CN113030963A - Bistatic ISAR sparse high-resolution imaging method combining residual phase elimination - Google Patents

Bistatic ISAR sparse high-resolution imaging method combining residual phase elimination Download PDF

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CN113030963A
CN113030963A CN202110153871.7A CN202110153871A CN113030963A CN 113030963 A CN113030963 A CN 113030963A CN 202110153871 A CN202110153871 A CN 202110153871A CN 113030963 A CN113030963 A CN 113030963A
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echo signal
sparse
residual phase
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phase
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CN113030963B (en
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史林
刘利民
曾瑞
马俊涛
郭宝锋
胡文华
朱晓秀
尹园威
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Army Engineering University of PLA
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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
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    • 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
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Abstract

The invention is suitable for the technical field of radar signal processing, and provides a bistatic ISAR sparse high-resolution imaging method combining residual phase elimination, which comprises the following steps: converting the distance space-variant phase into a translational residual phase according to the first echo signal by setting the central coordinate of the range gate as the equivalent rotation central distance coordinate to obtain a corrected second echo signal; constructing a phase error matrix and a corresponding compressed sensing matrix based on the translational residual phase, and obtaining a sparse imaging model corresponding to a second echo signal according with a sparse high-resolution bistatic ISAR imaging scene according to the phase error matrix and the compressed sensing matrix based on the translational residual phase; and performing image and noise modeling based on statistical prior, performing sparse high-resolution imaging reconstruction and residual phase error iterative correction on the sparse imaging model through full Bayesian inference sparsity, and outputting a target reconstructed image, thereby obtaining an image with higher quality.

Description

Bistatic ISAR sparse high-resolution imaging method combining residual phase elimination
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly relates to a bistatic ISAR sparse high-resolution imaging method and terminal equipment with combined residual phase elimination.
Background
For bistatic ISAR imaging, it is difficult in some cases to obtain continuous long-term stable echoes. If the radar pulse is interfered or the target flickers, the signal to noise ratio of echoes of a plurality of pulses cannot meet the imaging requirement, and corresponding echoes need to be discarded in the subsequent processing process; for a multi-task multifunctional bistatic ISAR system, the searching, tracking and imaging tasks of one or even a plurality of targets need to be completed, and in the limited observation time of the targets, the radar needs to be switched between different beam forms or different beam directions. In these cases, there is a discontinuity in the observed aperture for a single target, resulting in azimuthally sparse aperture sampling.
Sparse apertures present a greater challenge for bistatic ISAR imaging. The performance of a traditional phase self-focusing algorithm is reduced due to sparse aperture, the requirement on compensation precision is difficult to meet, a translational compensation residual phase is generated, when the over-resolution unit migration correction is needed in a high-resolution scene, in the process of correcting a distance space-variant quadratic phase term (over-Doppler unit migration correction) introduced by rotation, the equivalent rotation center position is difficult to obtain accurately, defocusing introduced by the distance space-variant quadratic term cannot be corrected completely, the influence of data loss is difficult to overcome by the traditional over-distance unit migration correction method, the performance is reduced, and the imaging quality is low. The existing bistatic sparse aperture ISAR imaging algorithm is difficult to adapt to the bistatic ISAR high-resolution sparse aperture imaging application scene on the assumption that phase self-focusing is completely realized or the phase self-focusing is considered but the Doppler-crossing unit migration is not considered to correct the residual phase.
Disclosure of Invention
In view of this, the embodiment of the present invention provides a bistatic sparse high-resolution imaging method and a terminal device with residual phase elimination combined, so as to solve the problem of low imaging quality of the bistatic sparse aperture ISAR imaging algorithm in the prior art.
The first aspect of the embodiment of the invention provides a bistatic ISAR sparse high-resolution imaging method combining residual phase elimination, which comprises the following steps:
preprocessing a bistatic ISAR sparse aperture echo signal of a preset imaging arc section to obtain a first echo signal;
when the center coordinate of the range gate is set to be the equivalent rotation center distance coordinate, converting the distance space-variant phase into a translation residual phase according to the first echo signal to obtain a corrected second echo signal;
constructing a phase error matrix based on the translational residual phase and a corresponding compressed sensing matrix, and obtaining a sparse imaging model corresponding to the second echo signal according with a sparse high-resolution bistatic ISAR imaging scene according to the phase error matrix based on the translational residual phase and the compressed sensing matrix;
and performing image and noise modeling based on statistical prior, performing sparse high-resolution imaging reconstruction and residual phase error iterative correction on the sparse imaging model through full Bayesian inference sparsity, and outputting a target reconstructed image.
Optionally, the first echo signal is:
Figure BDA0002933735530000021
wherein the content of the first and second substances,
Figure BDA0002933735530000022
a first bistatic ISAR sparse aperture echo signal representing the scattering point p after envelope alignment and phase autofocus processing,
Figure BDA0002933735530000023
indicating fast time, tmRepresenting the imaging time, σPTo representAt the imaging time t0Scattering coefficient of scattering point P, TpRepresenting the pulse width of the bistatic radar, c representing the propagation velocity of the electromagnetic wave in free space, mu representing the frequency modulation rate of the bistatic radar, Rp_rot(tm) A rotation term representing the preset imaging arc segment, j represents an imaginary number,
Figure BDA0002933735530000024
representing the residual translational phase of the mth pulse.
Optionally, when the center coordinate of the range gate is set to be the equivalent rotation center distance coordinate, the distance space-variant phase is converted into the translational residual phase according to the first echo signal, so as to obtain a corrected second echo signal, where the method includes:
according to the double-base ground angle time-varying and rotation quadratic term, carrying out the Robert expansion processing on the rotation term in the first echo signal;
obtaining a third echo signal according to the rotation term after the le-tay expansion processing and the first echo signal;
when the central coordinate of the distance wave gate is set to be the equivalent rotation center distance coordinate, determining the distance error amount caused by the position deviation of the equivalent rotation center according to the equivalent rotation center distance coordinate;
and converting the distance space-variant phase in the third echo signal into a translational residual phase according to the distance error amount to obtain a corrected second echo signal.
Optionally, the performing the le-tay expansion processing on the rotation term in the first echo signal according to the double-base angle time-varying and rotation quadratic term includes:
according to
Figure BDA0002933735530000031
Carrying out the Rotay expansion processing on the rotation term in the first echo signal;
wherein, yPRepresents the ordinate value, K, of the scattering point P in the xOy coordinate system0、K1Respectively representing the value of the bistatic time-varying coefficient, ω0To represent the eyesNominal equivalent rotational angular velocity, xPRepresents the abscissa value of the scattering point P in the xOy coordinate system.
Optionally, the third echo signal is
Figure BDA0002933735530000032
Wherein the content of the first and second substances,
Figure BDA0002933735530000033
is representative of the third echo signal or signals,
Figure BDA0002933735530000034
representing the part of the third echo signal except for the distance coordinate related term,
Figure BDA0002933735530000035
representing the portion that does not contain the distance space-variant phase term and translational residual phase error.
