CN116819466A - Double-base ISAR azimuth calibration and geometric correction method based on minimum entropy of image - Google Patents
Double-base ISAR azimuth calibration and geometric correction method based on minimum entropy of image Download PDFInfo
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Abstract
The application provides a double-base ISAR azimuth calibration and geometric correction method based on minimum entropy of an image, which utilizes the condition that ISAR translational quantity does not contribute to an imaging result to estimate and compensate the translational quantity, and can reduce the defocusing influence of the translational quantity on the imaging result; taking the influence of space-variant defocus terms and geometric deformation terms on imaging, which are brought by the rotation quantity of the bistatic ISAR, into consideration, compensating the range migration by the rock-fill transformation, reconstructing a second-order space-variant error compensation function, solving space-variant factor parameters by minimizing an optimization cost function, and substituting the space-variant factor parameters into the compensation function to compensate the high-order error phase, thereby improving the compensation precision; because the rotation speed of the target relative to the radar and the space-variant factor have a determined analytic expression relationship, the rotation speed of the target relative to the radar is estimated by using the space-variant factor, and the focusing imaging result is further calibrated; in addition, geometric correction is carried out by constructing a geometric correction function, so that the extraction precision of the target information is improved.
Description
Technical Field
The application belongs to the technical field of radar target positioning, and particularly relates to a bistatic ISAR azimuth calibration and geometric correction method based on minimum entropy of an image.
Background
The inverse synthetic aperture radar ISAR plays an important role in aviation and aerospace target detection due to the characteristics of all-weather, high resolution, long distance and the like. With the rapid development of inverse synthetic aperture radar ISAR, although the existing imaging radar can provide higher resolution, when detecting space targets such as small satellites, the features of the space targets need to be accurately described by higher resolution. In the double-base inverse synthetic aperture radar ISAR imaging, the rotation speed of a moving target can lead the phase error of the double-base ISAR target to have two-dimensional space-variant characteristics, and the time-variant property of the double-base angle of the target can lead the two-dimensional space-variant phase error of the double-base ISAR target to have a high-order form related to time, so that the double-base ISAR imaging is defocused, the azimuth is widened and the like. In addition, compared with single-base ISAR, the double-base angle of double-base ISAR can cause deformation of imaging results, and can influence subsequent target recognition and classification.
Liang Siyang et al, "bistatic ISAR image distortion correction method" discloses a method for constructing a compensation function based on the combination of a Phase Gradient (PGA) algorithm and radar prior measurement information solution Doppler information to complete distortion correction of an image. Since this scheme is affected by the two-dimensional space-variant property of the phase error and the imaging depends on the accuracy of the a priori information of the initial double base angle, the imaging effect is poor.
Ai Xiaofeng et al disclose in the literature a method for transversely scaling an ISAR image of a composite bistatic radar precession target by extracting the positions of strong scattering centers at the same moment in combination with single/bistatic ISAR to form a scattering center pair, and iteratively solving transverse scaling coefficients by using an image registration mode, thereby realizing ISAR imaging scaling. The scheme is extremely easy to generate errors due to the two-dimensional space-variant characteristic of phase errors and the influence of double-base angle change on the focusing position, and the scheme needs to establish accurate prior information of the correlation pairing of the scattering centers and the double-base angle, so that the defects of low accuracy and low applicability can be caused.
Disclosure of Invention
In order to solve the problems in the prior art, the application provides a bistatic ISAR azimuth calibration and geometric correction method based on minimum entropy of an image. The technical problems to be solved by the application are realized by the following technical scheme:
the application provides a double-base ISAR azimuth calibration and geometric correction method based on minimum entropy of an image, which comprises the following steps:
s100, receiving echo signals of a moving object in a signal-to-noise ratio environment, and sequentially performing distance pulse compression processing and translational compensation on the echo signals to obtain a translational compensated echo signal matrix;
s200, projecting the echo matrix after translational compensation onto an imaging plane to obtain a new echo signal matrix, and approximating the double-base angle modulation factor to obtain an approximate echo signal matrix;
s300, transforming the approximate echo signal matrix by using the wedge stone transformation, and constructing a compensation function;
s400, constructing a cost function by taking the echo signal matrix after the lithographically transformed is used as a variable, and obtaining an optimal value of space-variant error phase parameters by carrying out iterative optimization on the cost function;
s500, substituting an optimal value of the space-variant error phase parameter into a compensation function, and compensating an echo signal matrix subjected to the lithotomy shape transformation by using the compensation function to obtain a focusing imaging result after two-dimensional space-variant error correction;
s600, estimating the rotation speed of the target relative to the radar by using an optimal value of the space-variant error phase parameter, and calibrating the focusing imaging result by using a mode of correcting the resolution of the focusing imaging result by using the estimated rotation speed;
s700, determining errors between real projection coordinates of scattering points in the same distance unit and coordinates after calibration according to a focusing imaging result, and constructing a geometric correction function by utilizing the errors;
s800, performing geometric correction on the calibrated focusing imaging result by using a geometric correction function to obtain an image after geometric correction.
