CN117849799B - Harmonic synthetic aperture radar residual motion error compensation method - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
- G01S13/9021—SAR image post-processing techniques
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
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Abstract
The invention discloses a method for compensating residual motion error of a harmonic synthetic aperture radar, which comprises the following steps: step 1, constructing a harmonic synthetic aperture radar echo model; step 2, echo signal data separation; step 3, coarse focusing of SAR images; step 4, estimating the residual error phase; and 5, error phase compensation. The invention adopts the residual phase error estimated by the fundamental frequency image data to compensate the harmonic SAR image, fully utilizes the advantage of higher signal-to-noise ratio of the fundamental frequency image, has higher estimation precision compared with the method of directly adopting the harmonic image to estimate the phase error curve, and can effectively improve the focusing performance of the harmonic image.
Description
Technical Field
The invention belongs to the field of harmonic synthetic aperture radars, and particularly relates to a method for compensating residual motion errors of a harmonic synthetic aperture radar.
Background
Most of the scatterers in the nature are linear scatterers, a traditional radar is adopted to irradiate a natural scene, and a large amount of clutter exists in reflected waves. The harmonic radar uses the harmonic radiation characteristic of the nonlinear target to image and detect, effectively inhibits clutter and interference, and discovers stealth/hidden targets. The harmonic radar has the advantage of filtering linear scatterers in nature, and can effectively filter clutter generated by linear targets. Because the devices adopted by the modes of inflating false targets, strong interference, decoy, anti-stealth and the like do not have harmonic reflection characteristics, the modes are only effective to the traditional fundamental frequency radar, have no effect on the harmonic radar, and can effectively filter the interference or camouflage by adopting the harmonic radar. Compared with a synthetic aperture radar working at a fundamental frequency, a harmonic synthetic aperture radar (Harmonic Synthetic Aperture Radar: H-SAR) can effectively filter interference of the fundamental frequency, and the H-SAR image is not filled with various clutter scatterers like the traditional SAR image. Since the conventional natural scatterers do not have harmonic scattering characteristics, the H-SAR image is clean, and a large part of the scatterers in the natural world can be automatically filtered, so that the scatterers with the harmonic characteristics of interest are highlighted.
Although the harmonic radar has the advantages of stronger anti-stealth, anti-false target and anti-interference in the field of target detection and imaging, the harmonic radar has a difficult problem that the harmonic scattering energy of a nonlinear target is low, the harmonic signal to noise ratio received by a receiver is low, and residual motion errors cannot be accurately estimated by directly adopting harmonic data, so that the defocusing of an H-SAR image is finally caused, and the application of the H-SAR is seriously influenced by the defects. In practice, the nonlinear target reflects the fundamental frequency signal and the harmonic signal simultaneously when receiving the radar signal radiation, and the receiver can receive the fundamental frequency signal and the harmonic signal simultaneously. Since motion errors are generated by platform motion, it is independent of whether operating at fundamental frequencies or at harmonics. The signal-to-noise ratio of the harmonic wave is low, the residual motion error curve is difficult to accurately estimate by directly adopting the harmonic wave signal, and compared with the harmonic wave signal, the signal-to-noise ratio of the fundamental frequency signal is high, so that the relatively accurate residual motion error curve can be extracted.
Disclosure of Invention
The invention utilizes the fundamental frequency signal to estimate the residual motion error to compensate the harmonic signal, thereby improving the imaging performance of the harmonic signal.