Optionally, the distance error amount is
YΔ＝(nc-N/2)Δy；
Wherein, YΔRepresents the distance error amount, ncAnd the actual discrete subscripts of the equivalent rotation center are shown, N is the number of distance units corresponding to the selected effective imaging area in the range gate, and deltay is the length corresponding to one distance unit.
Optionally, the second echo signal is
Figure BDA0002933735530000041
Wherein the content of the first and second substances,
Figure BDA0002933735530000042
represents the second echo signal phimAnd the representation represents a translation residual phase term after the distance space-variant term error is converted into a translation residual error term and is updated.
Optionally, after the obtaining of the corrected second echo signal, the method further includes:
obtaining a total echo signal based on the number of scattering points and the second echo signal;
the total echo signal is
Figure BDA0002933735530000043
Wherein the content of the first and second substances,
Figure BDA0002933735530000044
representing said total echo signal, ApDenotes the complex amplitude of the scattering points, P1, 2 … P, P denoting the number of scattering points.
Optionally, the translational residual phase-based phase error matrix is
Figure BDA0002933735530000045
Wherein E represents a phase error matrix based on the translational residual phase,
Figure BDA0002933735530000046
representing the i-th element in the translational residual phase based phase error matrix,
Figure BDA0002933735530000047
denotes the item IlA translational residual phase term, L ═ 1,2 … L, L representing the total number of effective aperture echo data;
the compressed sensing matrix is
Figure BDA0002933735530000051
Wherein F represents a compressed sensing matrix under a sparse aperture;
Figure BDA0002933735530000052
indicating a sense of compressionIn the ith effective aperture echo data in the matrix, M is 1,2 … (M-1), M represents the total number of doppler elements, and PRT represents the observation time corresponding to a single pulse.
Optionally, the obtaining of the sparse imaging model corresponding to the second echo signal that conforms to the sparse high-resolution bistatic ISAR imaging scene is:
S＝EFA+n；
wherein S represents a range image sequence under the sparse aperture, A represents a bistatic ISAR image to be solved, and n represents a complex noise matrix.
Compared with the prior art, the embodiment of the invention has the following beneficial effects: according to the method, the central coordinate of the range gate is set as the distance coordinate of the equivalent rotation center, so that the distance error amount caused by the position deviation of the equivalent rotation center can be determined, quadratic term errors which are difficult to eliminate in the prior art are converted into translation residual errors, distance space-variant quadratic distortion term correction can be accurately carried out, then the translation compensation residual phase errors and the distance space-variant compensation residual phase errors are modeled into observation model errors, a bistatic ISAR image is sparsely represented based on a matching Fourier basis, sparse high-resolution imaging reconstruction and residual phase error iterative correction are carried out on a sparsely formed image model, a target reconstruction image is output, and accordingly the image with high quality can be improved.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise.
FIG. 1 is a schematic flow chart of an implementation of a bistatic ISAR sparse high-resolution imaging method with joint residual phase elimination according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a corrected second echo signal according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a sparse aperture provided by an embodiment of the present invention;
FIG. 4 is a schematic diagram of outputting a reconstructed image of the object according to an embodiment of the present invention;
FIG. 5(a) is a schematic diagram of a one-dimensional range profile with an RMS sparsity of 40% under an ideal scattering point model provided by an embodiment of the present invention;
FIG. 5(b) is a schematic diagram of a one-dimensional distance image with an RMS sparsity of 70% under an ideal scattering point model provided by an embodiment of the invention;
FIG. 5(c) is a schematic diagram of a one-dimensional range profile with GMS sparsity of 40% under an ideal scattering point model provided by an embodiment of the present invention;
FIG. 5(d) is a diagram of a one-dimensional range profile with GMS sparsity of 70% under an ideal scattering point model according to an embodiment of the present invention;
FIG. 5(e) is a schematic diagram of MFT imaging with an RMS sparsity of 40% under an ideal scattering point model provided by an embodiment of the present invention;
FIG. 5(f) is a schematic diagram of MFT imaging with an RMS sparsity of 70% under an ideal scattering point model provided by an embodiment of the present invention;
FIG. 5(g) is a diagram of MFT imaging with GMS sparsity of 40% under an ideal scattering point model provided by an embodiment of the present invention;
FIG. 5(h) is a diagram of MFT imaging with GMS sparsity of 70% under an ideal scattering point model provided by an embodiment of the present invention;
FIG. 6(a) is a schematic diagram of a one-dimensional distance image with an RMS sparsity of 40% under an electromagnetic scattering model provided by an embodiment of the invention;
FIG. 6(b) is a schematic diagram of a one-dimensional distance image with an RMS sparsity of 70% under an electromagnetic scattering model provided by an embodiment of the invention;
fig. 6(c) is a schematic diagram of a one-dimensional range profile with a GMS sparsity of 40% in an electromagnetic scattering model provided in an embodiment of the present invention;
fig. 6(d) is a schematic diagram of a one-dimensional range profile with a GMS sparsity of 70% in the electromagnetic scattering model provided in the embodiment of the present invention;
FIG. 6(e) is a schematic diagram of MFT imaging with an RMS sparsity of 40% under an electromagnetic scattering model provided by an embodiment of the invention;
FIG. 6(f) is a schematic diagram of MFT imaging with RMS sparsity of 70% under an electromagnetic scattering model provided by an embodiment of the invention;
fig. 6(g) is a schematic diagram of MFT imaging with GMS sparsity of 40% under the electromagnetic scattering model provided by the embodiment of the present invention;
fig. 6(h) is a schematic diagram of an MFT imaging with GMS sparsity of 70% under an electromagnetic scattering model provided by an embodiment of the present invention;
FIG. 7(a) is a graph of a weight-based sparsity/of an ideal scattering point model of 40% in RMS sparse aperture form provided by an embodiment of the invention1A schematic of norm imaging;
FIG. 7(b) is a schematic diagram of CGMS prior-based imaging with an ideal scattering point model of sparsity of 40% in RMS sparse aperture form according to an embodiment of the present invention;
FIG. 7(c) is a graph of a weight-based sparsity/of an ideal scattering point model of 70% in RMS sparse aperture form provided by an embodiment of the invention1A schematic of norm imaging;
FIG. 7(d) is a schematic diagram of CGMS prior-based imaging with an ideal scattering point model of 70% sparsity in RMS sparse aperture form provided by an embodiment of the invention;
FIG. 7(e) is a weight-based method for weighting l with an ideal scattering point model of 40% sparsity in GMS sparse aperture format according to an embodiment of the present invention1A schematic of norm imaging;
FIG. 7(f) is a diagram of CGMS prior-based imaging with an ideal scattering point model of sparsity of 40% in GMS sparse aperture form according to an embodiment of the present invention;
FIG. 7(g) is a weight-based method for weighting l with 70% sparsity of an ideal scattering point model provided by an embodiment of the present invention in GMS sparse aperture form1A schematic of norm imaging;
