CN113985412A - Moving target three-dimensional imaging method for vector modeling optimization inversion - Google Patents

Moving target three-dimensional imaging method for vector modeling optimization inversion Download PDF

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CN113985412A
CN113985412A CN202111297706.5A CN202111297706A CN113985412A CN 113985412 A CN113985412 A CN 113985412A CN 202111297706 A CN202111297706 A CN 202111297706A CN 113985412 A CN113985412 A CN 113985412A
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CN113985412B (en
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王家东
刘若晨
李亚超
石光明
张志军
刘旭
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Xidian University
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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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    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9021—SAR image post-processing techniques
    • 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
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Abstract

The invention discloses a moving target three-dimensional imaging method for vector modeling optimization inversion, which mainly solves the problems of high hardware and imaging complexity and low imaging precision in the prior art. The scheme is as follows: carrying out preprocessing of line-breaking frequency modulation, translational compensation and fast time dimension Fourier transform on echo signals received by the ISAR monostatic radar system in one observation time period; constructing a three-dimensional reconstruction coordinate system X ' -Y ' -Z ' by using the self motion parameters of the radar, and constructing an expression of three-dimensional reconstruction coordinates X, Y and Z of the scattering point in the three-dimensional reconstruction coordinate system by using the coordinate system; establishing a sparse optimization problem for solving a target three-dimensional reconstruction coordinate by using the expression and the preprocessed ISAR echo signal; and solving the sparse optimization problem by adopting an orthogonal matching pursuit algorithm to obtain the three-dimensional reconstruction coordinates of the target, and finally obtaining the three-dimensional reconstruction image. The invention has low imaging complexity and high imaging precision, and can be used for moving target identification, target classification and feature extraction.

Description

Moving target three-dimensional imaging method for vector modeling optimization inversion
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a moving target three-dimensional reconstruction method which can be used for moving target identification, target classification and feature extraction.
Background
The three-dimensional imaging of the inverse synthetic aperture radar ISAR is widely concerned in the field of ISAR research, and has very important significance in the aspects of moving target identification, target classification, feature extraction and the like. The method for accurately reconstructing the three-dimensional coordinates of the aerial target by using the echo signals obtained by continuously measuring the moving target by the ISAR can be practically applied to the fields of other military activities such as moving target identification, target classification, feature extraction and the like. Conventional three-dimensional ISAR imaging methods can be roughly divided into two categories: the first type is a three-dimensional imaging technology based on interferometric inverse synthetic aperture radar (InISAR), which observes a target through a plurality of receiving radars or transmitting radars simultaneously to obtain a plurality of two-dimensional ISAR images, and performs interference processing on the plurality of two-dimensional ISAR images to form a three-dimensional image. Although the kind of the InISAR three-dimensional imaging technology has the advantage of simple and easy signal processing process, the high dimensional resolution of the kind of the InISAR three-dimensional imaging technology is seriously dependent on the number of receiving radars, and the complexity of hardware equipment and the difficulty of design of a transmitting signal are high. The second type is an ISAR three-dimensional imaging technique using a cooperative target motion, which calculates a three-dimensional coordinate of a target using a signal parameter obtained by estimation and a motion parameter of the target by performing parameter estimation on a received echo signal. The method has high imaging complexity and needs to know the motion parameters of the target, so that the method cannot image the non-cooperative target and has certain limitation.
In the document, "Three-Dimensional air Imaging Based ON Shipborne Radar", published in "IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS", J2016, 3.M., the method provides a Three-Dimensional Imaging method, which obtains Doppler frequency AND modulation frequency of signals by performing parameter estimation ON received echoes, AND performs Three-Dimensional Imaging by using motion parameters of a Radar AND the estimated signal parameters. However, the method cannot realize the three-dimensional coordinate joint estimation, and has high algorithm complexity and low estimation precision.
