Image entropy-based bi-static ISAR azimuth scaling and geometric correction method

Abstract

The application provides a kind of based on image minimum entropy dual-base ISAR azimuth scaling and geometric correction method, utilize the condition that ISAR translation momentum has no contribution to imaging result, translation momentum is estimated and is compensated, can reduce the defocusing influence of translation momentum to imaging result;Considering the influence of the space-variant defocusing term and geometric deformation term caused by the rotation momentum of dual-base ISAR on imaging, the distance migration is compensated by the warping deformation, then the second-order space-variant error compensation function is reconstructed, the space-variant factor parameters are solved by minimizing the optimization cost function, and the high-order error phase is compensated by substituting into the compensation function, so as to improve the compensation precision;Since there is a certain analytical expression relationship between the target relative radar rotation speed and the space-variant factor, the target relative radar rotation speed is estimated by using the space-variant factor, and the focusing imaging result is further scaled;In addition, the geometric correction function is constructed to carry out geometric correction, and the target information extraction precision is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar target positioning, and particularly relates to a double-base ISAR azimuth scaling and geometric correction method based on image minimum entropy. BACKGROUND

[0002] Due to the characteristics of all-day, all-weather, high resolution and long distance, inverse synthetic aperture radar (ISAR) plays an important role in aviation and space target detection. With the rapid development of inverse synthetic aperture radar (ISAR), although the existing imaging radar can provide high resolution, when detecting small satellites and other space targets, higher resolution is needed to accurately describe the characteristics. In double-base inverse synthetic aperture radar (ISAR) imaging, the rotation speed of the moving target will cause the phase error of the double-base ISAR target to have two-dimensional space variation characteristics, and the time-varying nature of the target double-base angle will make the two-dimensional space-varying phase error of the double-base ISAR target have a high-order form about time, resulting in defocusing, azimuth widening and other phenomena in double-base ISAR imaging. In addition, compared with single-base ISAR, the double-base angle of double-base ISAR will also cause deformation of the imaging result, which will affect the subsequent target recognition and classification.

[0003] The method of "double-base ISAR image distortion correction method" of Liang Siyang et al. discloses a method of combining phase gradient (PGA) algorithm and radar prior measurement information to solve Doppler information and construct a compensation function to complete the distortion correction of the image. Due to the influence of the two-dimensional space variation characteristics of the phase error, and the dependence of the imaging on the accuracy of the initial double-base angle as prior information, the imaging effect is not good.

[0004] The method of "a compound double-base radar precession target ISAR image transverse scaling method" of Ai Xiaofeng et al. discloses a method of extracting a single / double-base ISAR strong scattering center position at the same time to form a scattering center pair, and iteratively solving the transverse scaling coefficient by using image registration, so as to realize ISAR imaging scaling. Due to the two-dimensional space variation characteristics of the phase error and the influence of the double-base angle change on the focusing position, the scheme is prone to error, and the scheme needs to establish accurate prior information of the scattering center association pairing and the double-base angle, which will cause the problems of low accuracy and low applicability. SUMMARY

[0005] In order to solve the above problems in the prior art, the application provides a double-base ISAR azimuth scaling and geometric correction method based on image minimum entropy. The technical problems to be solved by the application are solved by the following technical scheme.

[0006] The application provides a double-base ISAR azimuth scaling and geometric correction method based on image minimum entropy, which comprises the following steps:

[0007] S100, receive echo signals of a moving target in a signal-to-noise ratio environment, and sequentially perform a range direction pulse compression processing and a translational motion compensation on the echo signals to obtain a translational motion compensated echo signal matrix;

[0008] S200, project the translational motion compensated echo matrix onto an imaging plane to obtain a new echo signal matrix, and obtain an approximate echo signal matrix by approximating a double base angle modulation factor;

[0009] S300, transform the approximate echo signal matrix by using a Shearlet transform, and construct a compensation function;

[0010] S400, construct a cost function by taking the Shearlet transformed echo signal matrix as a variable, and obtain an optimal value of an air variable error phase parameter by iteratively optimizing the cost function;

[0011] S500, substitute the optimal value of the air variable error phase parameter into the compensation function, and compensate the Shearlet transformed echo signal matrix by using the compensation function to obtain a focused imaging result after two-dimensional air variable error correction;

[0012] S600, estimate a target relative radar rotation speed by using the optimal value of the air variable error phase parameter, and calibrate the focused imaging result in a resolution correction manner by using the estimated rotation speed to realize calibration of the focused imaging result;

[0013] S700, determine an error between a real projection coordinate and a calibrated coordinate of a scattering point in a same distance unit according to the focused imaging result, and construct a geometric correction function by using the error;

[0014] S800, geometrically correct the calibrated focused imaging result by using the geometric correction function to obtain an image after geometric correction.