1. According to the method, the influence of the high-order error of the phase space variant on the imaging quality is considered, the space factor is optimized and solved through constructing the cost function, the space defocusing term is compensated by utilizing the information to construct the compensation function, and the target relative radar rotating speed is accurately estimated to obtain the calibration result, so that the noise resistance and the calibration accuracy of the method are improved.
2. According to the application, the double-base angle change is subjected to fitting calculation according to the radar tracking measurement result, and the imaging result is compensated by constructing the deformation correction function to obtain accurate calibration, so that the final ISAR imaging quality is improved.
The present application will be described in further detail with reference to the accompanying drawings and examples.
Drawings
FIG. 1 is a schematic flow chart of a method for scaling and geometric correction of a bistatic ISAR orientation based on minimum entropy of an image;
FIG. 2 is a flow chart of the double-base ISAR space-variant error correction and azimuth calibration provided by the application;
FIG. 3 is a flow chart of a dual-base ISAR geometric deformation correction provided by the application;
FIG. 4a is a simulated point scattering model provided by the present application;
FIG. 4b is a schematic diagram of the motion geometry of the simulation experiment target provided by the application;
FIG. 5 is a graph showing the variation of the experimental double base angles of the simulation satellite with time;
fig. 6 shows the imaging result after Keystone provided by the present application;
FIG. 7 is a representation of the results of space variant error corrected imaging and scaling provided by the present application;
fig. 8 is an image result after geometric deformation correction provided by the present application.
Detailed Description
The present application will be described in further detail with reference to specific examples, but embodiments of the present application are not limited thereto.
As shown in FIG. 1, the application provides a method for scaling and geometrically correcting a double-base ISAR azimuth based on minimum entropy of an image, which comprises the following steps:
s100, receiving echo signals of a moving object in a signal-to-noise ratio environment, and sequentially performing distance pulse compression processing and translational compensation on the echo signals to obtain a translational compensated echo signal matrix;
in an alternative embodiment of the present application, S100 includes:
s110, transmitting a linear frequency modulation signal to a moving target through a transmitting radar A in a double-base inverse synthetic aperture radar ISAR, and receiving an echo matrix of target scattering in a low signal-to-noise ratio environment through a receiving radar B in the double-base inverse synthetic aperture radar ISAR;
the echo matrix consists of echo data, the size of the echo matrix is N multiplied by M, N represents the distance unit number of the echo, and M represents the azimuth unit number of the echo.
S120, performing distance pulse compression processing on the echo matrix by using a matched filtering method to obtain the echo matrix after distance pulse compression;
s130, estimating a translational component of the target according to a translational compensation method, and calculating each element of a translational compensation matrix according to the translational component to obtain the translational compensation matrix;
the translation compensation method comprises the following steps: envelope alignment and point-of-interest self-focusing algorithms.
And S140, carrying out dot multiplication on the translational compensation matrix and the echo matrix after the distance pulse compression to obtain an echo signal matrix after the translational compensation.
The translation compensated echo signal matrix is expressed as:
wherein ,S(kr T) represents the echo signal matrix after translational compensation, k r The wave number is represented by a number of waves,f c represents radar carrier frequency, c represents speed of light, t represents slow time, W (k) r T) represents the echo spectral envelope, σ i Representing the intensity of the scattering points of the target,represents a double base angle modulation factor, β (t) represents a double base angle, θ represents an azimuth angle, α represents a pitch angle, (x) i ,y i ,z i ) Indicating the location of the ith scattering point.