Disclosure of Invention
The invention aims to provide a moving target three-dimensional imaging method for vector modeling optimization inversion aiming at the defects of the prior art, so that the three-dimensional coordinates of a target are jointly estimated under the condition that the motion parameters of the target are unknown, the hardware and imaging complexity is reduced, the estimation precision is improved, and the application range is expanded.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
(1) sequentially carrying out line-breaking frequency modulation, translation compensation and fast time dimension Fourier transform on echo signals received by the ISAR single-base radar system in one observation time period to obtain preprocessed ISAR echoes;
(2) constructing a three-dimensional reconstruction coordinate system X ' -Y ' -Z ' by using the self motion parameters of the radar;
(3) and constructing expressions of three-dimensional reconstruction coordinates X, Y and Z of the target scattering point in the three-dimensional reconstruction coordinate system by using the constructed three-dimensional reconstruction coordinate system X ' -Y ' -Z ':
Figure BDA0003336968860000021
where r is the vector of scattering points to the center of the scattering points, i (0) is t m0 time point, tmIs slow time, RΔIs the projection distance of the vector from the scattering point of the target to the center of the scattering point along the distance dimension direction, v is the motion speed of the radar, and w is the vector n of the scattering point of the target in the middle direction4Is projected length of (a), theta is a middle direction vector n4And the direction vector direction n of the azimuth dimension2The included angle between them;
(4) establishing a sparse optimization problem for solving a target three-dimensional reconstruction coordinate by using the preprocessed ISAR echo and the expression of the three-dimensional reconstruction coordinates x, y and z:
Figure BDA0003336968860000022
wherein argmax (·) represents taking the maximum value operation of the function argument, | | · | | | represents toTaking modulo operation, | ·| luminance2Is represented by2Norm, s is the preprocessed echo signal, a (α) is a parameterized redundant dictionary, α is a set of dictionary atoms, [ α ═ α [ [ α ]1，α2,…,αi,…,αN]N is the number of dictionary atoms, alphai＝[xp,yq,zr]TIs the ith parameter vector, x, in the parameterized redundant dictionarypIs the p-th parameter, y, in the set of distance-dimensional parametersqIs the q parameter, z, of the set of orientation-dimensional parameters of the scattering pointrIs the r-th parameter in the height dimension parameter set,
Figure BDA0003336968860000025
is the target three-dimensional reconstruction coordinate, eta is the estimated signal amplitude, and epsilon is the signal residual error;
(5) solving the sparse optimization problem by adopting an orthogonal matching pursuit OMP algorithm to obtain a three-dimensional reconstruction coordinate vector of the target
Figure BDA0003336968860000023
Performing three-dimensional reconstruction of ISAR target, wherein
Figure BDA0003336968860000024
Is the three-dimensional reconstructed coordinate vector of the kth scattering point of the object,
Figure BDA0003336968860000031
m is the number of scattering points of the target, (. C)TIs a transposition operation in which the phase of the input signal is inverted,
Figure BDA0003336968860000032
and
Figure BDA0003336968860000033
is the three-dimensional reconstructed coordinates of the k-th scattering point.
Compared with the prior art, the invention has the following advantages:
firstly, the sparse optimization problem of solving the three-dimensional reconstruction coordinates of the target is established, the three-dimensional coordinates of the target can be directly subjected to joint estimation, and compared with the traditional method for three-dimensional imaging by adopting parameter estimation, the method omits the step of estimating the initial frequency and the frequency modulation of the echo signal, and has low imaging complexity;
secondly, the ISAR single-base radar system is adopted to observe the target, so that the hardware complexity is low and the implementation is convenient compared with an InISAR three-dimensional imaging technology;
thirdly, the invention can image the cooperative target and the non-cooperative target by utilizing the Doppler effect generated by the radial motion of the radar, compared with the ISAR three-dimensional imaging technology utilizing the motion of the cooperative target, and has wide application range.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a geometric diagram of a three-dimensional reconstruction of a moving object according to the present invention;
FIG. 3 is a schematic diagram of direction vectors in the azimuth dimension and the elevation dimension in the reconstructed coordinates according to the present invention;
fig. 4 is a diagram of simulation results of three-dimensional reconstruction imaging of a moving object using the present invention.