fig. 7(h) is a schematic diagram of CGMS prior-based imaging with an ideal scattering point model with sparsity of 70% in GMS sparse aperture form according to an embodiment of the present invention;
FIG. 8(a) is a schematic diagram of an embodiment of the present inventionWeight-based l with a sparsity of 40% for the electromagnetic scattering model in the RMS sparse aperture form1A schematic of norm imaging;
FIG. 8(b) is a schematic diagram of CGMS prior-based imaging with sparsity of 40% in the form of RMS sparse aperture for an electromagnetic scattering model provided by an embodiment of the invention;
FIG. 8(c) is a graph of a weight-based sparsity/of an electromagnetic scattering model of 70% in RMS sparse aperture form, according to an embodiment of the present invention1A schematic of norm imaging;
FIG. 8(d) is a schematic diagram of CGMS prior-based imaging with a sparsity of 70% in the RMS sparse aperture form for an electromagnetic scattering model provided by an embodiment of the invention;
FIG. 8(e) is a weight-based method for weighting l with a sparsity of 40% in GMS sparse aperture form for an electromagnetic scattering model provided by an embodiment of the present invention1A schematic of norm imaging;
fig. 8(f) is a schematic diagram of CGMS prior-based imaging with a sparsity of 40% in GMS sparse aperture form for an electromagnetic scattering model provided by an embodiment of the present invention;
FIG. 8(g) is a weight-based method for weighting l with a sparsity of 70% in GMS sparse aperture form for an electromagnetic scattering model provided by an embodiment of the present invention1A schematic of norm imaging;
fig. 8(h) is a schematic diagram of CGMS prior-based imaging with a sparsity of 70% in a GMS sparse aperture form for an electromagnetic scattering model provided in an embodiment of the present invention;
FIG. 9 is a schematic diagram of comparison of imaging indexes based on an ideal scattering point model under different sparsity conditions according to an embodiment of the present invention;
fig. 10 is a schematic diagram of comparison of imaging indexes based on an electromagnetic scattering model under different sparsity conditions according to an embodiment of the present invention.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular system structures, techniques, etc. in order to provide a thorough understanding of the embodiments of the invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.
In order to explain the technical means of the present invention, the following description will be given by way of specific examples.
Fig. 1 is a schematic flow chart of an implementation process of a bistatic ISAR sparse high-resolution imaging method with combined residual phase cancellation according to an embodiment of the present invention, which is described in detail below.
Step 101, preprocessing a bistatic ISAR sparse aperture echo signal of a preset imaging arc section to obtain a first echo signal.
Optionally, this step may include performing translational compensation processing on the bistatic ISAR sparse aperture echo signal of the preset imaging arc segment to obtain a first echo signal.
In this embodiment, t of bistatic ISAR imagingmAt the moment, the instantaneous distance between the scattering point p and the bistatic radar receiving and transmitting station is Rp(tm)，Rp(tm) Can be expressed as
Rp(tm)＝Ro(tm)+Rp_rot(tm)； (1)
Ro(tm) Is tmInstantaneous slant distance, R, corresponding to the centroid of the target at that momentp_rot(tm) And the change of the slope distance caused by the target equivalent rotation term is a rotation term of the preset imaging arc segment.
Because the precision required by the envelope alignment is in the magnitude of the distance resolution, generally corresponding to the magnitude of dozens of centimeters, after translational compensation, namely envelope alignment and phase autofocus, under the condition of a sparse aperture, if a residual translational phase exists, the bistatic ISAR echo signal of the scattering point p and the first echo signal can be represented again as
Figure BDA0002933735530000091
Wherein the content of the first and second substances,
Figure BDA0002933735530000092
a first bistatic ISAR sparse aperture echo signal representing the scattering point p after envelope alignment and phase autofocus processing,
Figure BDA0002933735530000093
indicating fast time, tmRepresenting the imaging time, σPIs shown at the imaging instant t0Scattering coefficient of scattering point P, TpRepresenting the pulse width of the bistatic radar, c representing the propagation velocity of the electromagnetic wave in free space, mu representing the frequency modulation rate of the bistatic radar, Rp_rot(tm) A rotation term representing the preset imaging arc segment, j represents an imaginary number,
Figure BDA0002933735530000094
representing the residual translational phase, i.e., the initial phase compensation error, of the mth pulse.
And 102, when the center coordinate of the range gate is set to be the equivalent rotation center distance coordinate, converting the distance space-variant phase into a translation residual phase according to the first echo signal, and obtaining a corrected second echo signal.
Optionally, as shown in fig. 2, the step may include the following steps:
step 201, according to the double-base angle time-varying and rotation quadratic term, carrying out the Theile expansion processing on the rotation term in the first echo signal.
Optionally, the rotation term in the first echo signal is Rp_rot(tm) When deployed as a le Tay, can be expressed as
Figure BDA0002933735530000101
Wherein, yPRepresenting the longitudinal coordinate value of the scattering point P in an xOy coordinate system, wherein the xOy coordinate system is a right-hand rectangular coordinate system established by taking the target centroid O as the origin and the bipartite ground angle bisector as the y axis, and K0、K1Respectively representing the value of the bistatic time-varying coefficient, ω0Representation ofTarget equivalent rotational angular velocity, xPRepresents the abscissa value of the scattering point P in the xOy coordinate system.
And step 202, obtaining a third echo signal according to the rotation term after the le-tay expansion processing and the first echo signal.
Optionally, in this step, the formula (3) may be taken into the formula (2), and then the third echo signal may be approximated to be
Figure BDA0002933735530000102
Figure BDA0002933735530000103
Wherein the content of the first and second substances,
Figure BDA0002933735530000104
is representative of the third echo signal or signals,
Figure BDA0002933735530000105
representing the part of the third echo signal except for the distance coordinate related term,
Figure BDA0002933735530000111
representing the portion that does not contain the distance space-variant phase term and translational residual phase error.
Along with the distance coordinate ypVarying linear phase term (linear distortion term exp (-j4 π y)PK1tmLambda) will cause the image to be skewed with distance coordinate ypVarying quadratic phase term (quadratic distortion term)
Figure BDA0002933735530000112
Will result in defocusing of the image. Therefore, it is necessary to correct the distance distortion term to obtain a true image shape and reduce defocus. Wherein the equivalent rotation center coordinates and the corresponding discrete subscripts need to be estimated to accurately correct the distance space-variant quadratic distortion term. Due to the azimuth compression based on the Fourier base class, the sparse aperture can cause high side lobe,Grating lobes and energy leakage cause that the search estimation method of the equivalent rotation center distance coordinate cannot be effectively implemented under the condition that the full aperture is given based on the image contrast maximum criterion.
