CN114779191A - Passive bistatic SAR moving target polar coordinate format phase error analysis and correction method - Google Patents

Passive bistatic SAR moving target polar coordinate format phase error analysis and correction method Download PDF

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CN114779191A
CN114779191A CN202210659563.6A CN202210659563A CN114779191A CN 114779191 A CN114779191 A CN 114779191A CN 202210659563 A CN202210659563 A CN 202210659563A CN 114779191 A CN114779191 A CN 114779191A
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moving target
phase error
pfa
bistatic sar
constructing
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CN114779191B (en
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王昕�
张玲
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Nanjing University of Posts and Telecommunications
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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
    • G01S7/40—Means for monitoring or calibrating
    • 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
    • G01S13/904—SAR modes
    • G01S13/9058—Bistatic or multistatic SAR
    • 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
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

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Abstract

The invention relates to a passive bistatic SAR moving target polar coordinate format phase error analysis and correction method, which comprises the steps of firstly constructing a passive bistatic SAR signal acquisition geometric model to obtain a moving target echo signal, then carrying out distance compression and motion compensation on the signal to obtain a signal before bistatic PFA processing, and then carrying out distance direction and azimuth direction interpolation processing on the signal to obtain an echo signal after PFA processing; secondly, performing bistatic PFA moving target image error spectrum derivation, and reversely deducing a new phase error expression by using a series inversion method; and finally, performing matched filtering on the new phase error and constructing a phase error matrix word to obtain a refocused image of the hybrid moving target. The method has simple derivation process, and can realize the imaging of the ground moving target under the condition of the passive bistatic SAR arbitrary trajectory flight.

Description

Passive bistatic SAR moving target polar coordinate format phase error analysis and correction method
Technical Field
The invention relates to the technical field of synthetic aperture radar imaging, in particular to a passive bistatic SAR moving target polar coordinate format phase error analysis and correction method, which is used for passive bistatic SAR moving target imaging under a non-parallel track.
Background
Synthetic Aperture Radar (SAR) systems are one of the leading technologies in the development of modern radars, and have a wide range of military and civil values by imaging ground scenes through a signal processing technology. The technique utilizes a pulse compression technique and a synthetic aperture principle to realize two-dimensional high-resolution imaging of a target. The synthetic aperture radar is a high-resolution imaging radar, can work all day long and all weather, and therefore plays an important role in the civil field. In recent years, bistatic synthetic aperture radars based on external radiation sources have become one of the research hotspots in the field of remote sensing imaging. The passive bistatic SAR does not transmit signals, only receives signals of an external radiation source, and the construction cost is low. The system safety performance is high because the receiver is difficult to be directly detected. The passive bistatic SAR can observe, position and identify a static target and can detect and image a moving object in an irradiated scene. PFA (polar format imaging algorithm) employs a planar wavefront assumption, which is a classical algorithm of SAR beamforming mode. The algorithm has small calculation amount and simple flow. The PFA algorithm has a wide application in single-base and double-base radar systems due to its unique characteristics. When the PFA algorithm is applied to SAR moving target imaging, a defocusing phenomenon of a moving target image can be caused due to the introduction of a motion parameter. Chinese patent application CN 110736988A discloses a bistatic PFA moving target parameter estimation and imaging method, which expands the phase term of a moving target in a frequency domain, constructs an azimuth matching filter by using a quadratic term coefficient, estimates the moving parameter of the moving target based on an image contrast criterion, and refocuses the moving target image by using the estimated parameter; however, the method is complex in derivation of the phase error spectrum of the moving target, and the constructed filter is an azimuth filter and only aims at the compensation of the azimuth. However, because moving targets in different motion states are focused, the same filter cannot be used, and a plurality of filters are required to be constructed if the ground moving targets are imaged under the condition of arbitrary track flight of the passive bistatic SAR, so that the workload is large.
Disclosure of Invention
In order to solve the technical problem, the invention provides a passive bistatic SAR moving target polar coordinate format phase error analysis and correction method, the phase error of a moving target is deduced again by a series inversion method, a new phase error formula is utilized to construct a matched filter to directly compensate the whole phase, not only the compensation in the azimuth direction is realized, but also the defocusing and the range migration in the range direction can be compensated; meanwhile, a phase error matrix dictionary is constructed according to the phase error function, and hybrid moving target refocusing under different motion states is realized by utilizing an ISTA algorithm. The method has a simpler derivation process, and is suitable for the situation of the passive bistatic SAR flying in any track as can be known through experimental simulation.