Detailed Description
Embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the method for three-dimensional imaging of a moving object by vector modeling optimization inversion of the embodiment includes the following steps:
step 1, processing an original signal to obtain a preprocessed ISAR echo signal.
1.1) transmitting signals by ISAR monostatic Radar System
Figure BDA0003336968860000034
Figure BDA0003336968860000035
Wherein, TpIs the pulse width, fcIs the carrier frequency, gamma is the fast time dimension frequency,
Figure BDA0003336968860000036
is a fast time, tmIs a slow time;
1.2) transmitting signals in one observation time period
Figure BDA0003336968860000037
After reflection and propagation, the ISAR monostatic radar system receives the received original echo signal
Figure BDA0003336968860000038
Comprises the following steps:
Figure BDA0003336968860000041
where A is the signal amplitude, c is the speed of light, RiThe distance from any scattering point of the target to the radar;
1.3) to the original echo signal
Figure BDA0003336968860000042
The signal is processed with the line-breaking frequency modulation and the translational compensation to obtain the compensated echo signal Sif(fi,tm)：
Figure BDA0003336968860000043
Wherein R isΔ＝Ri-Rref，RrefIs the distance from the target reference point to the radar, fiIs the signal frequency, fdIs the Doppler frequency, gammadIs the doppler modulation frequency;
1.4) to the compensated Signal Sif(fi,tm) Fast time dimension Fourier transform is carried out to obtain preprocessed ISAR echo signals
Figure BDA0003336968860000044
Figure BDA0003336968860000045
And 2, constructing a three-dimensional reconstruction coordinate system X ' -Y ' -Z '.
Referring to fig. 2, the specific implementation of this step is as follows:
2.1) setting X-Y-Z as a geodetic coordinate system, using O to represent the origin of the geodetic coordinate system, and using RaRepresenting radar, C represents the center of a scattering point of an aerial target, v represents the motion speed of the radar,
Figure BDA0003336968860000046
is the position vector of the center of the scattering point in the geodetic coordinate system and is recorded as rC(tm)，
Figure BDA0003336968860000047
Is the position vector of the radar in the geodetic coordinate system and is recorded as rR(tm) Calculating a unit vector i (t) of the radar sight line directionm)：
Figure BDA0003336968860000048
Wherein, tmIs a slow time, and the time is,
Figure BDA0003336968860000049
is at tmThe position vector of the center of the scattering point is 0, | · | is an absolute value operation;
2.2) Unit vector i (t) according to the Radar Sight line directionm) Calculating tmTime 0, radar line-of-sight unit vector i (0):
Figure BDA0003336968860000051
wherein r isR(0) Is tmRadar position vector at time 0, rCRIs tmThe distance from the radar to the center of a scattering point at time 0;
2.3)unit vector i (t) according to radar sight directionm) Calculating tmUnit vector i (t) of radar sight line direction at time 0m) First derivative of
Figure BDA0003336968860000052
2.3.1) Unit vector i (t) according to Radar Sight Directionm) Calculating a unit vector i (t) of the radar sight line directionm) First derivative of
Figure BDA0003336968860000053
Figure BDA0003336968860000054
Wherein the content of the first and second substances,
Figure BDA0003336968860000055
is rR(tm) The first derivative of (a);
2.3.2) first derivative of Unit vector according to Radar Sight Direction
Figure BDA0003336968860000056
Calculating tmFirst derivative of unit vector of radar sight line direction at 0 moment
Figure BDA0003336968860000057
Figure BDA0003336968860000058
Wherein the content of the first and second substances,
Figure BDA0003336968860000059
Figure BDA00033369688600000510
is rR(tm) At tmFirst derivative at time 0;
2.4) according to radarFirst derivative of unit vector of visual line direction
Figure BDA00033369688600000511
Calculating tmUnit vector i (t) of radar sight line direction at time 0m) Second derivative of (2)
Figure BDA00033369688600000512
2.4.1) first derivative of Unit vector according to Radar Sight Direction
Figure BDA0003336968860000061