S200, projecting the echo matrix after translational compensation onto an imaging plane to obtain a new echo signal matrix, and approximating the double-base angle modulation factor to obtain an approximate echo signal matrix;
ISAR imaging time is short, the beam scanning range can be considered as a plane in the imaging time, the influence of scattering points outside the plane on the imaging can be ignored, and a target is projected onto the imaging plane to obtain a new echo signal matrix.
The S200 of the present application includes:
s210, projecting the echo matrix after translational compensation to an imaging plane to obtain a new echo signal matrix; the new echo signal matrix projected onto the imaging plane is expressed as:
wherein ,(xi ′,y i ' indicates the ith scattering point (x) in the target i ,y i ,z i ) The projection on the imaging plane, θ 'represents the scan angle of the beam on the imaging plane, and scan angle θ' =ωt, ω represents the rotational speed of the target on the imaging plane relative to the radar.
S220, approximating the double base angle modulation factor by the following formula (3):
s230, substituting the approximate double-base angle modulation factor into the formula (2) to approximate the new echo signal matrix, so as to obtain an approximate echo signal matrix;
because the scanning angle theta 'is very small, the sine and cosine of the scanning angle theta' can be approximated, and the approximated double-base angle modulation factor and the approximated value of the scanning angle sine and cosine are substituted into the formula (2) to obtain an approximated echo signal matrix:
wherein ,a0 Representing the coefficient of the constant term of the double-base angle modulation factor, a 1 Representing the coefficient of the primary term of the double base angle modulation factor, a 2 And the quadratic term coefficient representing the double base angle modulation factor.
S300, transforming the approximate echo signal matrix by using the wedge stone transformation, and constructing a compensation function;
assume that the echo of the discrete range-doppler domain after the wedge Dan Xingbian transform process is f (n, k); at this time, the echo has only the higher-order space-variant error azimuth phase. Constructing a space-variant error compensation function of distance and azimuth to compensate the space-variant phase of echo data, and obtaining a focused imaging result through discrete Fourier transform:
the compensation function of the second-order distance and the azimuth space-variant error is as follows:
H r ＝exp(jq 1 nk 2 ) (6)；
H a ＝exp(jq 2 mk 2 ) (7)；
wherein, I (n,m) represents a discrete imaging result, N represents a corresponding distance unit number, n= [ -N/2, ], N/2-1]M represents the sequence number of the azimuth cell, m= [ -M/2, ], M/2-1]，q 1 Represents the coefficient of the distance space-variant factor, q 2 Represents the azimuth space-variant factor coefficient,the position coordinates of the echo in the azimuth time domain are represented by K, M, and N, respectively.
S400, constructing a cost function by taking the echo signal matrix after the lithographically transformed is used as a variable, and obtaining an optimal value of space-variant error phase parameters by carrying out iterative optimization on the cost function;
the S400 of the present application includes:
s410, constructing a cost function by taking the echo signal matrix after the wedge stone shape transformation as a variable;
wherein the cost function is expressed as:
wherein, the image entropy value Ent (·) is:
wherein ,representing the sum of the energies of the signals.
S420, performing iterative optimization on the cost function by using a BFGS algorithm to obtain an optimal value of the space-variant error phase parameter.
The minimum value exists in the cost function of the optimization problem, and numerical optimization solution can be carried out through various quasi-Newton methods to obtain space-variant error phase parameters { q) of the image entropy of the imaging result 1 ,q 2 Optimal value of }.
The following describes a minimized optimization solution for the cost function of the entropy value of the imaging result by using the BFGS algorithm, and the process includes:
(10a) Calculating space-variant error phase parameter { q } of image entropy of imaging result 1 ,q 2 One step of }
(10b) Initializing parameters, setting iteration coefficients i=1, compensating vector parameters q= (q) 1 ,q 2 ) T ＝(0,0) T Initializing a hessian matrix B by using an adjacent entropy change threshold epsilon 0 E, input defocused image I 0 (n,m)
(10c) Calculating entropy gradient g of current image i
(10d) Determining a current parameter search direction according to the following formula:
(10e) Solving the following equation by utilizing a one-dimensional parameter searching mode to determine the current optimal step length
wherein ,λi Is the step variable of the search.