The invention relates to a passive bistatic SAR moving target polar coordinate format phase error analysis and correction method, which comprises the following steps:
s1, constructing a passive bistatic SAR signal acquisition geometric model to obtain an initial moving target echo signal, and processing the initial moving target echo signal by PFA to obtain a processed moving target echo signal;
s2, deducing a moving target two-dimensional frequency phase error function expression from the processed moving target echo signal by using an MSR (minimum shift register) series inversion method;
s3, constructing a matched filter according to the deduced phase error expression;
s4, compensating the phase of the moving target in a two-dimensional frequency domain, realizing focusing, and simultaneously compensating residual distance migration and distance defocusing;
s5, constructing a phase error matrix dictionary according to the phase error function obtained by derivation in S2, and approximately realizing hybrid moving target refocusing in different motion states by utilizing an ISTA algorithm;
and S6, realizing moving target image refocusing in any track and any motion mode through a simulation experiment.
Further, an echo signal is obtained by constructing a passive bistatic SAR signal acquisition model, and the PFA echo signal processed by the PFA algorithm can be represented as:
Figure 835949DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 159614DEST_PATH_IMAGE002
which is representative of the amplitude of the echo signal,
Figure 736089DEST_PATH_IMAGE003
and
Figure 537823DEST_PATH_IMAGE004
is the coordinates of the moving object and is,
Figure 883354DEST_PATH_IMAGE005
and
Figure 374990DEST_PATH_IMAGE006
respectively azimuth spatial frequency and range spatial frequency,
Figure 907603DEST_PATH_IMAGE007
，
Figure 513028DEST_PATH_IMAGE008
is the carrier frequency of the transmitted signal and,
Figure 447486DEST_PATH_IMAGE009
is a variable of the time of the orientation,
Figure 112953DEST_PATH_IMAGE010
indicating the range-wise frequency.
Further, step 2 specifically comprises:
performing bistatic PFA moving target image error spectrum derivation, and expanding the phase terms along the distance direction and the azimuth direction of the bistatic SAR, namely, the phase terms are positioned in
Figure 398441DEST_PATH_IMAGE005
And
Figure 807557DEST_PATH_IMAGE006
the phase error expression is obtained by performing the expansion as follows:
Figure 737467DEST_PATH_IMAGE011
wherein the content of the first and second substances,
Figure 698470DEST_PATH_IMAGE012
，
Figure 346620DEST_PATH_IMAGE013
wherein, the first and the second end of the pipe are connected with each other,
Figure 152902DEST_PATH_IMAGE014
and
Figure 202897DEST_PATH_IMAGE015
the instantaneous azimuth angles of the transmitter and receiver respectively,
Figure 475747DEST_PATH_IMAGE016
and
Figure 1406DEST_PATH_IMAGE017
the instantaneous pitch angles of the transmitter and receiver respectively,
Figure 483815DEST_PATH_IMAGE018
is a differential distance term;
will be provided with
Figure 512951DEST_PATH_IMAGE019
In that
Figure 425544DEST_PATH_IMAGE020
The Taylor expansion to the second order yields:
Figure 907341DEST_PATH_IMAGE021
the expansion coefficients are respectively
Figure 196371DEST_PATH_IMAGE022
、
Figure 814434DEST_PATH_IMAGE023
And
Figure 288140DEST_PATH_IMAGE024
obtaining new orientation time variable by reverse-deducing by using series inversion method
Figure 398179DEST_PATH_IMAGE025
The results were as follows:
Figure 225321DEST_PATH_IMAGE026
each coefficient is respectively:
Figure 494628DEST_PATH_IMAGE027
will obtain
Figure 14602DEST_PATH_IMAGE025
Substituting the phase error expression to obtain a new phase error formula
Figure 470991DEST_PATH_IMAGE028
The following:
Figure 101824DEST_PATH_IMAGE029
。
further, in step 3, a matched filter is constructed according to the new phase error formula, and the matched filter is a conjugate of the phase error:
Figure 694479DEST_PATH_IMAGE030
。
further, in step 4, the constructed matched filter is used for compensating the moving target phase in a two-dimensional frequency domain and realizing focusing, namely, the bistatic PFA image is converted into the two-dimensional frequency domain, multiplied by the filter and then converted into an image domain, and the moving target image refocusing in a single state is realized.