Calculating a unit vector i (t) of the radar sight line directionm) Second derivative of (2)
Figure BDA0003336968860000062
Figure BDA0003336968860000063
Wherein the content of the first and second substances,
Figure BDA0003336968860000064
is rR(tm) The second derivative of (a);
2.4.2) second derivative according to unit vector of radar sight direction
Figure BDA0003336968860000065
Calculating tmSecond derivative of unit vector of radar sight line direction at 0 moment
Figure BDA0003336968860000066
Figure BDA0003336968860000067
Wherein r isCR＞＞vtm，rCR＞＞r(tm)，
Figure BDA0003336968860000068
Is at tmAt time 0
Figure BDA0003336968860000069
2.5) according to i (t)m) At tmUnit vector i (0), first derivative of radar gaze direction at time 0
Figure BDA00033369688600000610
And second derivative
Figure BDA00033369688600000611
Obtaining an echo s (t) of a slow time dimension of a scattering pointm)：
Figure BDA0003336968860000071
Where A is the signal amplitude, r is the vector from the scattering point to the center of the scattering point, O (t)m) Is tmThe higher order terms of (1);
2.6) from the results of 2.5), the direction of the X' coordinate axis in the three-dimensional reconstructed coordinate system is obtained: n is1I (0), and is called a distance-dimensional direction vector, the direction of the Y' coordinate axis in the three-dimensional reconstructed coordinate system: n is2The vector is called as an orientation dimension direction vector because the direction of the coordinate axis Z' in the three-dimensional reconstruction coordinate system is simultaneously vertical to n1And n2Then, the direction of the coordinate axis Z' is obtained: n is3The three-dimensional reconstruction coordinate system X ' -Y ' -Z ' is obtained by referring to i (0) × v-i (0) · v · i (0) and a height dimension direction vector as follows:
Figure BDA0003336968860000072
and 3, constructing expressions of three-dimensional reconstruction coordinates x, y and z of the scattering points in a three-dimensional reconstruction coordinate system.
3.1) constructing an expression of a distance dimensional coordinate X and an orientation dimensional coordinate Y of the scattering point in the three-dimensional reconstruction coordinate system according to the three-dimensional reconstruction coordinate system X ' -Y ' -Z ':
Figure BDA0003336968860000073
where R is the vector of scattering points to the center of the scattering points, RΔThe distance of the vector from the scattering point to the center of the scattering point projected along the distance dimension direction;
3.2) using the direction vector n of the orientation dimension in the three-dimensional reconstruction coordinate system X ' -Y ' -Z ' constructed2And a height dimension direction vector n3And constructing an expression of a reconstruction coordinate z of the scattering point under a three-dimensional reconstruction coordinate system:
3.2.1) with reference to FIG. 3, with PsRepresenting scattering points in a three-dimensional reconstructed coordinate system, setting a middle direction vector
Figure BDA0003336968860000074
Constructing a vector n of scattering points in the middle direction4Expression of the projected length w:
Figure BDA0003336968860000075
wherein the content of the first and second substances,
Figure BDA0003336968860000081
is at tmPosition vector r of radar under geodetic coordinate system at 0 momentR(tm) A second derivative of;
3.2.2) constructing an expression of a reconstructed coordinate z of the scattering point under a three-dimensional reconstructed coordinate system according to the expression of w:
Figure BDA0003336968860000082
where θ is the intermediate direction vector n4And the direction vector direction n of the azimuth dimension2The included angle between them;
3.2.3) use of the results, distances of 3.2.2)Off-dimensional direction vector n1And an azimuthal dimension direction vector n2And constructing expressions of reconstruction coordinates x, y and z of the scattering point under a three-dimensional reconstruction coordinate system:
Figure BDA0003336968860000083
and 4, establishing a sparse optimization problem for solving the three-dimensional reconstruction coordinates of the target.