[0015] 1、The present application considers the influence of high-order errors of phase air variation on imaging quality, optimizes and solves the air variable factor by constructing a cost function, further constructs a compensation function by using the information to compensate the air variable defocusing term, and accurately estimates the target relative radar rotation speed to obtain a calibration result, so that the noise resistance and calibration accuracy of the present application are improved.

[0016] 2、The present application calculates the double base angle variation according to the radar tracking measurement result, compensates the imaging result by constructing a shape correction function to obtain accurate calibration, thereby improving the final ISAR imaging quality.

[0017] The present application will be further described in detail below with reference to the drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1A flowchart of a method for dual-basis ISAR azimuth scaling and geometric correction based on image minimum entropy is provided in the present application.

[0019] Figure 2 A flowchart of dual-basis ISAR space-variant error correction and azimuth scaling is provided in the present application.

[0020] Figure 3 A flowchart of dual-basis ISAR geometric deformation correction is provided in the present application.

[0021] Figure 4a A simulation point scattering model is provided in the present application.

[0022] Figure 4b A simulation target motion geometry diagram is provided in the present application.

[0023] Figure 5 A simulation satellite experiment dual-basis angle curve changing with time is provided in the present application.

[0024] Figure 6 An imaging result after Keystone is provided in the present application.

[0025] Figure 7 An imaging and scaling result after space-variant error correction is provided in the present application.

[0026] Figure 8 An imaging result after geometric deformation correction is provided in the present application. DETAILED DESCRIPTION

[0027] The present application will be further described in detail below in combination with specific embodiments, but the embodiments of the present application are not limited thereto.

[0028] As shown in the accompanying drawings, Figure 1 a method for dual-basis ISAR azimuth scaling and geometric correction based on image minimum entropy is provided in the present application, which comprises:

[0029] S100, receiving echo signals of a moving target in a signal-to-noise ratio environment, and sequentially performing distance direction pulse compression processing and translation compensation on the echo signals to obtain a translation compensated echo signal matrix;

[0030] In an optional embodiment of the present application, S100 comprises:

[0031] S110, transmitting a linear frequency modulation signal to a moving target by a transmitting radar A in a dual-basis inverse synthetic aperture radar (ISAR), and receiving a target scattering echo matrix in a low signal-to-noise ratio environment by a receiving radar B in the dual-basis ISAR;

[0032] Wherein, the echo matrix is composed of echo data, the echo matrix size is N*M, N represents the distance unit number of echo, and M represents the azimuth unit number of echo.

[0033] S120, the echo matrix is processed by a distance direction pulse compression processing method of matched filtering to obtain a distance pulse compression echo matrix.

[0034] S130, the translational component of the target is estimated according to the translational compensation method, and each element of the translational compensation matrix is calculated according to the translational component to obtain the translational compensation matrix.

[0035] Wherein, the translational compensation method comprises: envelope alignment and feature point self-focusing algorithm.

[0036] S140, the translational compensation matrix is multiplied with the distance pulse compression echo matrix to obtain a translational compensation echo signal matrix.

[0037] The translational compensation echo signal matrix is represented as:

[0038]

[0039] Wherein, S(k r ,t) represents the translational compensation echo signal matrix, k r represents the wave number, f c represents the radar carrier frequency, c represents the light speed, t represents the slow time, W(k r ,t) represents the echo spectrum envelope, sigma i represents the target scattering point intensity, represents the bistatic angle modulation factor, beta(t) represents the bistatic angle, theta represents the azimuth angle, alpha represents the pitch angle, (x i ,y i ,z i ) represents the position of the i-th scattering point.

[0040] S200, the translational compensation echo matrix is projected onto the imaging plane to obtain a new echo signal matrix, and an approximate echo signal matrix is obtained by approximating the bistatic angle modulation factor.