Further, in step 5, a phase error matrix dictionary is constructed according to the phase error function, and the movable targets in different motion states are refocused simultaneously by utilizing an ISTA algorithm; the method comprises the following specific steps:
s5-1, constructing moving target mixed data of different motion states as input data of ISTA algorithm
Figure 385355DEST_PATH_IMAGE031
；
S5-2, constructing a phase error matrix dictionary according to the phase error function
Figure 467056DEST_PATH_IMAGE032
The dictionary comprises moving target phase errors in any motion state;
s5-3, calculating observation data
Figure 760634DEST_PATH_IMAGE033
；
S5-4, performing threshold contraction iteration;
s5-5, updating sparse constraint parameters, and when the iteration times reach
Figure 473375DEST_PATH_IMAGE034
Stopping the iteration to obtain
Figure 69572DEST_PATH_IMAGE031
Is estimated by
Figure 234974DEST_PATH_IMAGE035
；
Wherein the content of the first and second substances,
Figure 207610DEST_PATH_IMAGE035
setting the initial value of a refocused moving target image as an all-zero matrix;
Figure 774857DEST_PATH_IMAGE036
in order to observe the data, it is,
Figure 666590DEST_PATH_IMAGE034
is the number of iterations.
Further, in step 6, the accuracy of phase error derivation is verified through a simulation experiment, and hybrid moving target refocusing under different motion states is realized; the method comprises the following specific steps:
s6-1, arranging three point targets with different coordinates in an imaging area, and processing the echo data of the point targets by using a PFA algorithm under the conditions of SAR parallel flight and non-parallel flight, and the conditions of constant motion and non-constant motion of the point targets respectively to obtain an imaging result; and (5) eliminating the phase error of the imaging result by using the phase error compensation method in the step (4), and simultaneously compensating the residual range migration and the range defocusing.
S6-2, simulating mixed echo data of moving targets in different motion states, constructing a phase error matrix dictionary according to a phase error function, and realizing mixed moving target refocusing in different motion states by utilizing an ISTA algorithm.
The beneficial effects of the invention are as follows: for the passive bistatic SAR flying in any track, due to the randomness of the track and the speed, the phase error of a moving target is difficult to analyze and correct. The invention simplifies the derivation process by a series inversion method, compensates the phase error caused by PFA algorithm to moving target imaging, and the constructed filter can compensate the defocusing in the azimuth direction and also compensate the distance migration and defocusing remained in the distance direction, thereby realizing the refocusing of the moving target image under the condition of any trajectory flight; due to the fact that moving targets are focused in different motion states, a phase error matrix dictionary cannot be built by the same filter according to a phase error function, hybrid moving target refocusing in different motion states is achieved, and imaging of the moving targets on the ground under the condition of flight of the passive bistatic SAR in any track is achieved.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of a passive bistatic SAR signal sampling geometric model;
fig. 3(a) is a moving target image and a refocusing image processed by PFA in parallel uniform motion in front view;
FIG. 3(b) is a moving target image and a refocusing image processed by the PFA in the non-parallel flying uniform motion;
FIG. 3(c) is the moving target image and refocused image after the non-parallel plus squint uniform motion PFA treatment;
FIG. 4(a) is the front side view parallel flight non-uniform velocity motion PFA processed image and the refocused image;
FIG. 4(b) is the moving target image and refocused image after PFA treatment under the condition of non-parallel flight non-uniform motion;
FIG. 4(c) is a moving target image and a refocused image after PFA treatment under non-parallel plus squint non-uniform motion;
FIG. 5 is a PFA-treated image and a refocused image in the stationary case;
FIG. 6(a) is a sectional view of a PFA orientation and a sectional view of a refocusing orientation at a constant velocity in front side view;
FIG. 6(b) is a sectional view of the PFA orientation and a sectional view of the refocusing orientation in non-parallel uniform motion;
FIG. 6(c) is a sectional view of the PFA orientation and a sectional view of the refocusing orientation at a constant velocity in non-parallel plus oblique view;
FIG. 6(d) is a sectional view of the PFA orientation and a sectional view of the refocusing orientation in front view under non-uniform motion;
FIG. 6(e) is a sectional view of the PFA orientation and a sectional view of the refocusing orientation under non-parallel non-uniform motion;
FIG. 6(f) is a sectional view of the PFA orientation and a sectional view of the refocusing orientation at a constant motion in non-parallel plus squint;
FIG. 6(g) is a sectional view of the PFA orientation at rest and a sectional view of the refocusing orientation;
FIG. 7 is a schematic diagram of a matched filter compensating for a moving target;
FIG. 8 is a blended image of a moving object in different states of motion;
fig. 9 is an image restored using the ISTA algorithm.
Detailed Description
In order that the manner in which the present invention is attained and can be understood in detail, a more particular description of the invention briefly summarized above may be had by reference to the embodiments thereof which are illustrated in the appended drawings.