The technical scheme of the invention is that the method for compensating the residual motion error of the harmonic synthetic aperture radar comprises the following steps:
Step 1, constructing a harmonic synthetic aperture radar echo model; the harmonic synthetic aperture radar emits fundamental frequency signals, after the fundamental frequency signals irradiate a nonlinear target, echo signals reflected by the nonlinear target simultaneously contain fundamental frequency signals and harmonic signals, the echo signals received by the receiver contain N harmonic signals, and 1 harmonic signal is called the fundamental frequency signal;
Step 2, echo signal data separation; separating the received echo signal data by adopting a band-pass frequency domain filtering mode to obtain independent 1 st to Nth harmonic echo signal data;
Step 3, coarse focusing of SAR images; coarse focusing imaging is carried out on the 1 st to Nth harmonic signals, motion track errors are fitted by combining inertial navigation data and radar parameters, motion compensation data are generated, SAR imaging processing is carried out on the 1 st to Nth harmonic signal data respectively, and coarse focusing SAR images are obtained;
step 4, estimating the residual error phase; extracting a residual motion error phase, and extracting an error phase generated by the residual motion error by adopting a fundamental frequency signal SAR image;
step 5, error phase compensation; generating residual motion phase error coefficients of the 2 nd to nth harmonic signals by utilizing an error phase generated by residual motion errors obtained by the baseband signal SAR image estimation; and carrying out Fourier transform on the coarse focusing SAR image in the azimuth direction, converting the coarse focusing SAR image into a distance-Doppler domain, compensating the distance-Doppler data of the 2 nd to Nth harmonic coarse focusing SAR images by using the generated residual motion error coefficient, and then carrying out inverse Fourier transform on the compensated data in the azimuth direction so as to obtain fine focusing images of the 2 nd to Nth harmonic signals, wherein the fine focusing images of the 1 st to Nth harmonics are all obtained.
Further, the specific implementation method of step 1 is that the radar transmits a fundamental frequency signal, and the transmitted fundamental frequency signalThe waveforms are expressed as:
（1）
Wherein, Express fast time,/>Representing a distance dimension envelope,/>Representing the center frequency of the transmitted signal,/>Representing the frequency modulation rate of the transmitted fundamental frequency signal,/>An exponential function based on a natural constant, j representing a complex number;
after the fundamental frequency signal emitted by the radar irradiates the nonlinear target, the echo reflected by the nonlinear target simultaneously contains the fundamental frequency signal and the harmonic signal, and the echo signal received by the receiver Expressed as:
（2）
Wherein, Representing slow time,/>Representing two-dimensional data, forming a two-dimensional data matrix after digital acquisition,Representing slow time-dimensional signal envelope,/>Representing the number of harmonics,/>Representing the propagation velocity of the electromagnetic signal,Representing the instantaneous skew between the target and the radar;
assuming that the position coordinates of the nonlinear target in the distance-azimuth plane are According to the geometrical relationship between the radar platform and the nonlinear target, the instantaneous skew/>Expressed as:
（3）
Wherein, Representing radar movement speed,/>Representing the linear walking term coefficient,/>Representing the distance bending term coefficient.
Further, the specific implementation method of the step 2 is that the echo signals received by the receiver simultaneously contain fundamental frequency signals and harmonic signals, all subharmonic signals in the time domain are mixed together, all subharmonic signals are separated from the acquired echo signals before imaging processing, and imaging processing is carried out on all subharmonic signals respectively;
The method comprises the steps of realizing the separation of harmonic signal components by adopting a frequency domain filtering mode, firstly carrying out Fourier transformation on echo signals in a fast time dimension, at the moment, separating each subharmonic on a frequency spectrum, and extracting each subharmonic signal by adopting a band-pass filtering mode; baseband signal of nth harmonic obtained after distance Fourier transform, band-pass filtering, distance inverse Fourier transform and center frequency shift Expressed as:
（4）
Further, the specific implementation method of the step 3 is that the motion trail error is fitted by combining the inertial navigation data and radar parameters, motion compensation data is generated, residual error components are introduced due to limited accuracy of the inertial navigation data, and the instantaneous skew after the inertial navigation data compensation is carried out Expressed as:
（5）
Wherein, For residual motion error after motion compensation,/>In order to obtain the instantaneous pitch after motion compensation, at this time,/>By instantaneous skew/>And residual motion error/>Two parts are formed;
residual motion error after inertial navigation data compensation The sampling length of the range gate is smaller than 1, namely, the target energy can be concentrated in one range gate after the processing of range pulse pressure, motion compensation, range walk correction and range bend correction, and only the influence of residual motion errors on azimuth focusing is considered;
