phase error compensation function Δψ are set g2 A dispersion effect error detection threshold γ is calculated according to an image focusing theory g1 , the dispersion compensation factor is adjusted according to the contrast of the image matrix before and after compensation, and through cyclic iteration, the dispersion effect second-order phase error compensation of the SAR two-dimensional image matrix I is realized;

[0050] An output compensated image module: according to the SAR two-dimensional image matrix after the second-order and third-order phase error compensation, an image after the plasma sheath multi-order dispersion effect error compensation is output.

[0051] A two-step self-focusing processing-based plasma sheath multi-order dispersion effect error compensation device comprises:

[0052] A memory: for storing a computer program for implementing a two-step self-focusing processing-based plasma sheath multi-order dispersion effect error compensation method;

[0053] A processor: for executing the computer program to implement a two-step self-focusing processing-based plasma sheath multi-order dispersion effect error compensation method.

[0054] A computer readable storage medium stores a computer program, and the computer program is executed by a processor to implement the steps of a two-step self-focusing processing-based plasma sheath multi-order dispersion effect error compensation method.

[0055] The computer program product comprises a computer program, and the computer program realizes a plasma sheath multi-order dispersion effect error compensation method based on a two-step self-focusing processing when executed by a processor.

[0056] The application has the advantages that, compared with the prior art,

[0057] 1. The application has the characteristics of high multi-order dispersion effect error compensation precision. The application considers the comprehensive influence problem of multi-order dispersion effect errors caused by high electron density and high resolution in the radar imaging process of a hypersonic target caused by a plasma sheath, and adopts a two-step self-focusing processing method to accurately compensate for the second-order and third-order phase errors. Compared with the prior art which only solves the problem of second-order phase error compensation of dispersion effect, the application can more accurately realize multi-order dispersion effect error compensation and can realize accurate dispersion effect error compensation under high electron density and high resolution observation conditions.

[0058] 2. The application has the characteristics of high dispersion effect error compensation efficiency. The application only relies on the strong point target area of the hypersonic target in the SAR image for error compensation processing, without traversing all azimuth pulse signals for processing, so that high-efficiency plasma sheath multi-order dispersion effect error compensation under large field of view and high resolution conditions can be realized.

[0059] 3. The application has the characteristics of strong adaptability. The application only compensates for dispersion effect errors based on the SAR image data itself affected by the plasma sheath multi-order dispersion effect, and the compensation processing process is not affected by the height, speed and attitude of the aircraft, and can also be applied to SAR system imaging error processing under different wavebands, bandwidths, pulse widths and polarizations, and can be extended to plasma sheath multi-order dispersion effect error compensation in the imaging process of a hypersonic target by an ISAR ground-based imaging radar system.

[0060] 4. The application has the characteristics of simple compensation processing steps. The application can efficiently realize accurate compensation for multi-order dispersion effect errors in the radar imaging process of a hypersonic target through only four steps, and has the obvious characteristics of simple compensation processing steps.

[0061] In summary, the plasma sheath multi-order dispersion effect error compensation method has the advantages of high multi-order dispersion effect error compensation precision, high efficiency, strong adaptability and simple compensation processing steps. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 is a flowchart of the method proposed by the application.

[0063] Figure 2are SAR images before and after multi-order dispersion effect error compensation of a hypersonic target in embodiments of the present application, wherein (a) is an ideal SAR image, (b) is a SAR image affected by multi-order dispersion effect error, (c) is a SAR image after traditional compensation of only second-order phase error of dispersion effect, and (d) is a SAR image after two-step self-focusing processing.

[0064] Figure 3 are one-dimensional distance signal profiles before and after multi-order dispersion effect error compensation of a strong point target in SAR images in embodiments of the present application. DETAILED DESCRIPTION

[0065] The present application is described in detail below in combination with the drawings and embodiments.