[0041] The ISAR imaging time is short, and the beam scanning range can be considered as a plane in the imaging time, the influence of the distance from the scattering point outside the plane to the plane on the imaging can be ignored, and the target is projected onto the imaging plane to obtain a new echo signal matrix.

[0042] The S200 of the application comprises:

[0043] S210, projecting the echo matrix after the translation compensation to the imaging plane to obtain a new echo signal matrix; the new echo signal matrix projected to the imaging plane is represented as:

[0044]

[0045] wherein (x i ′,y i ′) represents the projection of the i-th scattering point (x i ,y i ,z i ) in the target on the imaging plane, θ′ represents the scanning angle of the wave beam on the imaging plane, the scanning angle θ′ = ωt, and ω represents the rotation speed of the target on the imaging plane relative to the radar.

[0046] S220, approximating the bistatic angle modulation factor by using the following formula (3):

[0047]

[0048] S230, substituting the approximate bistatic angle modulation factor into formula (2) to approximate the new echo signal matrix, to obtain an approximate echo signal matrix;

[0049] Since the scanning angle θ′ is very small, the approximate bistatic angle modulation factor and the approximate value of the sine of the scanning angle θ′ are substituted into formula (2) to obtain the approximate echo signal matrix:

[0050]

[0051] wherein a0 represents the constant term coefficient of the bistatic angle modulation factor, a1 represents the first-order term coefficient of the bistatic angle modulation factor, and a2 represents the second-order term coefficient of the bistatic angle modulation factor.

[0052] S300, transforming the approximate echo signal matrix by using the Shepp-Logan transform, and constructing a compensation function;

[0053] Suppose that the echo in the discrete range-Doppler domain after the Shepp-Logan transform processing is f(n,k); at this time, the echo only has a high-order spatially variant error azimuth phase. A range and azimuth spatially variant error compensation function is constructed to compensate for the spatially variant phase of the echo data, and a focused imaging result is obtained through discrete Fourier transform:

[0054]

[0055] wherein the compensation function of the second-order range and azimuth spatially variant error is as follows:

[0056] H r =exp(jq1nk 2 ) (6).

[0057] H a = exp (jq2mk 2 ) (7);

[0058] Wherein, I (n, m) indicates discrete imaging result, n indicates corresponding distance unit serial number, n = [-N / 2,..., N / 2-1], m indicates azimuth unit serial number, m = [-M / 2,..., M / 2-1], q1 indicates distance direction space-variant factor coefficient, q2 indicates azimuth direction space-variant factor coefficient, Indicate the position coordinates of azimuth time domain of echo, K indicates the number of azimuth units, M indicates the number of azimuth units, and N indicates the number of distance units.

[0059] S400, the echo signal matrix after the stone shape transformation is used as a variable to construct a cost function, and the optimal value of the space-variant error phase parameter is obtained by iteratively optimizing the cost function;

[0060] The S400 of the application comprises:

[0061] S410, the echo signal matrix after the stone shape transformation is used as a variable to construct a cost function;

[0062] Wherein, the cost function is expressed as:

[0063]

[0064] Wherein, the image entropy value Ent (·) is:

[0065]

[0066] Wherein, Indicate the total energy of the signal.

[0067] S420, the optimal value of the space-variant error phase parameter is obtained by iteratively optimizing the cost function using the BFGS algorithm.

[0068] The cost function of the optimization problem has a minimum value, which can be solved by various quasi-Newton methods to obtain the optimal value of the image entropy of the imaging result with respect to the space-variant error phase parameter {q1, q2}.

[0069] The BFGS algorithm is used to minimize and optimize the cost function of the image entropy of the imaging result, and the process comprises:

[0070] (10a) calculate the first-order gradient of the image entropy of the imaging result with respect to the space-variant error phase parameter {q1, q2}

[0071] (10b) initialize parameters, set the iteration coefficient i = 1, and set the compensation vector parameter q = (q1, q2)T = (0, 0) T , a neighboring entropy value change threshold ε, initializing a Hessian matrix B0= E, inputting a defocused image I0(n, m)

[0072] (10c) calculating an entropy value gradient g of the current image i

[0073] (10d) determining a current parameter search direction according to the following formula:

[0074]

[0075] (10e) determining a current optimal step size by solving the following formula using a one-dimensional parameter search method

[0076]

[0077] wherein λ i is a search step size variable.