Therefore, in the present embodiment, image correction can be performed by setting the center coordinates of the range gate as the equivalent rotation center distance coordinates.
And step 203, when the center coordinate of the distance wave gate is set to be the equivalent rotation center distance coordinate, determining the distance error amount caused by the position deviation of the equivalent rotation center according to the equivalent rotation center distance coordinate.
Optionally, in this step, if the true discrete subscript of the equivalent rotation center is ncThe amount of distance error due to the shift in the position of the equivalent center of rotation is
YΔ＝(nc-N/2)Δy； (6)
Wherein, YΔThe distance error is represented, N represents the number of distance units corresponding to the effective imaging area selected in the range gate, and it can be assumed that N is an even number and Δ y represents the length corresponding to one distance unit.
And 204, converting the space-variant phase in the third echo signal into a translational residual phase according to the distance error amount to obtain a corrected second echo signal.
According to formula (6), YΔDiscrete distance index n only from actual equivalent center of rotationcIt is related. For the correction of the linear distortion term, the deviation of the equivalent rotation center from the coordinate only causes the neat deviation of the image, the image quality is not influenced, and only the influence of the deviation of the equivalent rotation center from the coordinate on the quadratic distortion term is considered. Therefore, the distance distortion phase term correction is performed on the equation (4) by taking the distance wave gate center as the equivalent rotation center distance coordinate and performing the distance space-variant phase compensation, and the corrected second echo signal can be expressed as
Figure BDA0002933735530000121
Wherein the content of the first and second substances,
Figure BDA0002933735530000122
is representative of the second echo signal or signals,
Figure BDA0002933735530000123
distance error amount Y caused only by position deviation from equivalent rotation centerΔAnd the relation is independent of the distance coordinate of the scattering point P, namely the phase term eliminates the distance space variation, the distance space variation term error is converted into a translation residual error term, and the updated translation residual phase term is
Figure BDA0002933735530000124
After this step, may also include:
step 205, obtaining a total echo signal based on the number of scattering points and the second echo signal.
Optionally, if there are R scattering points in total, according to the equations (5) and (7), a corresponding total echo signal can be obtained, where the total echo signal is
Figure BDA0002933735530000125
Wherein the content of the first and second substances,
Figure BDA0002933735530000126
representing said total echo signal, ApDenotes the complex amplitude of the scattering points, p 1,2 … R, R denotes the number of scattering points,
Figure BDA0002933735530000127
ω0represents a target equivalent rotational speed, K0、K1Respectively representing the values of said bistatic time-varying coefficients, phimAnd the translation residual phase term is updated after the distance space-variant term error is converted into the translation residual error term.
103, constructing a phase error matrix based on the translational residual phase and a corresponding compressed sensing matrix, and obtaining a sparse imaging model corresponding to the second echo signal according to the phase error matrix based on the translational residual phase and the compressed sensing matrix, wherein the sparse imaging model corresponds to a sparse high-resolution bistatic ISAR imaging scene.
Using matched Fourier basis functions
Figure BDA0002933735530000128
And (3) carrying out pulse pressure on the echo data of a certain distance unit after the distance distortion term correction through MFT (finite frequency transfer) to obtain an orientation image formed by a set of narrow-width sinc functions, wherein the echo data has sparsity in a specific matching Fourier domain signal. If T is M · PRT, the total observation time, M is the total number of pulses under the full aperture, and PRT represents the observation time corresponding to a single pulse. The full aperture down azimuth resolution is
Figure BDA0002933735530000129
Then under full aperture conditions, the matching fourier sparse basis matrix may be represented as
Figure BDA0002933735530000131
Wherein, FfullRepresents the matching Fourier sparse basis matrix under the full aperture condition,
Figure BDA0002933735530000132
data in the mth doppler cell in the ith effective aperture echo data in the compressed sensing matrix is represented, i is 1,2, …, M is 1,2, …, M.
Matching Fourier transform after considering a particular integration path, the corresponding set of basis functions
Figure BDA0002933735530000133
The method has orthogonality, and the discrete matching Fourier sparse basis matrix has approximate orthogonality.
The sparse aperture can be generally categorized into a random missing sparse aperture form and a block missing sparse aperture form, and fig. 3 shows a schematic diagram of the sparse aperture, where white regions and black regions correspond to the missing aperture and the effective aperture, respectively.
Discretizing a two-dimensional imaging scene area, wherein the discretized scene area comprises N multiplied by M squares, wherein N and M respectively represent the number of distance units and the number of Doppler units. High resolution imaging can set the size deltax of the doppler cell to full aperture resolution,
Figure BDA0002933735530000134
Δ y is set to a corresponding size of the distance unit, i.e., Δ y ═ c/2fsK0. Assuming that S is L (L) under sparse aperture conditions<M) effective aperture echo data, by means of an effective aperture selection matrix
Figure BDA0002933735530000135
And selecting and combining the effective apertures to obtain L effective aperture echo data. Let I denote the set of valid pulse index sequences for the effective aperture selection matrix T-rule, and the azimuthal upward coordinate can be expressed as xi＝IiΔx,i∈[1,L]. Based on equations (9) and (10), and considering the influence of noise, the matrix model of echo imaging can be expressed as a matrix model under sparse aperture
S＝EFA+n； (11)
Wherein the content of the first and second substances,
Figure BDA0002933735530000136
for range image sequences under sparse apertures, define S ═ S·1…S·n]Wherein
Figure BDA0002933735530000137
Representing echo data in an nth range bin;
Figure BDA0002933735530000138
a matrix of residual phase errors is represented,
Figure BDA0002933735530000139
e denotes a phase error matrix based on the translational residual phase,
Figure BDA0002933735530000141
representing the i-th element in the translational residual phase based phase error matrix,
Figure BDA0002933735530000142
denotes the item IlA translational residual phase term, L ═ 1,2 … L, L representing the total number of effective aperture echo data;
Figure BDA0002933735530000143
representing an undersampled sparse matching Fourier basis matrix, i.e., a compressed sensing matrix, can be represented as
Figure BDA0002933735530000144
Wherein F represents a compressed sensing matrix under the sparse aperture, namely an effective compressed sensing matrix, according to FfullF is an under-sampling incoherent basis matrix, and under the conditions of certain signal prior sparsity constraint and observation signal loss ratio, the F meets the requirements of a K-RIP (K-RIP) condition and a row-column incoherent characteristic required by compressed sensing high-probability reconstruction;
Figure BDA0002933735530000145
the data in the mth doppler cell in the ith effective aperture echo data in the compressed sensing matrix is represented, L is 1,2 … L, L represents the total number of effective aperture echo data, M is 1,2 … M-1, M represents the total number of doppler cells, and PRT represents the observation time corresponding to a single pulse.