(10f) Setting upq i ＝q i-1 +s i And substituting it into the phase compensation function, the obtained focused image is denoted as I i (n, m) and then calculating the compensated image contrast gradient g i+1
(10g) If |Ent (I) i+1 )-Ent(I i )|<Epsilon, stop iteration and output parametersOtherwise, correcting the hessian matrix according to the following way, performing the next iteration, and jumping to the step (10 d)
y i ＝g i+1 -g i
S500, substituting an optimal value of the space-variant error phase parameter into a compensation function, and compensating an echo signal matrix subjected to the lithotomy shape transformation by using the compensation function to obtain a focusing imaging result after two-dimensional space-variant error correction;
the space-variant defocus factors in the space-variant error phase parameters obtained through optimization are brought into a compensation function, and then a focusing imaging result after two-dimensional space-variant error correction can be obtained;
wherein ,representing the true projection coordinates of the ith scattering point on the imaging plane, ρ a Representing azimuth resolution ρ r Representing the distance resolution, sinc represents the sine function, i.e. +.>
S600, estimating the rotation speed of the target relative to the radar by using an optimal value of the space-variant error phase parameter, and calibrating the focusing imaging result by using a mode of correcting the resolution of the focusing imaging result by using the estimated rotation speed;
the S600 of the present application includes:
s610, determining a distance resolution and an azimuth resolution of the focused imaging result after the two-dimensional space-variant error correction in S500 according to the wave number domain expression:
in the formula ,Δkr A range representing radial wave numbers, determined by radar parameters; a, a 0 ＝cos(β 0 2) is a constant term of a double-base modulation factor, is a constant which is closer to 1, is estimated by the position of a double-base radar and target visual angle parameters measured by the radar, lambda represents the radar wavelength, T a Representing radar coherence accumulation time.
S620, estimating the rotating speed according to the relation between the space-variant error phase parameter and the rotating speed of the target relative to the radar;
the relation between the space-variant error phase parameter and the rotating speed of the target relative to the radar is expressed as follows:
wherein ,krc Represents the radial wavenumber center, f prf Representing the azimuth pulse repetition frequency of the radar;
the equivalent rotational speed of the target relative to the radar is:
s630, substituting the equivalent rotation speed of the target relative to the radar into the azimuth resolution to obtain a calibration result of the focusing imaging result.
S700, determining errors between real projection coordinates of scattering points in the same distance unit and coordinates after calibration according to a focusing imaging result, and constructing a geometric correction function by utilizing the errors;
s700 includes:
s710, determining the error between the true projection coordinates of the scattering points in the same distance unit and the coordinates after calibration according to the abscissa focusing position of the focusing imaging result in S500:
wherein ,representing the true x-coordinate of the projection of the scattering point on the imaging plane, (x) i ′,y i ') represents the coordinates of the focal position of the scatter point in the imaging plane obtained by scaling; only the scattering points of the same distance units need to be shifted +.>Obtaining geometrically corrected image, y i ' can be defined by ρ r And the number of distance offset points, so that the amount of scattering point translation can be represented by ρ r and ρa And (3) representing.
S720, the translation may be achieved by multiplying each distance unit with a linear phase function, so a geometric correction function is constructed from the errors:
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 units, N represents the serial number of the corresponding distance unit, and the range of values is [ -N/2, -N/2+1, …, N/2-1].
S800, performing geometric correction on the calibrated focusing imaging result by using a geometric correction function to obtain an image after geometric correction.
The image after geometric correction is expressed as:
I 1 ＝FFT A [IFFT A [I]·H GC (n,m)] (17)；
wherein I represents an image obtained by imaging scaling, I 1 Representing the image after the geometric correction,FFT A [·]and IFFT A [·]Respectively representing the fast fourier transform and the inverse fast fourier transform operations of the azimuth direction.