[0078] (10f) setting q i = q i-1 + s i , and substituting it into a phase compensation function to obtain a focused image denoted as I i (n, m), and then calculating a compensated image contrast gradient g i+1

[0079] (10g) if |Ent(I i+1 )-Ent(I i )|<ε, stopping iteration and outputting the parameter otherwise, modifying the Hessian matrix according to the following formula, and proceeding with the next round of iteration, jumping to step (10d)

[0080] y i = g i+1 -g i

[0081]

[0082] S500, substituting the optimal value of the phase parameter of the spatially variant error into a compensation function, and compensating the echosignal matrix after the warping deformation using the compensation function to obtain a focused imaging result after two-dimensional spatially variant error correction;

[0083] substituting the spatially variant defocusing factor in the optimized spatially variant error phase parameter into the compensation function to obtain a focused imaging result after two-dimensional spatially variant error correction;

[0084]

[0085] wherein, represents the real projection coordinate of the i-th scattering point on the imaging plane, ρ a represents the azimuth resolution, ρ r represents the range resolution, sinc represents a sinc function, that is,

[0086] S600, using the optimal value of the space-variant error phase parameter to estimate the rotation speed of the target relative to the radar, and using the estimated rotation speed to correct the resolution of the focused imaging result in a manner, so as to realize the calibration of the focused imaging result;

[0087] The S600 of the application comprises:

[0088] S610, according to the wave number domain expression, the range resolution and the azimuth resolution of the focused imaging result after the two-dimensional space-variant error correction in S500 are determined:

[0089]

[0090]

[0091] In the formula, Δk r represents the range of the radial wave number, which is determined by the radar parameter; a0=cos(β0 / 2) is a constant term of the double-base modulation factor, which is a constant close to 1, and is estimated by the position of the double-base radar and the target viewing angle parameter measured by the radar; λ represents the wavelength of the radar; T a represents the radar coherent accumulation time.

[0092] S620, according to the relationship between the space-variant error phase parameter and the rotation speed of the target relative to the radar, the rotation speed is estimated;

[0093] Wherein, the relationship between the space-variant error phase parameter and the rotation speed of the target relative to the radar is represented as:

[0094]

[0095] Wherein, k rc represents the center of the radial wave number, f prf represents the azimuth pulse repetition frequency of the radar;

[0096] The equivalent rotation speed of the target relative to the radar is:

[0097]

[0098] S630, the equivalent rotation speed of the target relative to the radar is substituted into the azimuth resolution to obtain the calibration result of the focused imaging result.

[0099] S700, according to the focusing imaging result, determining the error between the real projection coordinate and the coordinate after scaling of the scattering point in the same distance unit, and constructing a geometric correction function by using the error;

[0100] S700 includes:

[0101] S710, according to the horizontal coordinate focusing position of the focusing imaging result in S500, determining the error between the real projection coordinate and the coordinate after scaling of the scattering point in the same distance unit:

[0102]

[0103] wherein, represents the real x coordinate of the projection of the scattering point on the imaging plane, (x i ′,y i ′) represents the coordinate of the focusing position of the scattering point on the imaging plane after scaling; only the scattering point in the same distance unit is translated , the geometric corrected image y i ′ can be obtained, y r and the distance offset point number, so the translation amount of the scattering point can be represented by p r and p a .

[0104] S720, the translation can be realized by multiplying a linear phase function on each distance unit, so a geometric correction function is constructed according to the error:

[0105]

[0106] wherein, M represents the number of azimuth units of the image, N represents the number of distance units of the image, m represents the serial number of the azimuth unit, and n represents the serial number of the corresponding distance unit, which takes the value range [-N / 2, -N / 2+1, …, N / 2-1].

[0107] S800, using the geometric correction function to geometrically correct the focusing imaging result after scaling to obtain the image after geometric correction.

[0108] The image after geometric correction is represented as:

[0109] I1=FFT A [IFFT A [I]·H GC (n,m)] (17);

[0110] wherein, I represents the image obtained by imaging and scaling, I1 represents the image after geometric correction, FFT A [·] and IFFT A[·] denotes a fast Fourier transform and a fast inverse Fourier transform operation in azimuth direction, respectively.