Figure BDA0002933735530000146
Representing a bistatic ISAR image to be solved, i.e. a sparse image matrix, which may be defined as a ═ a·1…A·N]Wherein A is·n＝[A1,n,A2,n,…,AM,n]TRepresenting a reconstruction azimuth direction corresponding to the echo data of the nth range cell in the second echo signal;
Figure BDA0002933735530000147
representing a complex noise matrix.
And 104, performing image and noise modeling based on statistical prior, performing sparse high-resolution imaging reconstruction and residual phase error iterative correction on the sparse imaging model through full Bayesian inference sparseness, and outputting a target reconstructed image.
Optionally, when modeling the image and noise based on statistical prior, sparse aperture imaging modeling may be further performed according to equation (11).
Optionally, the noise n is assumed to be complex white gaussian noise, and n follows zero mean with variance of β-1The complex Gaussian distribution of (A), then the noise is modeled as
Figure BDA0002933735530000148
The likelihood function of the one-dimensional image sequence S of the second echo signal also fits into a complex gaussian distribution as
Figure BDA0002933735530000151
Wherein I is an identity matrix. For Bayesian reasoning to be convenient, it is assumed that beta follows a Gamma distribution conjugated with a Gaussian prior, i.e.
p(β)＝Gamma(β|a,b)； (14)
In formula (14), Gamma (β | a, b) ═ Γ (a)-1baαa-1e-bβThe Gamma function is defined as
Figure BDA0002933735530000152
To obtain an information-free prior of the noise power, a, b are generally set to very small values, e.g. 10 ═ a-4。
Each pixel of the bistatic ISAR image A to be solved is assumed to obey CGSM prior which is composed of a complex Gaussian prior and a Gamma prior. Each independent pixel A in bistatic ISAR image A needing to be solvedm,nObeying a zero-mean complex gaussian distribution, wherein M is 1,2, …, M;n is 1,2, …, N, and the reciprocal of the variance is λm,n(scale factor), the coefficients are distributed independently, the conditional probability density function of the bistatic ISAR image A to be solved is
Figure BDA0002933735530000153
Reconstructed image A corresponding to echo data of any range unit·nFor it, the hyper-parameter λ is again·nAdding a layer of mutually independent Gamma distribution, then lambda·nHas a probability density function of
Figure BDA0002933735530000154
To obtain a hyperparameter lambda·nThe parameters c, d are generally set to very small values, e.g., c-d-10-4。
At this time, the sparse prior is a two-layer Bayesian probability model. Fig. 4 shows a probability map model based on sparse prior, in which the data in the shaded circles represent echo data, which are known quantities, the data in the circles represent unknown variables, and the data in the blocks represent hyper-parameters, and are initialized to a-b-c-d-10-4。
It can be seen from fig. 4 that, at this time, each pixel in the image model constructed based on statistical prior obeys not a single complex gaussian distribution but a two-layer prior distribution (which is related to the scale factor λ) in which the complex gaussian distribution and the Gamma distribution are combined·nThe edge distribution of the data is in accordance with the joint student-t distribution), and the layered complex Gaussian distribution prior model has stronger sparse promotion effect.
Then, the unknown variables in fig. 4 are solved, that is, the sparse through the full bayesian inference in step 104 is executed, the sparse high resolution imaging reconstruction and the residual phase error iterative correction are performed on the image rarity, and the target reconstructed image is output.
Optionally, the two layers of bayesian probabilistic model correspond to each otherEach column A of the template image·nAre independent of each other, so that each column of distance cell data S can be utilized·nReconstruction is performed in units of range, so data S is for a certain range unit·nCan be expressed as
S·n＝EFA·n+n·n； (17)
n·nRepresenting the nth column of complex noise data in the complex noise matrix.
The Variational Bayesian method (VB) can approximate the posterior probability with high precision when the joint posterior probability densities of all unknown variables are assumed to be mutually independent, and has higher calculation efficiency.
Therefore, in the embodiment, based on the VB method, the unknown variable joint posterior probability in the two-layer Bayesian probability model can be factorized into
p(A·n,λ·n,β|S·n；E)≈q(A·n)q(λ·n)q(β)； (18)
Wherein q (A)·n)、q(λ·n) Q (beta) represents A·n、λ·nAnd a posterior probability density estimate of β. These three posterior probability density estimates are solved in the logarithmic domain using the Variational Bayesian Expectation Maximization (VB-EM) method.
For log q (A)·n) The Expectation Maximization (EM) method can be used
Figure BDA0002933735530000179
Wherein the content of the first and second substances,<·>q(·)representing the expectation with respect to the probability density q (·), const represents a constant term.
By bringing equations (13) and (15) into equation (19) and ignoring the constant term, the expression vector can be obtained
Figure BDA0002933735530000171
log q(A·n) With respect to A·nCan be expressed as
Figure BDA0002933735530000172
Wherein, Λ·n＝diag(<λ1n>,<λ2n>,…,<λMn>) Is represented by a hyperparameter λmnAnd (M is 1,2, …, M) expected values.
Order to
Figure BDA0002933735530000173
A value of 0 gives A·nIs estimated as
Figure BDA0002933735530000174
Then q (A)·n) Can be regarded as obeying a mean value of mu·nThe covariance is ∑nHas a complex Gaussian distribution of
Figure BDA0002933735530000175
Wherein the content of the first and second substances,
Figure BDA0002933735530000176
Σn＝(<β>FHF+Λ·n)-1； (24)
mean value μ·nFor azimuthal image of the range cell
Figure BDA0002933735530000177
Is estimated, the reconstructed target image is
Figure BDA0002933735530000178
For q (λ)·n) Obtained by the VB-EM method
Figure BDA0002933735530000181
The formula (15) and the formula (16) are brought into the formula (25) with only lambda remainingnNeglecting the constant term, can obtain
Figure BDA0002933735530000182
Thus, λ·nA posterior probability density q (lambda)·n) Obeying a Gamma distribution, i.e.
Figure BDA0002933735530000183
Wherein the content of the first and second substances,
Figure BDA0002933735530000184
Σn-mmrepresentation matrix ΣnThe (M, M) -th element value in (a) is the element on the diagonal, and M is 1,2, … M.
Similarly, q (beta) can be obtained by VB-EM method
Figure BDA0002933735530000185
Therefore, the posterior probability density q (β) of β also follows a Gamma distribution, i.e.
Figure BDA0002933735530000186
Wherein the content of the first and second substances,
Figure BDA0002933735530000187
Figure BDA0002933735530000188
in the complete Bayes inference, a posterioriThe expectation of probability is typically used as an estimate of the unknown variable, i.e. the posterior probability density q (A) can be used·n)、q(λ·n) And q (beta) to estimate the unknown variables A, lambda and beta in the two-layer Bayesian probability model. Due to q (A)·n) Obeying a complex Gaussian distribution, q (λ)·n) And q (β) obey a Gamma distribution, so that a corresponding estimate can be obtained as
Figure BDA0002933735530000191
The unknown variables a, λ and β may be iteratively updated according to respective equations in equation (30).