[0066] A method for compensating multi-order dispersion effect error of a plasma sheath based on two-step self-focusing processing, comprising the following steps:

[0067] Step 1, strong point target search: a peak search method is used to search for a strong scattering point P in a SAR image A, the coordinates of which are (L a , L r ), a SAR two-dimensional image matrix I = A[L a -N+1:L a +N, L r -N+1:L r +N] is constructed with P as a central element, wherein N is a point number;

[0068] Step 2, compensation of second-order phase error of dispersion effect: an initial dispersion compensation factor γ1 is set, an iteration step Δγ1 is set, and a compensation function of second-order phase error of dispersion effect is constructed A dispersion effect error detection threshold γ g1 is calculated according to image focusing theory, the dispersion compensation factor is adjusted according to the contrast of the image matrix before and after compensation, and the second-order phase error of dispersion effect of the SAR two-dimensional image matrix I is compensated through cyclic iteration, specifically as follows:

[0069] Step 2.1, the dispersion compensation factor γ1 and the iteration step Δγ1 are set, the dispersion effect error detection threshold γ g1 is calculated according to image focusing theory, and the calculation formula is as follows:

[0070]

[0071] In the formula, B w is a bandwidth.

[0072] Step 2.2, a compensation function of second-order phase error of dispersion effect is constructed, and the calculation formula is as follows:

[0073]

[0074] Where j is the imaginary unit and f is the frequency;

[0075] Step 2.3: Perform a range-direction Fast Fourier Transform (FFT) on the original SAR two-dimensional image matrix I according to formula (3) to obtain the SAR two-dimensional range spectrum matrix I f , according to formula (4) multiplied by the dispersion effect second-order phase error compensation function After compensation, the inverse fast Fourier transform (IFFT) is performed according to formula (5) to obtain the SAR two-dimensional time domain matrix I after the second-order phase error compensation of the dispersion effect c , the calculation formula is:

[0076] I f =FFT(I) (3)

[0077]

[0078] I c =IFFT(I f_c ) (5)

[0079] Where, I f_c is the SAR two-dimensional range spectrum matrix after the second-order phase error compensation of the dispersion effect, FFT(·) is the fast Fourier transform operation, and IFFT(·) is the inverse fast Fourier transform operation;

[0080] In step 2.4, the SAR image contrasts C1 and C2 before and after the second-order phase error compensation due to the dispersion effect are calculated according to equations (6) and (7), respectively. The calculation formulas are:

[0081]

[0082]

[0083] Where I1(x,y) is the modulus of each element in the SAR two-dimensional image matrix before compensation for the second-order phase error due to dispersion effect, I2(x,y) is the modulus of each element in the SAR two-dimensional time domain matrix after compensation for the second-order phase error due to dispersion effect, x is the number of sampling points in azimuth, and y is the number of sampling points in range.

[0084] Step 2.5, compare the contrast ratios C1 and C2 before and after compensation: adjust the iteration step size. If C1>C2, Δγ1 is -Δγ1 / 2; if C1 <C2,则Δγ1取Δγ1。以此构造新的色散效应二阶相位误差补偿函数 And the dispersion effect of second-order phase error compensation processing. By constantly circulating iteration, when the iteration step length Δγ1 is less than the dispersion error detection threshold γ g1 , the loop ends, and the dispersion effect of second-order phase error compensation processing is completed.

[0085] Step 3, dispersion effect of third-order phase error compensation: set the initial dispersion compensation factor γ2, iteration step length Δγ2, construct the dispersion effect of third-order phase error compensation function Δψ, calculate the dispersion effect error detection threshold γ g2 According to the image focusing theory, adjust the dispersion compensation factor according to the contrast of the image matrix before and after compensation, and realize the dispersion effect of third-order phase error compensation of SAR two-dimensional image matrix I2 after the dispersion effect of second-order phase error compensation through loop iteration. Specifically:

[0086] Step 3.1, set the dispersion compensation factor γ2 and the iteration step length Δγ2, calculate the dispersion error detection threshold γ g2 , the calculation formula is:

[0087]

[0088] Step 3.2, construct the dispersion effect of third-order phase error compensation function, the calculation formula is:

[0089] Δψ=exp(-j(γ2+Δγ2)×f 3 ) (9)

[0090] Step 3.3, according to formula (10), the dispersion effect of second-order phase error compensation SAR two-dimensional image matrix I c Fast Fourier Transform (FFT) is carried out in the distance direction, and the dispersion effect of second-order phase error compensation SAR two-dimensional distance spectrum matrix I f_c is obtained. According to formula (11), multiply the dispersion effect of third-order phase error compensation function Δψ for compensation processing, and according to formula (12), carry out inverse fast Fourier transform (IFFT) to obtain the dispersion effect of third-order phase error compensation SAR two-dimensional time domain matrix I ct , the calculation formula is:

[0091] I f_c =FFT(I c ) (10)

[0092] I f_ct = I f_c ×Δψ (11)

[0093] I ct =IFFT(If_ct ) (12)