[0111] The application provides a double-base ISAR azimuth scaling and geometric correction method based on image minimum entropy, estimates and compensates the drift velocity by using the condition that the ISAR drift velocity does not contribute to the imaging result, and can reduce the defocusing influence of the drift velocity on the imaging result; the influence of the space-varying defocusing term and the geometric deformation term caused by the rotation velocity of the double-base ISAR on the imaging is considered, the range-to-Doppler migration is compensated by the warping deformation, a second-order space-varying error compensation function is re-constructed, the space-varying factor parameters are solved by minimizing the optimization cost function, and the high-order error phase is compensated by substituting the space-varying factor parameters into the compensation function, so that the compensation precision is improved; since there is a certain analytical expression relationship between the rotation velocity of the target relative to the radar and the space-varying factor, the rotation velocity of the target relative to the radar is estimated by using the space-varying factor, and the focused imaging result is further scaled. The geometric deformation term does not affect the imaging quality of the double-base ISAR, but affects the focusing position of the scattering point, the double-base angle modulation factor is obtained by calculating and fitting the double-base angle by using the radar tracking measurement information, the geometric correction function is constructed, and the target information extraction precision is improved.

[0112] The effectiveness of the application can be further illustrated by the following simulation.

[0113] Simulation content and result analysis:

[0114] Simulation experiment: the simulation radar parameters are shown in Table 1:

[0115] Table 1 Simulation radar parameter table

[0116] Carrier frequency Bandwidth Pulse repetition frequency Pulse width Number of pulses 35 GHz 1 GHz 300 Hz 1 us 2048

[0117] The point scattering model of the simulation target is shown in Figure 4a The satellite as a whole presents a square shape, and there is a solar panel with the same structure on the upper, lower, left and right sides, the distance from the edge of the solar panel to the center of the satellite is 28.5 m, and the width of the solar panel is 6 m.

[0118] The double-base ISAR geometric motion model of the simulation scene is shown in Figure 4b The target moves along the X-axis at a speed of 4000 m / s, the receiving radar and the transmitting radar are located on the X-axis, and the distance between the two is 120 km. The single-base equivalent radar is located between the transmitting radar and the receiving radar.

[0119] The change of the double-base angle of the satellite target within the imaging time is shown in Figure 5 It can be found that the double-base angle changes by about 0.5° within the observation time.

[0120] The simulation data is processed by using the method and the real parameters of the application respectively.

[0121] Figure 6 is the imaging result of azimuth FFT on the result of Keystone transform, it can be seen that the imaging result will appear obvious azimuth spread, which will affect the imaging quality, and obvious azimuth caustics will appear at the edge points, and the azimuth spread is serious.

[0122] Figure 7 is the result of two-dimensional space-variant error correction and calibration by using the method proposed in the present application, it can be found that all the scattering points in the imaging result are well focused, and the imaging result is clear in profile. Figure 5 The two boundary scattering points P1 = (-28.6038, -7.08826) and P2 = (-7.541, 27.6233) are shown in the figure, and the distances of the two scattering points to the target center are L1 = |OP1| = 29.47 m and L2 = |OP2| = 28.63 m respectively by calculation, because the target is approximately parallel to the imaging plane, so the projections of the two scattering points on the imaging plane are approximately the same as OP1 and OP2, that is, the real target projection should present a square boundary, and the distances of the edge points of the four solar panels to the target center are 28.5 m. Figure 4a It can be found that the imaging calibration result has obvious geometric deformation compared with the real projection result, and the outer boundary of the target is no longer a square but a rectangle. The angle θ1 = acos[OP1·OP2 T / (|OP1||OP2|)] = 88.65° of OP1 and OP2 is calculated, and it can be found that the adjacent solar panels no longer satisfy the vertical relationship.

[0123] Figure 8 is the result of geometric correction and secondary calibration by using the method proposed in the present application, it can be found that all the scattering points in the imaging result are well focused, and the imaging result is clear in profile. The same two scattering points P1 = (-28.6038, -7.08826) and P2 = (-7.28096, 27.6233) are selected, and the distances of the scattering points to the target center are L1 = |OP1| = 29.47 m and L2 = |OP2| = 28.57 m respectively by calculation, and the angle θ1 = acos[OP1·OP2 T / (|OP1||OP2|)] = 89.15° of OP1 and OP2 is calculated, and it can be found that the adjacent two solar panels are closer to satisfy the vertical relationship (the error is not more than 1°).

[0124] In summary, the simulation experiment verifies the correctness, effectiveness and reliability of the present application.