Wherein, sigmanRepresenting covariance, beta representing bibase angle, F representing compressed sensing matrix, FHConjugate matrix, Λ, representing a compressed sensing matrix·nIs represented by a hyperparameter λmnA diagonal matrix of expected values of (M ═ 1,2, …, M), EHA conjugate matrix, S, representing a translational residual phase matrix corresponding to a translational residual phase based phase error matrix·nC, d, a and b represent hyper-parameters for the echo data in the nth range bin, respectively.
After updating unknown variables A, lambda and beta every time, detecting whether N is equal to N; detecting whether the solving of the image pixels of all the distance units is finished or not;
and when N is not equal to N, continuously updating the unknown variables A, lambda and beta according to the formula (30), and when N is equal to N, obtaining an image reconstructed in one iteration.
In sparse iterative imaging, the information (amplitude and phase) of the solution iteration image is continuously close to that of the real image. The gain of the phase fine compensation comes from the gain of the iterative image information which gradually approaches the real image information in the sparse iterative imaging process. And estimating the phase error based on a maximum likelihood method according to the obtained reconstructed image and the echo data corresponding to the reconstructed image.
Assume that the reconstructed image estimated in the g-th iteration is
Figure BDA0002933735530000192
Then
Figure BDA0002933735530000193
Representing reconstructed images
Figure BDA0002933735530000194
Corresponding data
Figure BDA0002933735530000195
The phase error after the coarse compensation is estimated on the basis of the maximum likelihood method in the k line to obtain a phase error estimation cost function of the k pulse echo, namely, the residual phase error matrix after the distance space-variant phase compensation is processed on the basis of the maximum likelihood method according to the compressed sensing matrix to obtain the phase error estimation cost function of
Figure BDA0002933735530000201
Wherein the content of the first and second substances,
Figure BDA0002933735530000202
representing the phase error estimate cost function, S, for the kth pulse echo in the (g +1) th iterationk·Data corresponding to the k-th pulse echo is represented,
Figure BDA0002933735530000203
representing the phase error estimation cost function for the kth pulse echo in the g-th iteration,
Figure BDA0002933735530000204
represents the vector inner product, Fk·Representing the kth line of data in the compressed sensing matrix,
Figure BDA0002933735530000205
representing the reconstructed image obtained in the g-th iteration.
Optionally, the constraint condition is that
Figure BDA0002933735530000206
Term maximization, which is known from equation (31)
Figure BDA0002933735530000207
The solution of the phase error estimation cost function can be realized, so that the residual phase error matrix
Figure BDA0002933735530000208
Is updated by the expression of
Figure BDA0002933735530000209
Wherein the content of the first and second substances,
Figure BDA00029337355300002010
representing the updated residual phase error matrix, Sk·Data corresponding to the k-th pulse echo is represented,
Figure BDA00029337355300002011
representing the last obtained residual phase error matrix,
Figure BDA00029337355300002012
denotes Sk·The conjugate matrix of (a) is determined,
Figure BDA00029337355300002013
representing reconstructed images
Figure BDA00029337355300002014
Corresponding data
Figure BDA00029337355300002015
The (c) th row of (a),
Figure BDA00029337355300002016
conjugate matrix of representation, Fk·Representing the k row of data in the trial compressed sensing matrix,
Figure BDA00029337355300002017
representing the target image obtained in the g-th iteration. conj shows the phase, mu, of the complex number·nAs an azimuthal image of the range unit
Figure BDA00029337355300002018
N is 1,2 … N.
Optionally, after obtaining the residual phase error matrix, according to
Figure BDA00029337355300002019
Performing phase compensation on a range profile sequence under a sparse aperture corresponding to the second echo signal; residual phase error correction is achieved.
Optionally, can be based on
Figure BDA0002933735530000211
And carrying out next iteration to solve the target image, wherein the noise n is complex Gaussian white noise, the mean value obeys zero, and the variance is beta-1Complex gaussian distribution.
And detecting whether the iteration times reach a preset iteration time or whether the adjacent images of the current target reconstruction image meet the requirements.
Optionally, whether the adjacent image of the current target reconstruction image is detected
Figure BDA0002933735530000212
Optionally, eps is a preset threshold value, and may be set before the iterative computation flow starts.
And when the iteration times do not reach the preset iteration times or the adjacent images of the current target reconstruction image do not meet the requirements, continuing to perform residual phase error compensation and subsequent steps according to the image reconstructed by the current iteration and the new phase error estimation matrix.
And when the iteration times reach the preset iteration times or the adjacent images of the current target reconstructed image meet the requirements, outputting the image reconstructed by the current iteration, wherein the image is the target image.
Optionally, each distance in the g-th iterationDuring the off-cell sparse solution process, because
Figure BDA0002933735530000213
And
Figure BDA0002933735530000214
by solving for
Figure BDA0002933735530000215
Respectively is O (M)3+LM2)、O(LM2+ML2+ ML), solving
Figure BDA0002933735530000216
And beta(g+1)Respectively are O (M) and O (LM)2) If the amount of computation O (nlm) of the residual phase error is estimated pulse by equation (14), the total amount of computation corresponding to g iterations is O (GN (M)3+3LM2+ML2+ M +2LM)), equation (26) may be further converted to Σ based on the Woodbury formulan＝Λ·n -1-Λ·n -1FH(<β>-1I+FΛ·n -1FH)-1FΛ·n -1To reduce the amount of computation.
When simulation verification is carried out, a preset imaging guard is selected within the template visual time, and specific simulation parameters are set as shown in a table I.
Watch 1
Parameter name Numerical value Parameter name Numerical value
Carrier frequency/GHz 10 Pulse width/us 10
Signal bandwidth/MHz 600 Sampling frequency/MHz 750
Pulse repetition frequency/Hz 100 Pulse accumulation number/number 500
Distance resolution/m 0.3261 Azimuth resolution/m 0.2268
Under this simulation parameter setting, the over-range migration is negligible. Noise affects the sparsity of target signals, and different azimuth aperture missing modes affect the non-correlation performance between rows and columns of the observation matrix. In order to verify the effectiveness and robustness of the bistatic ISAR sparse high-resolution imaging method combining residual phase elimination in the application, two common sparse aperture modes including Random sparse aperture (RMS) and block sparse aperture (GMS) are investigated through simulation experiments. The performance of the sparse aperture high-resolution imaging algorithm is verified under the conditions of different aperture loss ratios (sparsity) and different signal-to-noise ratios.