4.1) obtaining a slow time dimension echo signal s' (t) of a scattering point relative to the three-dimensional reconstruction coordinates according to the result of the step 3m) Expression (c):
Figure BDA0003336968860000084
where A is the signal amplitude, c is the speed of light, fcIs the carrier frequency, tmIs the slow time, v is the speed of movement of the radar, rCRIs tmThe distance from the radar to the center of the scattering point at time 0,
Figure BDA0003336968860000085
is at tmPosition vector r of radar under geodetic coordinate system at 0 momentR(tm) O (t) is a second order leadm) Is tmThe higher order terms of (1);
4.2) obtaining, from the results of 4.1), a slow-time dimensional echo signal s' (t) with respect to the scattering point of the three-dimensional reconstructed coordinatesm) Expression (c):
Figure BDA0003336968860000086
where w ═ zsin θ + ycos θ is the vector n of the scattering point in the middle direction4Y is an expression of an orientation dimensional coordinate under a three-dimensional reconstruction coordinate system, z is an expression of a height dimensional coordinate under the three-dimensional reconstruction coordinate system, and theta is an intermediate direction vector n4And the direction vector direction n of the azimuth dimension2The included angle between them;
4.3) obtaining two-dimensional echo signals of scattering points related to three-dimensional reconstruction coordinates x, y and z according to the result of 4.2)
Figure BDA0003336968860000091
Expression (c):
Figure BDA0003336968860000092
wherein the content of the first and second substances,
Figure BDA0003336968860000093
is a fast time, TpIs the pulse width, gamma is the fast time dimension frequency, gammadIs the doppler modulation frequency;
4.4) respectively setting parameter sets of a distance dimension, an azimuth dimension and a height dimension of scattering points: x is the number ofpara、ypara、zparaLet the distance dimension parameter of the scattering point be xpara＝[x1,x2,…,xp,…,xP]Τ，xpIs the P-th parameter in the distance dimension parameter set, P is the number of parameters in the distance dimension parameter set, ypara＝[y1,y2,…,yq,…,yQ]ΤIs a set of azimuthal parameters of the scattering points, yqIs the Q parameter in the orientation dimension parameter set, Q is the number of the parameters in the orientation dimension parameter set, zpara＝[z1,z2,…,zr,…,zR]ΤIs a set of height-dimensional parameters of the scattering point, zrIs the R-th parameter in the height dimension parameter set, and R is the number of the parameters in the height dimension parameter set;
4.5) two-dimensional echo signals from scattering points with respect to three-dimensional reconstruction coordinates x, y, z
Figure BDA0003336968860000094
And a set of scattering point parameters, computing dictionary atoms
Figure BDA0003336968860000095
Figure BDA0003336968860000096
Wherein the content of the first and second substances,
Figure BDA0003336968860000097
||·||2is represented by2A norm;
4.6) according to dictionary atoms
Figure BDA0003336968860000101
Establishing a parameterized redundant dictionary a (α):
Figure BDA0003336968860000102
wherein α ═ α1，α2,…,αi,…,αN]Where N is the number of dictionary atoms, αi＝[xp,yq,zr]TIs the ith parameter vector in the parameterized redundant dictionary;
4.7) setting constraint conditions according to the parameterized redundant dictionary A (alpha):
Figure BDA0003336968860000103
wherein | · | purple sweet2Is represented by2The norm of the number of the first-order-of-arrival,
Figure BDA0003336968860000104
for the preprocessed echo signal, namely an observation signal, eta is the amplitude of the estimated signal, and epsilon is the residual error of the signal;
4.8) establishing a sparse optimization problem according to the parameterized redundant dictionary A (alpha) and constraint conditions:
Figure BDA0003336968860000105
wherein argmax (·) represents taking function argument maximum value operation, | | | · | | | represents vector modulo operation,
Figure BDA0003336968860000106
are the target three-dimensional reconstruction coordinates.
And 5, solving the sparse optimization problem to obtain a target three-dimensional reconstruction coordinate.