[0094] wherein, I f_ct is the SAR two-dimensional range spectrum matrix after the third-order phase error compensation of dispersion effect;

[0095] Step 3.4, according to formula (13) and formula (14), respectively, calculate the contrast C3 and C4 of SAR image before and after the third-order phase error compensation of dispersion effect, the calculation formula is:

[0096]

[0097] wherein, I3(x, y) is the modulus value of each element in the SAR two-dimensional image matrix before the third-order phase error compensation of dispersion effect, I4(x, y) is the modulus value of each element in the SAR two-dimensional time domain matrix after the third-order phase error compensation of dispersion effect;

[0098] Step 3.5, compare the size relationship of contrast C3 and C4 before and after compensation: adjust the iteration step, if C3>C4, then Δγ2 takes-Δγ2 / 2; if C3<C4, then Δγ2 takes Δγ2. With this, a new third-order phase error compensation function Δψ of dispersion effect is constructed, and the third-order phase error compensation processing of dispersion effect is carried out. Through continuous loop iteration, when the iteration step Δγ2 is less than the dispersion error detection threshold γ g2 , the loop ends, and the third-order phase error compensation processing of dispersion effect is completed.

[0099] Step 4, output the compensated image: according to the SAR two-dimensional image matrix after the second-order and third-order phase error compensation, output the image after the multi-order dispersion effect error compensation of plasma sheath.

[0100] A plasma sheath multi-order dispersion effect error compensation system based on two-step self-focusing processing, comprising:

[0101] Strong point target search module: using peak search method, search the strong scattering point P in SAR image A, and construct SAR two-dimensional image matrix I with P as the center element, for realizing step 1 of the method described in the application;

[0102] Dispersion effect second-order phase error compensation module: set the initial dispersion compensation factor γ1, the iteration step Δγ1, and construct the dispersion effect second-order phase error compensation function According to the image focusing theory, calculate the dispersion effect error detection threshold γ g1 , adjust the dispersion compensation factor according to the contrast of the image matrix before and after compensation, realize the dispersion effect second-order phase error compensation of SAR two-dimensional image matrix I through loop iteration, for realizing step 2 of the method described in the application;

[0103] A third-order phase error compensation module of dispersion effect: setting an initial dispersion compensation factor γ2, an iterative step Δγ2, constructing a third-order phase error compensation function Δψ of dispersion effect, calculating a dispersion effect error detection threshold γ according to the image focusing theory g2 , adjusting the dispersion compensation factor according to the contrast of the image matrix before and after compensation, and realizing the third-order phase error compensation of the SAR two-dimensional image matrix I2 subjected to the second-order phase error compensation of dispersion effect through cyclic iteration, which is used for realizing step 3 of the method of the application;

[0104] An output compensation image module: outputting the image after the multi-order dispersion effect error compensation of the plasma sheath according to the SAR two-dimensional image matrix after the second-order and third-order phase error compensation, which is used for realizing step 4 of the method of the application.

[0105] A plasma sheath multi-order dispersion effect error compensation device based on two-step self-focusing processing, comprising:

[0106] A memory: used for storing a computer program for realizing the plasma sheath multi-order dispersion effect error compensation method based on two-step self-focusing processing;

[0107] A processor: used for realizing the plasma sheath multi-order dispersion effect error compensation method based on two-step self-focusing processing when the computer program is executed.

[0108] A computer readable storage medium, which stores a computer program, the computer program is executed by a processor to realize the steps of the plasma sheath multi-order dispersion effect error compensation method based on two-step self-focusing processing.

[0109] A computer program product, comprising a computer program, the computer program is executed by a processor to realize the plasma sheath multi-order dispersion effect error compensation method based on two-step self-focusing processing.

[0110] The application effect of the application will be described in detail in combination with the embodiments.