The application provides a double-base ISAR azimuth calibration and geometric correction method based on minimum entropy of an image, which utilizes the condition that ISAR translational quantity does not contribute to an imaging result to estimate and compensate the translational quantity, and can reduce the defocusing influence of the translational quantity on the imaging result; taking the influence of space-variant defocus terms and geometric deformation terms on imaging, which are brought by the rotation quantity of the bistatic ISAR, into consideration, compensating the range migration by the rock-fill transformation, reconstructing a second-order space-variant error compensation function, solving space-variant factor parameters by minimizing an optimization cost function, and substituting the space-variant factor parameters into the compensation function to compensate the high-order error phase, thereby improving the compensation precision; because the rotation speed of the target relative to the radar and the space-variant factor have a determined analytic expression relationship, the rotation speed of the target relative to the radar is estimated by using the space-variant factor, and the focusing imaging result is further calibrated. The geometric deformation term does not influence the imaging quality of the double-base ISAR, but influences the focusing position of the scattering point, the double-base angle is calculated and fitted through radar tracking measurement information, the double-base angle modulation factor is obtained, a geometric correction function is constructed, and the extraction precision of target information is improved.
The effectiveness of the present application can be further illustrated by the following simulations.
Simulation content and result analysis:
simulation experiment: the simulated radar parameters are shown in table 1:
table 1 simulation radar parameter table
| Carrier frequency | Bandwidth of a communication device | Pulse repetition frequency | Pulse width | Pulse count |
| 35GHz | 1GHz | 300Hz | 1us | 2048 |
As shown in FIG. 4a, the point scattering model of the simulation target is that the satellite is square in whole, and solar sailboards with the same structural shape are respectively arranged at the upper, lower, left and right sides, the distance from the edge of the solar sailboard to the center of the satellite is 28.5m, and the width of the solar sailboard is 6m.
The double-base ISAR geometric motion model of the simulation scene is shown in FIG. 4b, the target moves linearly along the X-axis, the motion speed is 4000m/s, the receiving radar and the transmitting radar are located in the X-axis direction, and the distance between the receiving radar and the transmitting radar is 120km. Its monostatic equivalent radar is located between the transmitting radar and the receiving radar.
The change in the double base angle of the satellite target over the imaging time is shown in fig. 5, and it can be found that the double base angle becomes about 0.5 ° over the observation time.
The simulation data are processed by the method and the real parameters respectively.
Fig. 6 is an imaging result of performing azimuth FFT on a result after Keystone transformation, and it can be seen that obvious space-variant azimuth broadening occurs in the imaging result, imaging quality is affected, obvious azimuth focal dispersion occurs at edge points, and the azimuth broadening is serious.
Fig. 7 is a graph showing the results of two-dimensional space-variant error correction and scaling using the method presented herein, where it can be found that all scattering points in the imaging result are well focused and the imaging result is well defined. FIG. 5 shows two boundary scattering points P 1 = (-28.6038, -7.08826) and P 2 = (-7.541,27.6233), two scattering points can be obtained by calculationThe distance between the mark centers is L respectively 1 ＝|OP 1 |=29.47 m and L 2 ＝|OP 2 Because the target is approximately parallel to the imaging plane, |=28.63 m, its projection onto the imaging plane is approximately the same as fig. 4a, i.e. the real target projection should present a square boundary, and the distance from the edge points of the four solar panels to the center of the target is 28.5m. It can be found that the imaging scaling results show a significant geometrical deformation compared to the real projection results, the outer boundary of the object no longer being square but rectangular. Calculating OP 1 and OP2 Included angle theta of (2) 1 ＝acos[OP 1 ·OP 2 T /(|OP 1 ||OP 2 |)]=88.65 °, it can be found that the vertical relationship between adjacent solar sailboards is no longer satisfied.
Fig. 8 is a graph showing the results of geometric correction and secondary calibration using the method presented herein, where it can be seen that all scattering points in the imaging result are well focused and the imaging result is well defined. Selecting two scattering points P identical to the previous one 1 = (-28.6038, -7.08826) and P 2 = (-7.28096,27.6233), the distances from the scattering point to the center of the target are calculated to be L 1 ＝|OP 1 |=29.47 m and L 2 ＝|OP 2 |=2857 m, OP is calculated 1 and OP2 Included angle theta of (2) 1 ＝acos[OP 1 ·OP 2 T /(|OP 1 ||OP 2 |)]=89.15°, it can be found that the vertical relationship between two adjacent solar sailboards is more closely satisfied (the error does not exceed 1 °).
In conclusion, the simulation experiment verifies the correctness, the effectiveness and the reliability of the application.
Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include one or more such feature. In the description of the present application, the meaning of "a plurality" is two or more, unless explicitly defined otherwise.
Although the application is described herein in connection with various embodiments, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed application, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the "a" or "an" does not exclude a plurality.
The foregoing is a further detailed description of the application in connection with the preferred embodiments, and it is not intended that the application be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the application, and these should be considered to be within the scope of the application.
Claims (10)
1. A method for bi-based ISAR orientation scaling and geometric correction based on minimum entropy of an image, comprising:
s100, receiving echo signals of a moving object in a signal-to-noise ratio environment, and sequentially performing distance pulse compression processing and translational compensation on the echo signals to obtain a translational compensated echo signal matrix;
s200, projecting the echo matrix after translational compensation to an imaging plane to obtain a new echo signal matrix, and approximating the double-base angle modulation factor to obtain an approximate echo signal matrix;
s300, transforming the approximate echo signal matrix by using a wedge stone transformation, and constructing a compensation function;
s400, constructing a cost function by taking the echo signal matrix subjected to the rock-fill-in transformation as a variable, and obtaining an optimal value of space-variant error phase parameters by carrying out iterative optimization on the cost function;
s500, substituting the optimal value of the space-variant error phase parameter into the compensation function, and compensating the echo signal matrix after the wedge stone shape transformation by using the compensation function to obtain a focusing imaging result after two-dimensional space-variant error correction;
s600, estimating the rotating speed of the target relative to the radar by using an optimal value of the space-variant error phase parameter, and calibrating the focusing imaging result by using a mode of correcting the resolution of the focusing imaging result by using the estimated rotating speed;
s700, determining errors between real projection coordinates of scattering points in the same distance unit and coordinates after calibration according to the focusing imaging result, and constructing a geometric correction function by utilizing the errors;
s800, performing geometric correction on the calibrated focusing imaging result by using the geometric correction function to obtain an image after geometric correction.
2. The image minimum entropy-based bi-based ISAR orientation scaling and geometric correction method according to claim 1, wherein S100 comprises:
s110, transmitting a linear frequency modulation signal to a moving target through a transmitting radar in a double-base inverse synthetic aperture radar ISAR, and receiving an echo matrix scattered by the target in a low signal-to-noise ratio environment through a receiving radar in the double-base inverse synthetic aperture radar ISAR;
the echo matrix consists of echo data, the size of the echo matrix is N multiplied by M, N represents the distance unit number of the echo, and M represents the azimuth unit number of the echo;
s120, performing distance pulse compression processing on the echo matrix by using a matched filtering method to obtain an echo matrix after distance pulse compression;
s130, estimating a translational component of a target according to a translational compensation method, and calculating each element of a translational compensation matrix according to the translational component to obtain the translational compensation matrix;
and S140, carrying out dot multiplication on the translational compensation matrix and the echo matrix after the distance pulse compression to obtain an echo signal matrix after translational compensation.
3. The image minimum entropy-based bistatic ISAR azimuth scaling and geometry correction method according to claim 2, wherein the translation compensated echo signal matrix in S100 is expressed as:
wherein ,S(kr T) represents the echo signal matrix after translational compensation, k r The wave number is represented by a number of waves,f c represents radar carrier frequency, c represents speed of light, t represents slow time, W (k) r T) represents the echo spectral envelope, σ i Representing the target scattering point intensity, +.>Represents a double base angle modulation factor, β (t) represents a double base angle, θ represents an azimuth angle, α represents a pitch angle, (x) i ,y i ,z i ) Indicating the location of the ith scattering point.
4. A method of image minimum entropy based bi-based ISAR orientation scaling and geometric correction according to claim 3, wherein S200 comprises:
s210, projecting the echo matrix after translational compensation to an imaging plane to obtain a new echo signal matrix:
wherein ,(x′i ,y′ i ) Represents the i-th scattering point (x i ,y i ,z i ) Projection on the imaging plane, θ 'represents a scan angle of the beam on the imaging plane, and scan angle θ' =ωt, ω represents a rotation speed of the target on the imaging plane relative to the radar;
s220, approximating the double base angle modulation factor by the following formula (3):
s230, substituting the approximate double-base angle modulation factor into the formula (2) to approximate the new echo signal matrix, thereby obtaining an approximate echo signal matrix:
wherein ,a0 Representing the coefficient of the constant term of the double-base angle modulation factor, a 1 Representing the coefficient of the primary term of the double base angle modulation factor, a 2 And the quadratic term coefficient representing the double base angle modulation factor.