The total aperture number is set to 500, assuming effective aperture sampling numbers of 300 (sparsity of 40%) and 150 (sparsity of 70%), respectively. After envelope alignment and coarse phase self-focusing are completed by sparse aperture echo, translation phase errors are preliminarily corrected, distance space-variant phase compensation is carried out by assuming a wave gate center as an equivalent rotation center coordinate, echo data only containing residual translation errors are obtained, and an imaging experiment is carried out based on the echo data after distance space-variant phase correction. The SNR is set to 5dB by adding zero-mean complex white gaussian noise to the input echo data. A one-dimensional range image with RMS sparsity of 40% under the ideal scattering point model as shown in fig. 5(a), a one-dimensional range image with RMS sparsity of 70% under the ideal scattering point model as shown in fig. 5(b), a one-dimensional range image with GMS sparsity of 40% under the ideal scattering point model as shown in fig. 5(c), and a one-dimensional range image with GMS sparsity of 70% under the ideal scattering point model as shown in fig. 5 (d); the MFT imaging with the RMS sparsity of 40% under the ideal scattering point model as shown in fig. 5(e), the MFT imaging with the RMS sparsity of 70% under the ideal scattering point model as shown in fig. 5(f), the MFT imaging with the GMS sparsity of 40% under the ideal scattering point model as shown in fig. 5(g), and the MFT imaging with the GMS sparsity of 70% under the ideal scattering point model as shown in fig. 5 (h). A one-dimensional range profile with RMS sparsity of 40% under the electromagnetic scattering model as shown in fig. 6(a), a one-dimensional range profile with RMS sparsity of 70% under the electromagnetic scattering model as shown in fig. 6(b), a one-dimensional range profile with GMS sparsity of 40% under the electromagnetic scattering model as shown in fig. 6(c), and a one-dimensional range profile with GMS sparsity of 70% under the electromagnetic scattering model as shown in fig. 6 (d); the MFT imaging with the RMS sparsity of 40% under the electromagnetic scattering model shown in fig. 6(e), the MFT imaging with the RMS sparsity of 70% under the electromagnetic scattering model shown in fig. 6(f), the MFT imaging with the GMS sparsity of 40% under the electromagnetic scattering model shown in fig. 6(g), and the MFT imaging with the GMS sparsity of 70% under the electromagnetic scattering model shown in fig. 6 (h).
Under the conditions of GMS and RMS two sparse aperture forms and different sparsity, based on one-dimensional range profiles of two simulation target models and corresponding MFT imaging results, it can be seen that echo data are discontinuous due to sparse apertures, residual error phases exist, azimuth compression cannot be effectively completed based on MFT, and serious energy leakage and defocusing phenomena exist in images, so that the imaging quality needs to be further improved.
Weight-based l with a sparsity of 40% for the ideal scattering point model in RMS sparse aperture form1Norm and CGMS-prior based imaging are shown in fig. 7(a) and 7(b), respectively, with a sparsity of 70% based on weighting/1Norm and CGMS-based prior imaging are shown in fig. 7(c) and 7(d), respectively; weight-based l with sparsity of 40% for the ideal scattering point model in GMS sparse aperture form1Norm and CGMS-prior based imaging are shown in fig. 7(e) and 7(f), respectively, with a sparsity of 70% based on weighting/1Norm and CGMS-a-based imaging are shown in fig. 7(g) and 7(h), respectively.
Corresponding electromagnetic scattering model-based weighting l with sparsity of 40% in RMS sparse aperture form1Norm and CGMS-prior based imaging are shown in fig. 8(a) and 8(b), respectively, with a sparsity of 70% based on weighting/1Norm and CGMS-a-based imaging are shown in fig. 8(c) and 8(d), respectively. Corresponding electromagnetic scattering model-based weighting l with sparsity of 40% in GMS sparse aperture form1Norm and CGMS-prior based imaging are shown in fig. 8(e) and 8(f), respectively, with a sparsity of 70% based on weighting/1Norm and CGMS-a-based imaging are shown in fig. 8(g) and fig. 8(h), respectively. Then it can be seen from the imaging results of the two simulation models that both CS-based imaging algorithms are superior to MFT-based imaging algorithms in sparse aperture conditions, which can both obtain the basic shape of the target. When the sparsity is 40%, based on the weight l1The imaging result of the norm has a small amount of residual noise to influence the image quality, and an image with clear background and good focus is obtained based on a CGMS prior full Bayesian inference imaging algorithm; when sparsity drops to 70%, based on weighting/1The performance of the norm imaging algorithm is obviously reduced (the residual noise level is increased and the image focusing degree is reduced), and compared with the full Bayesian inference imaging algorithm based on CGMS prior, the image with good focusing degree and background definition can still be obtained. This is due to the relative weighting/1The norm imaging algorithm is based on a full Bayesian inference imaging algorithm and more effectively utilizes the posterior probability distribution information of the image and the corresponding high-order information. Meanwhile, under the condition that other conditions are the sameThe results under RMS conditions are better than those under GMS conditions, since RMS achieves sparse bases with the same sparsity with better incoherence than GMS. Therefore, the bistatic ISAR sparse high-resolution imaging method combined with residual phase elimination can obtain images with good focusing power and background definition.
In order to quantitatively compare the performance of the sparse aperture algorithm, the image quality is further measured based on a Target-to-Background Ratio (TBR) on the basis of the image contrast. Wherein, T and B respectively represent a target supporting area and a background supporting area, an area of target image energy gathering is selected as the target supporting area through a proper threshold, other parts of an imaging plane are set as the background supporting area, the TBR reflects the energy gathering capability and the noise suppression capability of the image, and the larger the value is, the smaller the energy leakage and the noise energy is. A higher image contrast value indicates a higher overall image focus.
As shown in fig. 9, the comparison diagram of the imaging index based on the ideal scattering point model under different sparsity conditions, and as shown in fig. 10, the comparison diagram of the imaging index based on the electromagnetic scattering model under different sparsity conditions, it can be seen that the TBR and the image contrast based on the two prior corresponding images are superior to those based on the weighting l1The value of the norm algorithm.
In addition, under the same SNR condition, when SNR is respectively 10dB and 5dB, the quality of the image obtained based on CGMS prior is higher than that based on weighting l1The norm algorithm obtains the quality of the image. But as the SNR decreases, based on the weight/1The norm algorithm and the quality of the image obtained based on CGMS prior are both reduced, and the corresponding TBR value and the image contrast value are both reduced. Based on weighting/when SNR is as low as 0dB1The norm image contains obvious residual noise, the TBR value and the image contrast value are obviously reduced, the residual noise also appears in the image obtained based on the CGMS priori, and the sparse imaging algorithm based on the CGMS priori has better robustness under the condition of low signal to noise ratio.
According to the bistatic ISAR sparse high-resolution imaging method with the combined residual phase elimination, the central coordinate of the range gate is set as the equivalent rotation central distance coordinate, so that the distance error amount caused by the bias of the equivalent rotation central position can be determined, quadratic errors which are difficult to eliminate in the prior art are converted into translational residual errors, so that distance space-variant quadratic distortion item correction can be accurately performed, the translational compensation residual phase errors and the distance space-variant compensation residual phase errors are modeled into observation model errors, the bistatic ISAR image is sparsely represented based on the matched Fourier basis, sparse high-resolution imaging reconstruction and residual phase error iterative correction are performed on the sparse imaging model, a target reconstruction image is output, and accordingly, high-quality images can be obtained. The bistatic ISAR sparse high-resolution imaging method combining residual phase elimination is higher in effectiveness and robustness, and has better sparse reconstruction performance under low signal-to-noise ratio.