[0111] Since the hypersonic SAR image affected by the plasma sheath multi-order dispersion effect is difficult to obtain in practice, in the embodiment, the ideal SAR image of the hypersonic target (as shown in (a) of FIG. 1) is used, and the SAR image of the hypersonic target affected by the plasma sheath multi-order dispersion effect (as shown in (b) of FIG. 1) is obtained through simulation, and the simulation parameters are shown in Table 1. Figure 2 Figure 2 Table 1 Embodiment Parameters

[0112] Table 1 Embodiment Parameters

[0113]

[0114] According to​Figure 1 A method for compensating the multi-order dispersion effect error of plasma sheath based on two-step self-focusing processing, comprising the following steps:

[0115] Step 1, strong point target search: using peak search method, searching for strong scattering point P in SAR image A of (b), taking P as the center element to construct SAR two-dimensional image matrix I; Figure 2 Step 1, strong point target search: using peak search method, searching for strong scattering point P in SAR image A of (b), taking P as the center element to construct SAR two-dimensional image matrix I;

[0116] Step 2, dispersion effect second-order phase error compensation: setting initial dispersion compensation factor γ1, iteration step Δγ1, constructing dispersion effect second-order phase error compensation function According to the image focusing theory, the dispersion effect error detection threshold γ is calculated g1 , according to the contrast of image matrix before and after compensation, adjusting the dispersion compensation factor, through loop iteration, realizing the dispersion effect second-order phase error compensation of SAR two-dimensional image matrix I, specifically:

[0117] Step 2.1, setting dispersion compensation factor γ1=2×10 -17 and iteration step Δγ1=1×10 -17 , according to the image focusing theory, calculating the dispersion effect second-order phase error detection threshold γ g1 =3.14×10 -26 , the calculation formula is:

[0118]

[0119] In the formula, B w is the bandwidth;

[0120] Step 2.2, constructing dispersion effect second-order phase error compensation function, the calculation formula is:

[0121]

[0122] In the formula, f is the frequency;

[0123] Step 2.3, according to formula (3), performing distance fast Fourier transform (FFT) on the original SAR two-dimensional image matrix I, obtaining SAR two-dimensional distance spectrum matrix I f , according to formula (4), multiplying dispersion effect second-order phase error compensation function for compensation processing, after compensation, according to formula (5), performing inverse fast Fourier transform (IFFT) to obtain SAR two-dimensional time domain matrix I c after dispersion effect second-order phase error compensation, the calculation formula is:

[0124] If = FFT(I) (3)

[0125]

[0126] I c = IFFT(I f_c ) (5)

[0127] wherein I f_c is the SAR two-dimensional range spectrum matrix after the dispersion effect second-order phase error compensation, FFT(·) is a fast Fourier transform operation, and IFFT(·) is an inverse fast Fourier transform operation;

[0128] Step 2.4, the SAR image contrasts C1 and C2 before and after the dispersion effect second-order phase error compensation are respectively calculated according to formula (6) and formula (7), and the calculation formula is:

[0129]

[0130] wherein I1(x, y) is a modulus value of each element in the SAR two-dimensional image matrix before the dispersion effect second-order phase error compensation, I2(x, y) is a modulus value of each element in the SAR two-dimensional time domain matrix after the dispersion effect second-order phase error compensation, x is a number of azimuth sampling points, and y is a number of range sampling points;

[0131] Step 2.5, the size relationship between the contrasts C1 and C2 before and after the compensation is compared: if C1 > C2, then Δγ1 takes -Δγ1 / 2; if C1 < C2, then Δγ1 takes Δγ1. A new dispersion effect second-order phase error compensation function Δφ is constructed, and the dispersion effect second-order phase error compensation processing is performed. Through continuous loop iteration, when the iteration step Δγ1 is less than the dispersion error detection threshold γ g1 , the loop ends, and the dispersion effect second-order phase error compensation processing is completed.

[0132] Step 3, dispersion effect third-order phase error compensation: an initial dispersion compensation factor γ2 is set, an iteration step Δγ2 is set, a dispersion effect third-order phase error compensation function Δψ is constructed, a dispersion error detection threshold γ g2 is calculated according to the image focusing theory, the dispersion compensation factor is adjusted according to the image matrix contrast before and after the compensation, and through loop iteration, the dispersion effect third-order phase error compensation of the SAR two-dimensional image matrix I2 after the dispersion effect second-order phase error compensation is realized, and the dispersion effect third-order phase error compensation is specifically:

[0133] Step 3.1, the dispersion compensation factor γ2 = 0.5×10 -26 and the iteration step Δγ2 = 0.5×10 -26 are set, the dispersion error detection threshold γ g2= 3.14 x 10 -27 , the calculation formula is:

[0134]

[0135] Step 3.2, construct the third-order phase error compensation function of dispersion effect, the calculation formula is:

[0136] Δψ = exp (-j (γ2+ Δγ2) x f 3 ) (9)