As shown in fig. 1, the invention provides a method for analyzing and correcting a passive bistatic SAR moving target polar coordinate format phase error, comprising the following steps:
s1, constructing a passive bistatic SAR signal acquisition geometric model to obtain an initial moving target echo signal, and processing the initial moving target echo signal by PFA to obtain a processed moving target echo signal;
s2, deriving a moving target two-dimensional frequency phase error expression from the processed moving target echo signal by using an MSR (minimum shift register) series inversion method;
s3, constructing a matched filter according to the deduced phase error expression;
s4, compensating the phase of the moving target in a two-dimensional frequency domain, realizing focusing, and simultaneously compensating residual distance migration and distance defocusing;
s5, constructing a phase error matrix dictionary according to the phase error function obtained by derivation in S2, and realizing hybrid target refocusing in different motion states by utilizing an ISTA algorithm;
s6, realizing moving target image refocusing in any track and any motion mode through simulation experiments.
Wherein, the specific steps of step S1 include: a passive bistatic beamforming SAR signal acquisition set model is shown in FIG. 2, and the ground is assumed to be a coordinate system
Figure 194654DEST_PATH_IMAGE037
Plane, imaging scene O coincides with the coordinate system origin. With a point target in the imaging region
Figure 95614DEST_PATH_IMAGE038
In which
Figure 251789DEST_PATH_IMAGE039
The motion parameter of the point object is
Figure 455368DEST_PATH_IMAGE040
And
Figure 329783DEST_PATH_IMAGE041
(ii) a Both the transmitter and the receiver are along
Figure 768855DEST_PATH_IMAGE037
The plane flies at a constant speed, and the instantaneous position coordinate of the transmitter is
Figure 186061DEST_PATH_IMAGE042
Velocity along the Y axis
Figure 419596DEST_PATH_IMAGE043
Flying; instantaneous position coordinates of the receiver are
Figure 922253DEST_PATH_IMAGE044
At an angle along the Y axis
Figure 899436DEST_PATH_IMAGE045
At a speed of
Figure 295783DEST_PATH_IMAGE046
Flying; instantaneous azimuth angles of transmitter and receiver are respectively
Figure 575585DEST_PATH_IMAGE047
And
Figure 690172DEST_PATH_IMAGE048
instantaneous pitch angle is respectively
Figure 205467DEST_PATH_IMAGE049
And
Figure 883352DEST_PATH_IMAGE050
(ii) a The transmitter transmits a chirp signal at a fixed pulse repetition frequency, and the moving target echo signal received by the receiver is as follows:
Figure 935939DEST_PATH_IMAGE052
wherein, the first and the second end of the pipe are connected with each other,
Figure 520504DEST_PATH_IMAGE053
which represents the time instant at the center of the aperture,
Figure 501229DEST_PATH_IMAGE054
which represents the propagation speed of the electromagnetic wave,
Figure 513048DEST_PATH_IMAGE055
in order to be a frequency-modulated slope,
Figure 71068DEST_PATH_IMAGE056
in order to be a fast-time variable,
Figure 334690DEST_PATH_IMAGE057
which represents the carrier frequency of the signal transmission signal,
Figure 294556DEST_PATH_IMAGE058
is a variable of the azimuth time, and,
Figure 352642DEST_PATH_IMAGE059
representing the azimuthal envelope of the transmitted signal,
Figure 663537DEST_PATH_IMAGE060
representing a distance direction envelope;
Figure 589905DEST_PATH_IMAGE061
represents the instantaneous distance of the transmitter to the point target:
Figure 279643DEST_PATH_IMAGE062
Figure 898844DEST_PATH_IMAGE063
represents the instantaneous distance of the receiver to the point target:
Figure 572402DEST_PATH_IMAGE064
performing matched filtering and motion compensation on the echo data to enable the echo phase of the center point of the scene to be zero, namely multiplying the following compensation function by the formula (1):
Figure 36881DEST_PATH_IMAGE065
wherein, the first and the second end of the pipe are connected with each other,
Figure 705760DEST_PATH_IMAGE066
representing the instantaneous distance of a transmitter to a point target
Figure 371227DEST_PATH_IMAGE067
Figure 391136DEST_PATH_IMAGE068
Indicating the distance of the receiver from the center of the scene,
Figure 659306DEST_PATH_IMAGE069
the signal before PFA treatment was obtained as:
Figure 586286DEST_PATH_IMAGE070
wherein:
Figure 281710DEST_PATH_IMAGE071
and a represents a signal amplitude.