[0125] Furthermore, the terms "first", "second", etc. are used only for descriptive purposes and do not connote or imply relative importance. Thus, a feature defined with "first", "second", etc. can implicitly or explicitly include one or more of the features.

[0126] Although the present application has been described in connection with various embodiments thereof, it will be understood that other variations and modifications of the described embodiments can be made by those skilled in the art upon reading the description of the application set forth above. In the claims, the word "comprising" does not exclude other components or steps not mentioned in the claims. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements.

[0127] The above description is further to make further detailed description of the present application in connection with specific preferred embodiments, and cannot be deemed to limit the specific implementation of the present application to these descriptions. For those skilled in the art, without departing from the concept of the present application, a number of simple deductions or substitutions can be made, which should be regarded as falling within the protection scope of the present application.

Claims

1. A method for bi-static ISAR azimuth scaling and geometric correction based on image minimum entropy, characterized in that, Comprise: S100, receive echo signals of a moving target in a signal-to-noise ratio environment, and sequentially perform range direction pulse compression processing and plane motion compensation on the echo signals to obtain a plane motion compensated echo signal matrix; S200, project the plane motion compensated echo matrix onto an imaging plane to obtain a new echo signal matrix, and obtain an approximate echo signal matrix by approximating a double base angle modulation factor; S300, transform the approximate echo signal matrix using a warping transform, and construct a compensation function; S400, construct a cost function by taking the warping transformed echo signal matrix as a variable, and obtain an optimal value of an air variable error phase parameter by iteratively optimizing the cost function; S500, substitute the optimal value of the air variable error phase parameter into the compensation function, and compensate the warping transformed echo signal matrix using the compensation function to obtain a two-dimensional air variable error corrected focusing imaging result; S600, estimate the rotational speed of the target relative to the radar using the optimal value of the air variable error phase parameter, and calibrate the focusing imaging result in a resolution correction manner using the estimated rotational speed to realize calibration of the focusing imaging result; S700, determine the error between the real projection coordinates and the calibrated coordinates of the scattering points in the same distance unit according to the focusing imaging result, and construct a geometric correction function using the error; S800, geometrically correct the calibrated focusing imaging result using the geometric correction function to obtain a geometrically corrected image.

2. The image entropy-based bi-static ISAR azimuth scaling and geometric correction method according to claim 1, characterized in that, S100 comprises: S110, transmitting a linear frequency modulation signal to a moving target by a transmitting radar in a double base inverse synthetic aperture radar (ISAR), and receiving a target scattering echo matrix in a low signal-to-noise ratio environment by a receiving radar in the double base ISAR; Wherein, the echo matrix is composed of echo data, and the echo matrix has a size of N×M, N represents the number of distance units of the echo, and M represents the number of azimuth units of the echo; S120, performing range direction pulse compression processing on the echo matrix using a matched filter method to obtain a range pulse compressed echo matrix; S130, estimating the plane motion component of the target according to a plane motion compensation method, and calculating each element of the plane motion compensation matrix according to the plane motion component to obtain a plane motion compensation matrix; S140, point multiplying the plane motion compensation matrix and the range pulse compressed echo matrix to obtain a plane motion compensated echo signal matrix.

3. The image entropy-based bi-static ISAR azimuth scaling and geometric correction method according to claim 2, characterized in that, The plane motion compensated echo signal matrix in S100 is represented as: where S(k r ,t) denotes the translational compensated echo signal matrix, k r denotes the wave number, f c denotes the radar carrier frequency, c denotes the speed of light, t denotes the slow time, W(k r ,t) denotes the echo spectrum envelope, σ i denotes the target scatterer intensity, denotes the bistatic angle modulation factor, β(t) denotes the bistatic angle, θ denotes the azimuth angle, α denotes the elevation angle, (x i ,y i ,z i ) denotes the position of the i-th scatterer.

4. The image entropy-based bi-static ISAR azimuth scaling and geometric correction method according to claim 3, characterized in that, S200 comprises: S210, projecting the plane motion compensated echo matrix onto an imaging plane to obtain a new echo signal matrix: Among them, (x′ i ,y′ i ) represents the i-th scattering point (x) in the target. i ,y i ,z i The projection of the beam onto the imaging plane, θ′ represents the scanning angle of the beam on the imaging plane, the scanning angle θ′=ωt, ω represents the rotational speed of the target relative to the radar on the imaging plane; S220, approximating a double base angle modulation factor using the following formula (3): S230, substituting the approximate double base angle modulation factor into formula (2) to approximate the new echo signal matrix to obtain an approximate echo signal matrix: Wherein, a0 represents a double base angle modulation factor constant term coefficient, a1 represents a double base angle modulation factor first order term coefficient, and a2 represents a double base angle modulation factor second order term coefficient.