[0137] Step 3.3, according to formula (10), the SAR two-dimensional image matrix I c is subjected to distance direction fast Fourier transform (FFT) to obtain the SAR two-dimensional range spectrum matrix I f_c after second-order phase error compensation of dispersion effect, according to formula (11), multiplied by the third-order phase error compensation function Δψ of dispersion effect for compensation processing, and according to formula (12), inverse fast Fourier transform (IFFT) is carried out to obtain the SAR two-dimensional time domain matrix I ct after third-order phase error compensation of dispersion effect, the calculation formula is:

[0138] I f_c = FFT (I c ) (10)

[0139] I f_ct = I f_c x Δψ (11)

[0140] I ct = IFFT (I f_ct ) (12)

[0141] In the formula, I f_ct is the SAR two-dimensional range spectrum matrix after third-order phase error compensation of dispersion effect;

[0142] Step 3.4, according to formula (13) and formula (14), the SAR image contrast C3 and C4 before and after third-order phase error compensation of dispersion effect are calculated respectively, the calculation formula is:

[0143]

[0144]

[0145] Where I3(x,y) is the modulus of each element in the SAR two-dimensional image matrix before compensation for the third-order phase error due to dispersion effect, and I4(x,y) is the modulus of each element in the SAR two-dimensional time domain matrix after compensation for the third-order phase error due to dispersion effect.

[0146] Step 3.5, compare the contrast ratios C3 and C4 before and after compensation: adjust the iteration step size. If C3>C4, Δγ2 is -Δγ2 / 2; if C3 <C4,则Δγ2取Δγ2。以此构造新的色散效应三阶相位误差补偿函数Δψ,并进行色散效应三阶相位误差补偿处理。通过不断循环迭代,当迭代步长Δγ2小于色散误差检测门限γ g2 When , the cycle ends and the third-order phase error compensation processing of the dispersion effect is completed.

[0147] Step 4: Output the compensated image: Based on the SAR two-dimensional image matrix after the second-order and third-order phase error compensation, output the plasma sheath multi-order dispersion effect error compensation image, such as Figure 2 As shown in (d) in .

[0148] Figure 2 (d) in the figure is the SAR image obtained after the multi-order dispersion effect error compensation processing is completed by the proposed method in this embodiment. Figure 2 In (b), it can be seen that the defocusing phenomenon of the strong point target (the area indicated by the yellow dotted box) caused by the multi-order dispersion effect error is effectively suppressed. Compared with the traditional method of compensating only the second-order phase error of the dispersion effect, the Figure 2 From the processing results of (c) in FIG, it can be clearly seen that the correction result obtained by the method proposed by the present invention has a better effect on compensating the multi-order dispersion effect error. Figure 3 From the results shown in the range signal profile of the strong point target, it can be seen that the range profile result of the strong point target obtained by the method proposed in the present invention can be basically restored to the range profile result in the ideal state (that is, the state not affected by the multi-order dispersion effect), and compared with the traditional processing method that only compensates for the second-order phase error of the dispersion effect, the compensation performance of the method of the present invention is significantly better.

[0149] Further, for Figure 3The point target distance signal profile is given, and the imaging quality evaluation result of the point target distance signal is given by the application, as shown in Table 2. It can be seen that after the method proposed in the application is used for processing, the resolution of the strong point target distance signal is restored to the ideal state (0.1321 m), the peak side lobe ratio and the integral side lobe ratio are restored to-13.27 dB and-10.11 dB (very close to the ideal state) respectively, and the processing result is obviously better than the traditional processing result of compensating only the second-order phase error of the dispersion effect. It can be seen that the method for compensating the multi-order dispersion effect error of the plasma sheath based on two-step self-focusing processing proposed in the application can realize accurate compensation of the multi-order dispersion effect error of the plasma sheath, and the correctness and effectiveness of the method are verified through the embodiments.

[0150] Table 2: Imaging quality evaluation result

[0151]

[0152] In summary, the above embodiments show that the method for compensating the multi-order dispersion effect error of the plasma sheath based on two-step self-focusing processing proposed in the application can realize accurate compensation of the multi-order dispersion effect error of the plasma sheath.