Figure 523336DEST_PATH_IMAGE072
Based on the planar wavefront assumption, the passive bistatic SAR differential distance
Figure 470563DEST_PATH_IMAGE073
Coordinates that can be based on a point target Q
Figure 379613DEST_PATH_IMAGE074
Performing Taylor expansion, taking the linear term as:
Figure 121304DEST_PATH_IMAGE075
wherein
Figure 115805DEST_PATH_IMAGE076
And
Figure 725778DEST_PATH_IMAGE077
for the instantaneous azimuth angle of the transmitter and receiver,
Figure 364701DEST_PATH_IMAGE078
and
Figure 401927DEST_PATH_IMAGE079
substituting equation (9) into equation (7) for the instantaneous pitch angles of the transmitter and receiver, the echo signal can be approximated in the range frequency domain as:
Figure 883724DEST_PATH_IMAGE080
wherein the content of the first and second substances,
Figure 172754DEST_PATH_IMAGE081
is the frequency of the range direction space,
Figure 790817DEST_PATH_IMAGE082
is the azimuth spatial frequency; the sampling positions of the spatial frequency domain are arranged according to a polar coordinate format, and are converted into a rectangular coordinate format to be sampled to be non-uniformly distributed. In order to improve the utilization rate of echo data, the coordinate system is generally rotated by the rotation angle before imaging
Figure 139890DEST_PATH_IMAGE083
After rotation
Figure 843404DEST_PATH_IMAGE084
And
Figure 795179DEST_PATH_IMAGE085
can be re-expressed as:
Figure 674273DEST_PATH_IMAGE086
wherein the content of the first and second substances,
Figure 787723DEST_PATH_IMAGE087
，
Figure 978533DEST_PATH_IMAGE088
expressed as azimuthal aperture center time, equation (11) can be re-expressed after rotating the coordinate system as:
Figure 609365DEST_PATH_IMAGE089
after the equation (12) is obtained, only two-dimensional resampling is needed to convert the echo data in the irregular format into uniformly sampled echo data which can realize discrete Fourier transform by two-dimensional fast Fourier transform, and imaging can be realized by the two-dimensional fast Fourier transform.
Step S2 specifically includes: as indicated by step S1, the coordinate system has been rotated
Figure 202021DEST_PATH_IMAGE090
Angle of a will
Figure 889967DEST_PATH_IMAGE091
The domain interpolation is a uniform parallelogram domain, so that the utilization rate of data can be improved, and the subsequent discussion and deduction of the invention are all established on the rotated coordinate system. The bistatic SAR polar coordinate format algorithm causes defocusing and geometric distortion of an imaging result due to the introduction of motion parameters. To obtain an image error spectrum of a moving object, at the aperture center instant, i.e. at the aperture center instant
Figure 568073DEST_PATH_IMAGE092
The phase term in equation (8) is based on spatial frequency
Figure 861651DEST_PATH_IMAGE093
And
Figure 184179DEST_PATH_IMAGE094
taylor expansion is carried out to obtain a phase expression:
Figure 170589DEST_PATH_IMAGE095
wherein:
Figure 335991DEST_PATH_IMAGE096
Figure 308627DEST_PATH_IMAGE097
using a series inversion method
Figure 610295DEST_PATH_IMAGE098
In that
Figure 642973DEST_PATH_IMAGE099
Performing Taylor expansion to the second order to obtain:
Figure 295671DEST_PATH_IMAGE100
the expansion coefficients are respectively:
Figure 931052DEST_PATH_IMAGE101
Figure 228172DEST_PATH_IMAGE102
Figure 556385DEST_PATH_IMAGE103
Figure 430800DEST_PATH_IMAGE105
obtaining a new value by reverse-deriving using a series inversion methodAzimuth time variable of
Figure 745238DEST_PATH_IMAGE106
The following:
Figure 287078DEST_PATH_IMAGE107
wherein:
Figure 23270DEST_PATH_IMAGE109
，
the obtained new azimuth time
Figure 453DEST_PATH_IMAGE106
Substituting equation (15) yields a new phase error expression:
Figure 272166DEST_PATH_IMAGE110
step S3, a new phase error is obtained according to a series inversion method to construct a matched filter, and the matched filter is the conjugate of the phase error:
Figure 791189DEST_PATH_IMAGE111
in step S4, the phase of the moving target is compensated and focused in a two-dimensional frequency domain by using the constructed matched filter, and the matched filter has the main function of eliminating the phase of each sampling point signal and realizing coherent accumulation of useful signals; as shown in fig. 7, the bistatic PFA image is transformed into two-dimensional frequency domain, multiplied by the filter, and then transformed into image domain, so that moving target image refocusing can be realized, which is not dependent on the azimuth filter, and residual range migration and range defocusing can be compensated.