Two-dimensional time domain data of nth harmonic signal obtained after distance pulse pressure, motion compensation, distance walk correction and distance bend correction processing The expression is as follows:
（6）
Wherein, Is the bandwidth of the fundamental frequency signal,/>Is a sine function;
at this time, the formula (6) is subjected to azimuth matched filtering, the obtained two-dimensional image is defocused in azimuth, and the azimuth defocused image obtained by the azimuth matched filtering of the n-order harmonic signal is 。
Further, the specific implementation method of the step 4 is that the imaging result of the fundamental frequency echo signal is processed by a phase gradient self-focusing algorithm to estimate the residual phase error;
Performing azimuth Fourier transform on the 1 st to Nth images to obtain range-Doppler data expressed as Wherein/>Is Doppler frequency;
using the fundamental frequency echo SAR image as the data to be processed, and obtaining the estimated value of the error phase gradient by using the weighted maximum likelihood criterion The method comprises the following steps:
（7）
Wherein M is the number of the selected range gate samples, Representing the weighting coefficient of the range gate, determined by the total energy of the range gate where it is located,/>To take complex phase function,/>To take complex conjugate,/>And (3) withRepresenting two adjacent Doppler frequency points of a range-Doppler domain;
Integrating the error phase gradient to obtain an error phase The method comprises the following steps:
（8）。
Further, the specific implementation method of the step 5 is that the error phase of the fundamental frequency echo SAR image estimated and obtained in the step 4 is utilized to construct error compensation coefficients of the 1 st to nth harmonic images, and the nth error compensation coefficient Expressed as:
（9）
Estimating the obtained error compensation coefficient And range-Doppler data/>Multiplying and carrying out inverse Fourier transform in azimuth direction to obtain an image after self-focusing processing and an nth harmonic image/>, after fine focusingExpressed as:
（10）
Wherein, Representing an inverse fourier transform in the azimuth direction; so far, the fine focus images of the 1 st to nth harmonic signals are all obtained.
The beneficial effects of the invention include:
The invention adopts the residual phase error estimated by the fundamental frequency image data to compensate the harmonic SAR image, fully utilizes the advantage of higher signal-to-noise ratio of the fundamental frequency image, has higher estimation precision compared with the method of directly adopting the harmonic image to estimate the phase error curve, and can effectively improve the focusing performance of the harmonic image.
Drawings
FIG. 1 is a flow chart of a method for compensating residual motion error of a harmonic synthetic aperture radar according to the present invention.
Detailed Description
The invention discloses a method for compensating residual motion errors of a harmonic synthetic aperture radar. The invention adopts the residual motion error compensation harmonic SAR image estimated by fundamental frequency data, the flow of the invention is shown in figure 1, step 1, a harmonic synthetic aperture radar transmits fundamental frequency signals, after the harmonic synthetic aperture radar irradiates a nonlinear target, echo signals reflected by the nonlinear target simultaneously comprise fundamental frequency signals and harmonic signals, echo signals received by a receiver comprise N harmonics, and 1 harmonic is called fundamental frequency; step 2, echo data separation, namely separating the received echo data in a band-pass frequency domain filtering mode to obtain independent 1 st to Nth harmonic echo data; step 3, coarse focusing imaging is carried out on the 1 st to Nth harmonic waves, motion track errors are fitted by combining inertial navigation data and radar parameters, motion compensation data are generated, SAR imaging processing is carried out on the 1 st to Nth harmonic wave data respectively, and because the accuracy of the inertial navigation data is limited, the obtained image is a coarse focusing image, the focusing effect of the image is poor, and the resolution and the image effect of the image are difficult to meet the actual requirements; and 4, extracting a residual motion error phase, and extracting an error phase generated by the residual motion error by using the fundamental frequency SAR image by utilizing the characteristic of higher signal-to-noise ratio of the fundamental frequency signal. Dividing a fundamental frequency signal SAR image along a distance direction-azimuth direction, dividing the fundamental frequency SAR image into a plurality of data blocks with overlapping, extracting an error phase curve of each data block by adopting a self-focusing algorithm, fitting the obtained error curve to obtain a final residual phase error curve, and extracting a residual motion error curve; and 5, generating residual motion phase error coefficients of the 2 nd to the Nth harmonic by combining the residual motion error curve obtained by the fundamental frequency SAR image estimation with the harmonic parameters. And carrying out Fourier transform on the coarse focusing image in the azimuth direction, converting the coarse focusing image into a distance-Doppler domain, compensating the distance-Doppler data of the 2 nd to Nth harmonic coarse focusing images by using the generated residual motion error coefficient, and then carrying out inverse Fourier transform on the compensated data in the azimuth direction so as to obtain the 2 nd to Nth harmonic fine focusing images, wherein the 1 st to Nth harmonic fine focusing images are all obtained.