It should be understood that, the sequence numbers of the steps in the foregoing embodiments do not imply an execution sequence, and the execution sequence of each process should be determined by its function and inherent logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.
The above-mentioned embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the embodiments of the present invention, and are intended to be included within the scope of the present invention.

Claims (10)

1. A bistatic ISAR sparse high-resolution imaging method combining residual phase elimination is characterized by comprising the following steps:
preprocessing a bistatic ISAR sparse aperture echo signal of a preset imaging arc section to obtain a first echo signal;
when the center coordinate of the range gate is set to be the equivalent rotation center distance coordinate, converting the distance space-variant phase into a translation residual phase according to the first echo signal to obtain a corrected second echo signal;
constructing a phase error matrix based on the translational residual phase and a corresponding compressed sensing matrix, and obtaining a sparse imaging model corresponding to the second echo signal according with a sparse high-resolution bistatic ISAR imaging scene according to the phase error matrix based on the translational residual phase and the compressed sensing matrix;
and performing image and noise modeling based on statistical prior, performing sparse high-resolution imaging reconstruction and residual phase error iterative correction on the sparse imaging model through full Bayesian inference sparsity, and outputting a target reconstructed image.
2. The bistatic ISAR sparse high resolution imaging method with joint residual phase cancellation as claimed in claim 1, wherein the first echo signal is:
Figure FDA0002933735520000011
wherein the content of the first and second substances,
Figure FDA0002933735520000012
a first bistatic ISAR sparse aperture echo signal representing the scattering point p after envelope alignment and phase autofocus processing,
Figure FDA0002933735520000013
indicating fast time, tmRepresenting the imaging time, σPIs shown at the imaging instant t0Scattering coefficient of scattering point P, TpRepresenting the pulse width of the bistatic radar, c representing the propagation velocity of the electromagnetic wave in free space, mu representing the frequency modulation rate of the bistatic radar, Rp_rot(tm) A rotation term representing the preset imaging arc segment, j represents an imaginary number,
Figure FDA0002933735520000014
representing the residual translational phase of the mth pulse.
3. The bistatic ISAR sparse high resolution imaging method with residual phase cancellation as claimed in claim 2, wherein said transforming the space-variant phase to translational residual phase according to the first echo signal when the center coordinate of the range gate is set as the equivalent rotation center distance coordinate, comprises:
according to the double-base ground angle time-varying and rotation quadratic term, carrying out the Robert expansion processing on the rotation term in the first echo signal;
obtaining a third echo signal according to the rotation term after the le-tay expansion processing and the first echo signal;
when the central coordinate of the distance wave gate is set to be the equivalent rotation center distance coordinate, determining the distance error amount caused by the position deviation of the equivalent rotation center according to the equivalent rotation center distance coordinate;
and converting the distance space-variant phase in the third echo signal into a translational residual phase according to the distance error amount to obtain a corrected second echo signal.
4. The bistatic ISAR sparse high resolution imaging method in combination with residual phase cancellation according to claim 3, wherein said performing a Robertian expansion process on the rotated terms in the first echo signal according to bistatic angular time-varying and rotated quadratic terms comprises:
according to
Figure FDA0002933735520000021
Carrying out the Rotay expansion processing on the rotation term in the first echo signal;
wherein, yPRepresents the ordinate value, K, of the scattering point P in the xOy coordinate system0、K1Respectively representing the value of the bistatic time-varying coefficient, ω0The expression represents the target equivalent rotational angular velocity, xPRepresents the abscissa value of the scattering point P in the xOy coordinate system.
5. The bistatic ISAR sparse high resolution imaging method with joint residual phase cancellation as claimed in claim 3 wherein said third echo signal is
Figure FDA0002933735520000022
Wherein the content of the first and second substances,
Figure FDA0002933735520000023
is representative of the third echo signal or signals,
Figure FDA0002933735520000024
representing the part of the third echo signal except for the distance coordinate related term,
Figure FDA0002933735520000031
representing the portion that does not contain the distance space-variant phase term and translational residual phase error.
6. The bistatic ISAR sparse high resolution imaging method with joint residual phase cancellation as claimed in claim 4 or 5, wherein the distance error amount is
YΔ＝(nc-N/2)Δy；
Wherein, YΔRepresents the distance error amount, ncAnd the actual discrete subscripts of the equivalent rotation center are shown, N is the number of distance units corresponding to the selected effective imaging area in the range gate, and deltay is the length corresponding to one distance unit.
7. The bistatic ISAR sparse high resolution imaging method with joint residual phase cancellation of claim 6, wherein the second echo signal is
Figure FDA0002933735520000032
Wherein the content of the first and second substances,
Figure FDA0002933735520000033
represents the second echo signal phimAnd the representation represents a translation residual phase term after the distance space-variant term error is converted into a translation residual error term and is updated.
8. The bistatic ISAR sparse high resolution imaging method with joint residual phase cancellation as claimed in claim 7, further comprising after said obtaining of the corrected second echo signal:
obtaining a total echo signal based on the number of scattering points and the second echo signal;
the total echo signal is
Figure FDA0002933735520000034
Wherein the content of the first and second substances,
Figure FDA0002933735520000035
representing said total echo signal, ApDenotes the complex amplitude of the scattering points, P1, 2 … P, P denoting the number of scattering points.
9. The bistatic ISAR sparse high resolution imaging method with joint residual phase cancellation as claimed in claim 8, wherein the translational residual phase based phase error matrix is
Figure FDA0002933735520000041
Wherein E represents a phase error matrix based on the translational residual phase,
Figure FDA0002933735520000042
representing the translational residual phase based phase error matrixThe first element of (a) is,
Figure FDA0002933735520000043
denotes the item IlA translational residual phase term, L ═ 1,2 … L, L representing the total number of effective aperture echo data;
the compressed sensing matrix is
Figure FDA0002933735520000044
Wherein F represents a compressed sensing matrix under a sparse aperture;
Figure FDA0002933735520000045
the data in the mth doppler cell in the ith effective aperture echo data in the compressed sensing matrix is shown, M is 1,2 … (M-1), M represents the total number of doppler cells, and PRT represents the observation time corresponding to a single pulse.
10. The bistatic ISAR sparse high resolution imaging method with joint residual phase cancellation as claimed in claim 8, wherein said obtaining the sparse imaging model corresponding to the second echo signal in line with the sparse high resolution bistatic ISAR imaging scenario is:
S＝EFA+n；
wherein S represents a range image sequence under the sparse aperture, A represents a bistatic ISAR image to be solved, and n represents a complex noise matrix.
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