In step S5, moving target refocusing in different motion states is achieved by the ISTA algorithm, which is a conventional unconstrained optimization problem:
Figure 178920DEST_PATH_IMAGE112
wherein the content of the first and second substances,
Figure 695352DEST_PATH_IMAGE113
is a regularization parameter. The specific iterative process of the algorithm is as follows:
(1) inputting: observation vector y, observation matrix Phi. And (3) outputting: reconstructed signal
Figure 411636DEST_PATH_IMAGE114
；
(2) Initialization:
Figure 747939DEST_PATH_IMAGE115
maximum number of iterations
Figure 66925DEST_PATH_IMAGE116
，
Figure 313230DEST_PATH_IMAGE117
Is that
Figure 59469DEST_PATH_IMAGE118
The initialization parameters of (1);
(3) circulation of
Figure 883068DEST_PATH_IMAGE119
；
(4) Gradient descent:
Figure 881111DEST_PATH_IMAGE120
；
(5) threshold shrinkage:
Figure 106556DEST_PATH_IMAGE121
；
(6) and (6) ending.
Wherein the content of the first and second substances,
Figure 164642DEST_PATH_IMAGE122
is the step of the step down in size,
Figure 475538DEST_PATH_IMAGE123
is a soft threshold puncturing function defined as follows:
Figure 136326DEST_PATH_IMAGE124
applying an ISTA algorithm to SAR imaging, wherein an initial value of a refocused moving target image is set as an all-zero matrix;
Figure 91644DEST_PATH_IMAGE125
in order to observe the data in the field,
Figure 710844DEST_PATH_IMAGE126
is the number of iterations. The method comprises the following specific steps:
(1) constructing moving target mixed data of different motion states as input data of ISTA algorithm
Figure 243456DEST_PATH_IMAGE127
；
(2) Construction of a phase error matrix dictionary from a phase error function
Figure 317723DEST_PATH_IMAGE128
The dictionary comprises a moving target phase error in any motion state;
(3) calculating observation data
Figure 517760DEST_PATH_IMAGE129
；
(4) Performing threshold contraction iteration;
(5) updating sparse constraint parameters when the iteration number reaches
Figure 42282DEST_PATH_IMAGE126
Stopping the iteration to obtain
Figure 937557DEST_PATH_IMAGE127
Is estimated by
Figure 205727DEST_PATH_IMAGE130
；
Wherein, the first and the second end of the pipe are connected with each other,
Figure 132708DEST_PATH_IMAGE130
setting the initial value of the moving target image to be a refocused moving target image as an all-zero matrix;
Figure 562552DEST_PATH_IMAGE125
in order to observe the data in the field,
Figure 335336DEST_PATH_IMAGE126
is the number of iterations.
In step S6, moving target phase refocusing in any motion mode of any track can be realized through experimental simulation.
The experimental simulated radar parameters are shown in table 1:
(1) respectively simulating under the conditions of front side view and oblique side view, wherein the simulation scene size is
Figure 16984DEST_PATH_IMAGE131
In a
Figure 660455DEST_PATH_IMAGE132
Three moving targets are distributed in the plane, the coordinates are respectively (0, -250, 0), (0, 0, 0) and (0, 150, 0), and the parameter is that when the moving target moves at a uniform speed
Figure 792359DEST_PATH_IMAGE133
When the receiver does not move at a constant speed, the motion parameters are (-2, m/s and 5 m/s), and under the condition of front sideview, the track deviation angle of the receiver
Figure 396647DEST_PATH_IMAGE134
At 0 deg., the transmitter platform and the receiver platform both fly parallel along the Y axis at a speed of 340 m/s. Under squint conditions, the squint angle of the transmitter platform motion is 10 degrees, the squint angle of the receiver platform is 10 degrees, the transmitter and the receiver fly in a non-parallel manner, the speed of the transmitter platform is 340m/s, the speed of the receiver platform is 340 x 1.2m/s, and the transmitter is parallel to the Y axisThe line direction flies, and the receiver flies along the direction which forms an included angle of 20 degrees with the Y axis.