The specific technical scheme comprises the following steps:
Step 1, constructing a harmonic radar echo model;
radar emits a chirp signal, an emitted signal The waveform can be expressed as:
（1）
Wherein, Express fast time,/>Representing a distance dimension envelope,/>Representing the center frequency of the transmitted signal,/>Representing the frequency modulation rate of the transmitted signal,/>An exponential function based on a natural constant, j representing a complex number;
The radar emits fundamental frequency signals, after the radar irradiates the nonlinear target, the echo reflected by the nonlinear target simultaneously contains the fundamental frequency signals and harmonic signals, and the echo signals received by the receiver Can be expressed as:
（2）
Wherein, Representing slow time,/>Representing two-dimensional data, forming a two-dimensional data matrix after digital acquisition,Representing slow time-dimensional signal envelope,/>Representing the number of harmonics,/>Representing the propagation velocity of the electromagnetic signal,Representing the instantaneous skew between the target and the radar.
Assuming that the position coordinates of the target in the distance-azimuth plane areAccording to the geometrical relationship between the radar platform and the target, the instantaneous slant distance/>Can be expressed as:
（3）
Wherein, Representing radar movement speed,/>Representing the linear walking term coefficient,/>Representing the distance bending term coefficient.
Step2, echo data separation;
The echo received by the receiver contains fundamental frequency signals and harmonic signals at the same time, and all subharmonics are mixed together in the time domain, so that the echo signals cannot be directly imaged, and therefore all subharmonics need to be separated from the acquired echo signals before imaging processing, and the imaging processing is carried out on all subharmonics respectively.
The invention adopts a frequency domain filtering mode to realize the separation of harmonic signal components, firstly, the collected signals are subjected to Fourier transformation in a fast time dimension, at the moment, all subharmonics are separated in frequency spectrum, and all subharmonics can be extracted by adopting a band-pass filtering mode. Baseband signal of nth harmonic obtained after distance Fourier transform, band-pass filtering, distance inverse Fourier transform and center frequency shiftCan be expressed as:
（4）
Step 3, coarse focusing of SAR images;
Combining inertial navigation data and radar parameters to fit motion track errors, generating motion compensation data, introducing residual error components due to limited accuracy of the inertial navigation data, and compensating the inertial navigation data to obtain instantaneous inclined distance Can be expressed as:
（5）
Wherein, For residual motion error after motion compensation,/>In order to obtain the instantaneous pitch after motion compensation, at this time,/>From motion error free pitch/>And residual motion error/>Two parts.
Assuming residual motion error after inertial navigation data compensationThe sampling length of the range gate is smaller than 1, namely, the target energy can be concentrated in one range gate after the processing of range pulse pressure, motion compensation, range walk correction and range bend correction, and only the influence of residual motion errors on azimuth focusing is considered.
Two-dimensional time domain data of nth harmonic obtained after distance pulse pressure, motion compensation, distance walk correction and distance bend correction processingCan be expressed as:
（6）
Wherein, Is the bandwidth of the fundamental frequency signal,/>Is a sine function.
At this time, the formula (6) is subjected to azimuth matched filtering, the obtained two-dimensional image is defocused in azimuth, and the azimuth defocused image obtained by the azimuth matched filtering of the n-order harmonic is。
Step 4, estimating the residual error phase;
Because the 2 nd to nth harmonics are weaker than the fundamental frequency echo energy, the invention carries out phase gradient self-focusing algorithm processing on the imaging result of the fundamental frequency echo signal to estimate residual phase errors.
Performing azimuth Fourier transform on the 1 st to Nth images to obtain range-Doppler data expressed asWherein/>Is the doppler frequency.