Claims

1. A method for compensating errors of plasma sheath multi-order dispersion effects based on two-step self-focusing processing, characterized in that: The following steps are involved: Step 1: Strong point target search: Use the peak search method to search for strong scattering points P in the SAR image A, and construct the SAR two-dimensional image matrix I with P as the central element; Step 2: Dispersion effect second-order phase error compensation: Set the initial dispersion compensation factor γ1, iterative step size Δγ1, construct the dispersion effect second-order phase error compensation function Δφ, and calculate the dispersion effect error detection threshold γ based on image focusing theory. g1 , the dispersion compensation factor is adjusted according to the contrast of the image matrix before and after compensation, and the second-order phase error compensation of the dispersion effect of the SAR two-dimensional image matrix I is realized through cyclic iteration; Step 3: Dispersion effect third-order phase error compensation: Set the initial dispersion compensation factor γ2, iterative step size Δγ2, construct the dispersion effect third-order phase error compensation function Δψ, and calculate the dispersion effect error detection threshold γ according to image focusing theory. g2 , adjusting the dispersion compensation factor according to the contrast of the image matrix before and after compensation, and realizing the third-order phase error compensation of the dispersion effect on the SAR two-dimensional image matrix I2 after the second-order phase error compensation of the dispersion effect through cyclic iteration; Step 4, outputting the compensated image: outputting the plasma sheath multi-order dispersion effect error compensated image based on the SAR two-dimensional image matrix after second-order and third-order phase error compensation.

2. The method for compensating plasma sheath multi-order dispersion effect errors based on two-step self-focusing processing according to claim 1, characterized in that: The specific process of step 1, searching for strong point targets is as follows: Search for the strong scattering point P in the SAR image, whose coordinates are (L a , L r ), with P as the central element, construct the SAR two-dimensional image matrix I=A[L a -N+1:L a +N,L r -N+1:L r +N], where N is the number of points.

3. The method for compensating plasma sheath multi-order dispersion effect errors based on two-step self-focusing processing according to claim 1, characterized in that: The specific process of the second-order phase error compensation due to dispersion effect in step 2 is as follows: Step 2.1: Set the dispersion compensation factor γ1 and the iteration step size Δγ1, and calculate the second-order phase error detection threshold γ of the dispersion effect according to the image focusing theory. g1 , the calculation formula is: Where B w is bandwidth; Step 2.2: Construct the second-order phase error compensation function for dispersion effect. The calculation formula is: Where j is the imaginary unit and f is the frequency; Step 2.3: Perform a range-direction Fast Fourier Transform (FFT) on the original SAR two-dimensional image matrix I according to formula (3) to obtain the SAR two-dimensional range spectrum matrix I f , according to formula (4) multiplied by the dispersion effect second-order phase error compensation function After compensation, the inverse fast Fourier transform (IFFT) is performed according to formula (5) to obtain the SAR two-dimensional time domain matrix I after the second-order phase error compensation of the dispersion effect c , the calculation formula is: I f =FFT(I) (3) I c =IFFT(I f_c ) (5) Where, I f_c is the SAR two-dimensional range spectrum matrix after the second-order phase error compensation of the dispersion effect, FFT(·) is the fast Fourier transform operation, and IFFT(·) is the inverse fast Fourier transform operation; In step 2.4, the SAR image contrasts C1 and C2 before and after the second-order phase error compensation due to the dispersion effect are calculated according to equations (6) and (7), respectively. The calculation formulas are: Where I1(x,y) is the modulus of each element in the SAR two-dimensional image matrix before compensation for the second-order phase error due to dispersion effect, I2(x,y) is the modulus of each element in the SAR two-dimensional time domain matrix after compensation for the second-order phase error due to dispersion effect, x is the number of sampling points in azimuth, and y is the number of sampling points in range. Step 2.5, compare the magnitude relationship between the contrast ratios C1 and C2 before and after compensation: adjust the iteration step size. If C1 > C2, then Δγ1 takes -Δγ1 / 2; if C1 < C2, then Δγ1 takes Δγ1. Based on this, construct a new second-order phase error compensation function Δφ for the dispersion effect and perform the second-order phase error compensation process for the dispersion effect. Through continuous cyclic iteration, when the iteration step size Δγ1 is less than the dispersion error detection threshold γ g1 , the loop ends and the second-order phase error compensation process for the dispersion effect is completed.