Figure 272199DEST_PATH_IMAGE135
The experiment is divided into that the constant motion and the non-constant motion of a moving target are respectively carried out under the conditions of front side view parallel flight, non-parallel flight and non-parallel plus oblique view, and simulation analysis is carried out under the static condition; respectively obtain: fig. 3(a) to 3(c) are images and refocused images after PFA processing of a moving target in the case of uniform motion, fig. 4(a) to 4(c) are images and refocused images after PFA processing of a moving target in the case of non-uniform motion, fig. 5 is images and refocused images after PFA processing in the case of static, response characteristic analysis is performed on the moving target in order to more clearly see defocus, and fig. 6(a) to 6(g) are results of response analysis of the moving target in the above several cases, which are respectively a cross-sectional view of the azimuth direction of the moving target and a cross-sectional view of refocused image of the moving target after PFA processing.
Fig. 3(a) is a moving target image and a refocused image after the PFA treatment of the front-side view parallel uniform motion, fig. 3(b) is a moving target image and a refocused image after the PFA treatment of the non-parallel flying uniform motion, fig. 3(c) is a moving target image and a refocused image after the PFA treatment of the non-parallel plus oblique uniform motion, fig. 4(a) is an image and a refocused image after the PFA treatment of the front-side view parallel flying non-uniform motion, fig. 4(b) is a moving target image and a refocused image after the PFA treatment under the condition of the non-parallel flying non-uniform motion, and fig. 4(c) is a moving target image and a refocused image after the PFA treatment under the non-parallel plus oblique non-uniform motion. And fig. 5 images after PFA treatment and refocused images at rest. FIGS. 6(a) to 6(g) are a cross-sectional view in the azimuth direction and a cross-sectional view in the refocus after the PFA treatment.
(2) And simulating moving target echo data X in 5 different motion states, wherein the speed of 2 targets is-5.2 m/s, and the speed of the other 3 moving targets is 5.2 m/s. The refocused moving target image is obtained by the ISTA iteration, wherein fig. 8 is a moving target mixed image. Fig. 9 is a blended moving object refocused image.
The passive bistatic PFA moving target phase is deduced and analyzed, the MSR method is used for deducing the phase error of the moving target, so that a matched filter is constructed to compensate the whole phase, finally, a phase error matrix dictionary is constructed according to a phase error function, hybrid moving target refocusing in different moving states is realized by utilizing an ISTA algorithm, and moving target image refocusing in any motion parameter of any track can be realized.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all equivalent variations made by using the contents of the present specification and the drawings are within the protection scope of the present invention.

Claims (7)

1. The passive bistatic SAR moving target polar coordinate format phase error analysis and correction method is characterized by comprising the following steps:
s1, constructing a passive bistatic SAR signal acquisition geometric model to obtain an initial moving target echo signal, and processing the initial moving target echo signal by PFA to obtain a processed moving target echo signal;
s2, deducing a moving target two-dimensional frequency phase error function expression from the processed moving target echo signal by using an MSR (minimum shift register) series inversion method;
s3, constructing a matched filter according to the deduced phase error expression;
s4, compensating the phase of the moving target in a two-dimensional frequency domain, realizing focusing, and simultaneously compensating residual range migration and range defocusing;
s5, constructing a phase error matrix dictionary according to the phase error function obtained by derivation in S2, and realizing hybrid target refocusing in different motion states by utilizing an ISTA algorithm;
s6, realizing moving target image refocusing in any track and any motion mode through simulation experiments.
2. The passive bistatic SAR moving target polar coordinate format phase error analysis and correction method as claimed in claim 1, characterized in that, by constructing a passive bistatic SAR signal acquisition model, an echo signal is obtained, and a PFA echo signal processed by PFA algorithm can be expressed as:
Figure 761700DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 168190DEST_PATH_IMAGE002
which is representative of the amplitude of the echo signal,
Figure 416768DEST_PATH_IMAGE003
and
Figure 280819DEST_PATH_IMAGE004
is the coordinates of the moving object and is,
Figure 564033DEST_PATH_IMAGE005
and
Figure 855337DEST_PATH_IMAGE006
respectively azimuth spatial frequency and range spatial frequency,
Figure 591212DEST_PATH_IMAGE007
，
Figure 258954DEST_PATH_IMAGE008
is the carrier frequency of the transmitted signal and,
Figure 396674DEST_PATH_IMAGE009
is a variable of the time of the orientation,
Figure 655617DEST_PATH_IMAGE010
indicating the range-wise frequency.