5. A method of image minimum entropy based bistatic ISAR azimuth scaling and geometry correction according to claim 3, wherein the echo of the discrete range-doppler domain after the processing of the wedge Dan Xingbian in S300 is f (n, k); the imaging result of focusing by discrete fourier transform is expressed as:
the compensation function is:
H r ＝exp(jq 1 nk 2 ) (6)；
H a ＝exp(jq 2 mk 2 ) (7)；
wherein I (N, m) represents a discrete imaging result, N represents a corresponding distance unit number, n= [ -N/2, ], N/2-1]M represents the sequence number of the azimuth cell, m= [ -M/2, ], M/2-1]，q 1 Represents the coefficient of the distance space-variant factor, q 2 Represents the azimuth space-variant factor coefficient,position coordinates of azimuth time domain of echo, K represents azimuth unit number, M represents azimuth unit number, N tableShowing the number of distance units.
6. The image minimum entropy-based bi-based ISAR orientation scaling and geometric correction method according to claim 5, wherein S400 includes:
s410, constructing a cost function by taking the echo signal matrix subjected to the stone-shaped transformation as a variable;
wherein the cost function is expressed as:
wherein, the image entropy value Ent (·) is:
wherein ,representing the sum of the energies of the signals;
s420, performing iterative optimization on the cost function by using a BFGS algorithm to obtain an optimal value of the space-variant error phase parameter.
7. The image minimum entropy-based bistatic ISAR orientation calibration and geometry correction method according to claim 6, wherein the focused imaging result after two-dimensional space-variant error correction in S500 is expressed as:
wherein ,representing the true projection coordinates of the ith scattering point on the imaging plane, ρ a Representing azimuth resolutionRate ρ r Representing the distance resolution, sinc represents the sine function, ++>
8. The image minimum entropy-based bi-based ISAR orientation scaling and geometric correction method according to claim 7, wherein S600 includes:
s610, determining a distance resolution and an azimuth resolution of the focused imaging result after the two-dimensional space-variant error correction in S500 according to the wave number domain expression:
wherein Δkr represents the range of radial wave numbers, determined by radar parameters; a, a 0 ＝cos(β 0 2) is a constant term of a double-base modulation factor, is a constant which is closer to 1, is estimated by the position of a double-base radar and target visual angle parameters measured by the radar, lambda represents the radar wavelength, T a Representing radar coherent accumulation time;
s620, estimating the rotating speed according to the relation between the space-variant error phase parameter and the rotating speed of the target relative to the radar;
the relation between the space-variant error phase parameter and the rotating speed of the target relative to the radar is expressed as follows:
wherein ,krc Represents the radial wavenumber center, f prf Representing the azimuth pulse repetition frequency of the radar;
the equivalent rotational speed of the target relative to the radar is:
s630, substituting the equivalent rotation speed of the target relative to the radar into the azimuth resolution to obtain a calibration result of the focusing imaging result.
9. The image minimum entropy-based bi-based ISAR orientation scaling and geometry correction method according to claim 8, wherein S700 comprises:
s710, determining the error between the true projection coordinates of the scattering points in the same distance unit and the coordinates after calibration according to the abscissa focusing position of the focusing imaging result in S500:
wherein ,representing the true x-coordinate of the projection of the scattering point on the imaging plane, (x) i ′,y i ') represents the coordinates of the focal position of the scatter point in the imaging plane obtained by scaling;
s720, constructing a geometric correction function 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 units, N represents the serial number of the corresponding distance unit, and the range of values is [ -N/2, -N/2+1, …, N/2-1].
10. The image minimum entropy-based bi-based ISAR orientation scaling and geometric correction method according to claim 9, wherein the image after geometric correction in S800 is represented as:
I 1 ＝FFT A [IFFT A [I]·H GC (n,m)] (17)；
wherein I represents an image obtained by imaging scaling, I 1 Representing the image after geometric correction, FFT A [·]And IFFT A [·]Respectively representing the fast fourier transform and the inverse fast fourier transform operations of the azimuth direction.
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