5. The image entropy-based bi-static ISAR azimuth scaling and geometric correction method according to claim 3, characterized in that, The discrete range Doppler domain echo after the wedge-shaped transformation in S300 is f(n, k); the focused imaging result obtained by the discrete Fourier transform is represented as: The compensation function is: H r = exp(jq1nk 2 ) (6); H a = exp(jq2mk 2 ) (7); wherein I(n,m) represents a discrete imaging result, n represents a corresponding distance unit sequence number, n=[-N / 2,...,N / 2-1], m represents a sequence number of an azimuth unit, m=[-M / 2,...,M / 2-1], q1 represents a range space-variant factor coefficient, q2 represents an azimuth space-variant factor coefficient, represents a position coordinate of an azimuth time domain of an echo, K represents an azimuth unit number, M represents an azimuth unit number, and N represents a range unit number.

6. The image entropy-based bi-static ISAR azimuth scaling and geometric correction method according to claim 5, characterized in that, S400 includes: S410, the echo signal matrix after the wedge-shaped transformation is taken as a variable to construct a cost function; The cost function is represented as: The image entropy value Ent(·) is: wherein represents the sum of the energies of the signals; S420, the BFGS algorithm is used to iteratively optimize the cost function to obtain the optimal value of the space-variant error phase parameter.

7. The image entropy-based bi-static ISAR azimuth scaling and geometric correction method according to claim 6, characterized in that, The focused imaging result after the two-dimensional space-variant error correction in S500 is represented as: wherein, denotes the real projection coordinate of the i-th scattering point on the imaging plane, p a denotes the azimuthal resolution, p r denotes the range resolution, sinc denotes the sine function, 8. The image entropy-based bi-static ISAR azimuth scaling and geometric correction method according to claim 7, characterized in that, S600 includes: S610, according to the wave number domain expression, the distance resolution and the azimuth resolution of the focused imaging result after the two-dimensional space-variant error correction in S500 are determined: where Δkrrepresents the range of radial wave numbers, determined by radar parameters; a0= cos(β0 / 2) is a constant term of the bistatic modulation factor, which is a constant close to 1, estimated by the position of the bistatic radar and the target aspect parameter measured by the radar, λ represents the radar wavelength, T a represents the radar coherent accumulation time; S620, the rotational speed of the target relative to the radar is estimated according to the relationship between the space-variant error phase parameter and the rotational speed of the target relative to the radar; The relationship between the space-variant error phase parameter and the rotational speed of the target relative to the radar is represented as: where k rc represents the radial wavenumber center, f prf represents the azimuth pulse repetition frequency of the radar; The equivalent rotational speed of the target relative to the radar is: S630, the equivalent rotational speed of the target relative to the radar is substituted into the azimuth resolution to obtain the calibration result of the focused imaging result.

9. The image entropy-based bi-static ISAR azimuth scaling and geometric correction method according to claim 8, characterized in that, S700 includes: S710, according to the horizontal coordinate focusing position of the focused imaging result in S500, the error between the real projection coordinates of the scattering points in the same distance unit and the coordinates after the calibration is determined: wherein, x' represents the real x coordinate of the projection of the scattering point on the imaging plane, (x i ′,y i ′) represents the coordinates of the scattering point on the focusing position of the imaging plane obtained after calibration; S720, a geometric correction function is constructed according to the error: Wherein, M represents the number of azimuth units of the image, N represents the number of distance units of the image, m represents the serial number of the azimuth unit, and n represents the serial number of the corresponding distance unit, which takes the value range [-N / 2, -N / 2+1, …, N / 2-1].

10. The image entropy-based bi-static ISAR azimuth scaling and geometric correction method according to claim 9, characterized in that, The image after the geometric correction in S800 is represented as: I1= FFT A [IFFT A [I]·H GC (n,m)] (17); wherein I denotes the image obtained by imaging calibration, I1 denotes the image after geometric correction, FFT A [·] and IFFT A [·] denote the azimuthal fast Fourier transform and the fast inverse Fourier transform operation, respectively.

Images