3. The passive bistatic SAR moving target polar coordinate format phase error analysis and correction method according to claim 2, wherein the step 2 is specifically:
carrying out bistatic PFA moving target image error spectrum derivation, and expanding the phase terms along the distance direction and the azimuth direction of the bistatic SAR, namely, the phase terms are positioned at
Figure 878788DEST_PATH_IMAGE005
And
Figure 819062DEST_PATH_IMAGE006
the phase error expression is obtained by performing the expansion as follows:
Figure 811289DEST_PATH_IMAGE011
wherein, the first and the second end of the pipe are connected with each other,
Figure 506712DEST_PATH_IMAGE012
，
Figure 217179DEST_PATH_IMAGE014
wherein, the first and the second end of the pipe are connected with each other,
Figure 695565DEST_PATH_IMAGE015
and
Figure 807878DEST_PATH_IMAGE016
the instantaneous azimuth angles of the transmitter and receiver respectively,
Figure 408623DEST_PATH_IMAGE017
and
Figure 606386DEST_PATH_IMAGE018
the instantaneous pitch angles of the transmitter and receiver respectively,
Figure 888463DEST_PATH_IMAGE019
is a differential distance term;
will be provided with
Figure 852353DEST_PATH_IMAGE020
In that
Figure 92841DEST_PATH_IMAGE021
The Taylor expansion to the second order yields:
Figure 512321DEST_PATH_IMAGE022
the expansion coefficients are respectively
Figure 660406DEST_PATH_IMAGE023
、
Figure 481731DEST_PATH_IMAGE024
And
Figure 627542DEST_PATH_IMAGE025
obtaining new orientation time variable by reverse-deducing by using series inversion method
Figure 534318DEST_PATH_IMAGE026
The results were as follows:
Figure 423776DEST_PATH_IMAGE027
each coefficient is respectively:
Figure 161925DEST_PATH_IMAGE028
will obtain
Figure 744216DEST_PATH_IMAGE026
Substituting the phase error expression to obtain a new phase error formula
Figure 138289DEST_PATH_IMAGE029
The following:
Figure 565859DEST_PATH_IMAGE030
。
4. the passive bistatic SAR moving target polar format phase error analysis and correction method according to claim 3, wherein in step 3, a matched filter is constructed according to a new phase error formula, the matched filter being the conjugate of the phase error:
Figure 96197DEST_PATH_IMAGE031
。
5. the passive bistatic SAR moving target polar coordinate format phase error analysis and correction method as claimed in claim 1, characterized in that in step 4, the constructed matched filter is used to compensate the moving target phase in the two-dimensional frequency domain and realize focusing, that is, the bistatic PFA image is transformed to the two-dimensional frequency domain multiplied by the filter and then transformed to the image domain, so as to realize moving target image refocusing in a single state.
6. The passive bistatic SAR moving target polar coordinate format phase error analysis and correction method as claimed in claim 1, characterized in that in step 5, a phase error matrix dictionary is constructed according to a phase error function, and the movable targets in different motion states are refocused at the same time by using an ISTA algorithm; the method comprises the following specific steps:
s5-1, constructing moving target mixed data of different motion states as input data of the ISTA algorithm
Figure 849390DEST_PATH_IMAGE032
；
S5-2, constructing a phase error matrix dictionary according to the phase error function
Figure 730758DEST_PATH_IMAGE033
The dictionary comprises moving target phase errors in any motion state;
s5-3, calculating observation data
Figure 227598DEST_PATH_IMAGE034
；
S5-4, performing threshold contraction iteration;
s5-5, updating the sparse constraint parameter when the iteration number reaches
Figure 674760DEST_PATH_IMAGE035
Stopping the iteration to obtain
Figure 333275DEST_PATH_IMAGE032
Is estimated value of
Figure 701939DEST_PATH_IMAGE036
；
Wherein the content of the first and second substances,
Figure 468382DEST_PATH_IMAGE036
setting the initial value of the moving target image to be a refocused moving target image as an all-zero matrix;
Figure 238892DEST_PATH_IMAGE037
in order to observe the data, it is,
Figure 865046DEST_PATH_IMAGE035
is the number of iterations.
7. The passive bistatic SAR moving target polar coordinate format phase error analysis and correction method as claimed in claim 1, characterized in that in step 6, the correctness of phase error derivation is verified through simulation experiments and hybrid moving target refocusing under different moving states is realized; the method comprises the following specific steps:
s6-1, arranging three point targets with different coordinates in an imaging area, and processing the echo data of the point targets by using a PFA algorithm under the conditions of SAR parallel flight and non-parallel flight, and the conditions of constant motion and non-constant motion of the point targets respectively to obtain an imaging result; eliminating the phase error of the imaging result by the phase error compensation method in the step 4, and simultaneously compensating the residual range migration and range defocusing;
s6-2, simulating the mixed echo data of the moving target in different motion states, constructing a phase error matrix dictionary according to a phase error function, and realizing the refocusing of the mixed moving target in different motion states by utilizing an ISTA algorithm.
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