4. The method for compensating plasma sheath multi-order dispersion effect errors based on two-step self-focusing processing according to claim 1, characterized in that: The specific process of the third-order phase error compensation due to dispersion effect in step 3 is as follows: Step 3.1: Set the dispersion compensation factor γ2 and the iteration step size Δγ2, and calculate the dispersion error detection threshold γ according to the image focusing theory. g2 , the calculation formula is: Where B w is bandwidth; Step 3.2: Construct the third-order phase error compensation function for dispersion effect. The calculation formula is: Δψ=exp(-j(γ2+Δγ2)×f 3 ) (9) Where j is the imaginary unit and f is the frequency; Step 3.3: According to formula (10), the SAR two-dimensional image matrix I after the second-order phase error compensation of the dispersion effect is c Perform Fast Fourier Transform (FFT) in the range direction to obtain the SAR two-dimensional range spectrum matrix I after the second-order phase error compensation of the dispersion effect f_c According to formula (11), the third-order phase error compensation function Δψ of the dispersion effect is multiplied to perform compensation processing. After compensation, the inverse fast Fourier transform (IFFT) is performed according to formula (12) to obtain the SAR two-dimensional time domain matrix I after the third-order phase error compensation of the dispersion effect ct , the calculation formula is: I f_c =FFT(I c ) (10) I f_ct = I f_c ×Δψ (11) I ct =IFFT(I f_ct ) (12) Where, I f_ct is the SAR two-dimensional range spectrum matrix after the third-order phase error compensation of the dispersion effect; In step 3.4, the SAR image contrasts C3 and C4 before and after the third-order phase error compensation due to the dispersion effect are calculated according to equations (13) and (14), respectively. The calculation formulas are: Where I3(x,y) is the modulus of each element in the SAR two-dimensional image matrix before compensation for the third-order phase error due to dispersion effect, I4(x,y) is the modulus of each element in the SAR two-dimensional time domain matrix after compensation for the third-order phase error due to dispersion effect, x is the number of sampling points in azimuth, and y is the number of sampling points in range. Step 3.5, compare the magnitude relationship between the contrast ratios C3 and C4 before and after compensation: adjust the iteration step size. If C3 > C4, then Δγ2 is taken as -Δγ2 / 2; if C3 < C4, then Δγ2 is taken as Δγ2. Thus, a new third-order phase error compensation function Δψ for the dispersion effect is constructed, and the third-order phase error compensation for the dispersion effect is processed. Through continuous cyclic iteration, when the iteration step size Δγ2 is less than the dispersion error detection threshold γ g2 , the loop ends, and the third-order phase error compensation for the dispersion effect is completed.

5. A plasma sheath multi-order dispersion effect error compensation system based on a two-step self-focusing process according to the method of any one of claims 1 to 4, characterized in that: include: Strong point target search module: uses the peak search method to search for strong scattering points P in the SAR image A, and constructs the SAR two-dimensional image matrix I with P as the central element; Dispersion effect second-order phase error compensation module: Set the initial dispersion compensation factor γ1, iterative step size Δγ1, construct the dispersion effect second-order phase error compensation function Δφ, and calculate the dispersion effect error detection threshold γ based on image focusing theory g1 , adjust the dispersion compensation factor according to the contrast of the image matrix before and after compensation, and realize the second-order phase error compensation of the dispersion effect of the SAR two-dimensional image matrix I through cyclic iteration; Dispersion effect third-order phase error compensation module: Set the initial dispersion compensation factor γ2, iterative step size Δγ2, construct the dispersion effect third-order phase error compensation function Δψ, and calculate the dispersion effect error detection threshold γ based on image focusing theory g2 , adjusting the dispersion compensation factor according to the contrast of the image matrix before and after compensation, and realizing the third-order phase error compensation of the dispersion effect on the SAR two-dimensional image matrix I2 after the second-order phase error compensation of the dispersion effect through cyclic iteration; Output compensated image module: outputs the plasma sheath multi-order dispersion effect error compensated image based on the SAR two-dimensional image matrix after second-order and third-order phase error compensation.

6. A plasma sheath multi-order dispersion effect error compensation device based on two-step self-focusing processing, characterized in that: include: Memory: used to store a computer program for implementing the method for compensating for multi-order dispersion effect errors of a plasma sheath based on a two-step self-focusing process as claimed in any one of claims 1 to 4; Processor: configured to implement the plasma sheath multi-order dispersion effect error compensation method based on two-step self-focusing processing as claimed in any one of claims 1 to 4 when executing the computer program.

7. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the plasma sheath multi-order dispersion effect error compensation method based on two-step self-focusing processing are implemented as described in any one of claims 1 to 4.

8. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for compensating for multi-order dispersion effect errors of a plasma sheath based on two-step self-focusing processing as claimed in any one of claims 1 to 4 is implemented.

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