Using the fundamental frequency echo SAR image as the data to be processed, and obtaining the estimated value of the error phase gradient by using the weighted maximum likelihood criterionThe method comprises the following steps:
（7）
Wherein M is the number of the selected range gate samples, Representing the weighting coefficient of the range gate, determined by the total energy of the range gate where it is located,/>To take complex phase function,/>To take complex conjugate,/>And (3) withRepresenting two adjacent doppler bins of the range-doppler domain.
Integrating the error phase gradient to obtain an error phaseThe method comprises the following steps:
（8）
In practical application, because the motion residual error has a null property, the coarse focused image needs to be two-dimensionally segmented according to the distance direction and the azimuth direction, the error phase curve of each image data block is estimated, and each image data block is respectively compensated by using the error phase curve obtained by estimation.
Step 5, error phase compensation;
constructing error compensation coefficients of the 1 st to nth harmonic images by using the error phases of the fundamental frequency images estimated and obtained in the step 4, and the nth error compensation coefficient Can be expressed as:
（9）
Estimating the obtained error compensation coefficient And range-Doppler data/>Multiplying and carrying out inverse Fourier transform in azimuth direction to obtain an image after self-focusing treatment, and carrying out fine focusing on the nth harmonic image/>Can be expressed as:
（10）
Wherein, Representing an inverse fourier transform in the azimuth direction. So far, the fine focus images of the 1 st to nth harmonics are all obtained.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (6)
1. A method for compensating residual motion error of a harmonic synthetic aperture radar, the method comprising the steps of:
Step 1, constructing a harmonic synthetic aperture radar echo model; the harmonic synthetic aperture radar emits fundamental frequency signals, after the fundamental frequency signals irradiate a nonlinear target, echo signals reflected by the nonlinear target simultaneously contain fundamental frequency signals and harmonic signals, the echo signals received by the receiver contain N harmonic signals, and 1 harmonic signal is called the fundamental frequency signal;
Step 2, echo signal data separation; separating the received echo signal data by adopting a band-pass frequency domain filtering mode to obtain independent 1 st to Nth harmonic signal data;
Step 3, coarse focusing of SAR images; coarse focusing imaging is carried out on the 1 st to Nth harmonic signals, motion track errors are fitted by combining inertial navigation data and radar parameters, motion compensation data are generated, SAR imaging processing is carried out on the 1 st to Nth harmonic signal data respectively, and coarse focusing SAR images are obtained;
step 4, estimating the residual error phase; extracting a residual motion error phase, and extracting an error phase generated by the residual motion error by adopting a fundamental frequency signal SAR image;
step 5, error phase compensation; generating residual motion phase error coefficients of the 2 nd to nth harmonic signals by utilizing an error phase generated by residual motion errors obtained by the baseband signal SAR image estimation; and carrying out Fourier transform on the coarse focusing SAR image in the azimuth direction, converting the coarse focusing SAR image into a distance-Doppler domain, compensating the distance-Doppler data of the 2 nd to Nth harmonic coarse focusing SAR images by using the generated residual motion error coefficient, and then carrying out inverse Fourier transform on the compensated data in the azimuth direction so as to obtain fine focusing images of the 2 nd to Nth harmonic signals, wherein the fine focusing images of the 1 st to Nth harmonics are all obtained.
2. The method according to claim 1, wherein the specific implementation method of step 1 is that the harmonic synthetic aperture radar transmits a fundamental frequency signal, and the transmitted fundamental frequency signalThe waveforms are expressed as:
（1）
Wherein, Express fast time,/>Representing a distance dimension envelope,/>Representing the center frequency of the transmitted signal,/>Representing the frequency modulation rate of the transmitted fundamental frequency signal,/>An exponential function based on a natural constant, j representing a complex number;
The fundamental frequency signal emitted by the harmonic synthetic aperture radar is irradiated to the nonlinear target, and then the echo signal reflected by the nonlinear target simultaneously comprises the fundamental frequency signal and the harmonic signal, and the echo signal received by the receiver Expressed as:
（2）
Wherein, Representing slow time,/>Representing two-dimensional data, forming a two-dimensional data matrix after digital acquisition,/>Representing slow time-dimensional signal envelope,/>Representing the number of harmonics,/>Representing the propagation velocity of an electromagnetic signal,/>Representing the instantaneous skew between the target and the radar;
assuming that the position coordinates of the nonlinear target in the distance-azimuth plane are According to the geometrical relationship between radar and nonlinear targets, instantaneous skew/>Expressed as:
（3）
Wherein, Representing radar movement speed,/>Representing the linear walking term coefficient,/>Representing the distance bending term coefficient.
3. The method according to claim 2, wherein the specific implementation method of step 2 is that the echo signals received by the receiver simultaneously contain fundamental frequency signals and harmonic signals, the harmonic signals are mixed together in the time domain, the harmonic signals are separated from the acquired echo signals before imaging processing, and the imaging processing is performed on the harmonic signals;
The method comprises the steps of realizing the separation of harmonic signal components by adopting a frequency domain filtering mode, firstly carrying out Fourier transformation on echo signals in a fast time dimension, at the moment, separating each subharmonic on a frequency spectrum, and extracting each subharmonic signal by adopting a band-pass filtering mode; baseband signal of nth harmonic obtained after distance Fourier transform, band-pass filtering, distance inverse Fourier transform and center frequency shift Expressed as:
（4）。
4. The method of claim 3, wherein the specific implementation method of step 3 is that the motion trail error is fitted by combining inertial navigation data and radar parameters to generate motion compensation data, and residual error components are introduced due to limited accuracy of the inertial navigation data, and the instantaneous pitch after the inertial navigation data compensation is carried out Expressed as:
（5）
Wherein, For residual motion error after motion compensation,/>In order to obtain the instantaneous pitch after motion compensation, at this time,/>By instantaneous skew/>And residual motion error/>Two parts are formed;
residual motion error after inertial navigation data compensation The sampling length of the range gate is smaller than 1, namely, the target energy can be concentrated in one range gate after the processing of range pulse pressure, motion compensation, range walk correction and range bend correction, and only the influence of residual motion errors on azimuth focusing is considered;
Two-dimensional time domain data of nth harmonic signal obtained after distance pulse pressure, motion compensation, distance walk correction and distance bend correction processing The expression is as follows:
（6）
Wherein, Is the bandwidth of the fundamental frequency signal,/>Is a sine function;
at this time, the formula (6) is subjected to azimuth matched filtering, the obtained two-dimensional image is defocused in azimuth, and the azimuth defocused image obtained by the azimuth matched filtering of the n-order harmonic signal is I.e. the coarse focus SAR image of the 1 st to nth harmonic signals.
5. The method according to claim 4, wherein the specific implementation method of step 4 is that the imaging result of the fundamental frequency echo signal is processed by a phase gradient self-focusing algorithm to estimate a residual phase error;
Performing azimuth Fourier transform on the coarse focusing SAR image of the 1 st to Nth harmonic signals to obtain range-Doppler data expressed as Wherein/>Is Doppler frequency;
Using coarse focusing SAR image of fundamental frequency signal as data to be processed, obtaining estimated value of error phase gradient by using weighted maximum likelihood criterion The method comprises the following steps:
（7）
Wherein M is the number of the selected range gate samples, Representing the weighting coefficient of the range gate, determined by the total energy of the range gate where it is located,/>To take complex phase function,/>To take complex conjugate,/>And/>Representing two adjacent Doppler frequency points of a range-Doppler domain;
Estimation of error phase gradient Integrating to obtain residual error phase/>The method comprises the following steps:
（8）。
6. The method of claim 5, wherein the specific implementation method of step 5 is that error compensation coefficients of 1 st to nth harmonic signal SAR images are constructed by using the error phases of the fundamental frequency signal SAR images estimated and obtained in step 4, and the nth error compensation coefficient is constructed Expressed as:
（9）
Estimating the obtained error compensation coefficient And range-Doppler data/>Multiplying and carrying out inverse Fourier transform in azimuth direction to obtain an image after self-focusing processing and an nth harmonic image/>, after fine focusingExpressed as:
（10）
Wherein, Representing an inverse fourier transform in the azimuth direction; so far, the fine focus images of the 1 st to nth harmonic signals are all obtained.
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