The prior art for solving the sparse optimization problem includes MP algorithm, CoSaMP algorithm and OMP algorithm, but the present embodiment uses, but is not limited to, OMP algorithm, and the specific implementation steps thereof are as follows:
5.1) inputting an observation signal s and a threshold epsilon, and taking the number M of scattering points as iteration times;
5.2) setting the initial residual signal res to s, the iteration count k to 1, the target three-dimensional reconstruction parameter set
Figure BDA0003336968860000107
5.3) calculating a correlation matrix P (α) from the parameterized redundant dictionary A (α) in the form of AΗ(α) xres, wherein (·)ΗRepresents a conjugate transpose;
5.4) obtaining a target three-dimensional reconstruction parameter according to the correlation matrix P (alpha):
Figure BDA0003336968860000108
5.5) updating the target three-dimensional reconstruction parameter set:
Figure BDA0003336968860000109
5.6) calculating the amplitude of the residual signal by means of the least-squares method
Figure BDA00033369688600001010
5.7) mixing
Figure BDA00033369688600001011
Comparison with a threshold epsilon, k with the number of iterations M:
if it is
Figure BDA0003336968860000111
Or k < M, the residual signal is updated:
Figure BDA0003336968860000112
let k be k +1, return 5.3);
if it is
Figure BDA0003336968860000113
And k is more than or equal to M, the iteration is stopped to obtain a target three-dimensional reconstruction parameter set
Figure BDA0003336968860000114
Wherein the content of the first and second substances,
Figure BDA0003336968860000115
m is the number of scattering points,
Figure BDA0003336968860000116
and
Figure BDA0003336968860000117
solving a sparse optimization problem to obtain a three-dimensional reconstruction coordinate of a kth scattering point;
5.8) reconstructing the parameter set according to the target three-dimensional
Figure BDA0003336968860000118
And obtaining a three-dimensional reconstruction image.
The effect of the invention can be further illustrated by the following simulation experiment:
simulation parameter
Setting three-dimensional reconstruction simulation parameters of the aerial target as shown in table 1:
the simulation software used MATLAB R2017a,
TABLE 1 simulation parameters for three-dimensional reconstruction of aerial targets
Figure BDA0003336968860000119
Second, simulation content
The invention simulates three-dimensional imaging of the ISAR radar to the air target under the parameters. The results are shown in FIG. 4.
In fig. 4, the abscissa is a distance dimension coordinate in the three-dimensional reconstruction coordinate system, the ordinate is an orientation dimension coordinate in the three-dimensional reconstruction coordinate system, and the ordinate is a height dimension coordinate in the three-dimensional reconstruction coordinate system. The scattering points in the graph 4 are the scattering points of the target, and as can be seen from the graph 4, the sparse optimization problem of the three-dimensional reconstruction coordinates is established by establishing the dictionary atoms related to the three-dimensional reconstruction coordinates of the target scattering points, the target three-dimensional coordinates can be jointly solved, the problem that the hardware and imaging complexity of the traditional radar three-dimensional imaging algorithm are high is effectively solved, the imaging application range is expanded, ISAR three-dimensional images with clear distance direction, direction and height direction are obtained, and the high resolution of the three-dimensional imaging is realized.
The foregoing description is only an example of the present invention and is not intended to limit the invention, so that it will be apparent to those skilled in the art that various changes and modifications in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims (6)

1. A three-dimensional imaging method of a moving target for vector modeling optimization inversion is characterized by comprising the following steps:
(1) sequentially carrying out line-breaking frequency modulation, translation compensation and fast time dimension Fourier transform on echo signals received by the ISAR single-base radar system in one observation time period to obtain preprocessed ISAR echoes;
(2) constructing a three-dimensional reconstruction coordinate system X ' -Y ' -Z ' by using the self motion parameters of the radar;
(3) and constructing expressions of three-dimensional reconstruction coordinates X, Y and Z of the target scattering point in the three-dimensional reconstruction coordinate system by using the constructed three-dimensional reconstruction coordinate system X ' -Y ' -Z ':
Figure FDA0003336968850000011
where r is the vector of scattering points to the center of the scattering points, i (0) is tm0 time point, tmIs slow time, RΔIs the projection distance of the vector from the scattering point of the target to the center of the scattering point along the distance dimension direction, v is the motion speed of the radar, and w is the vector n of the scattering point of the target in the middle direction4Is projected length of (a), theta is a middle direction vector n4And the direction vector direction n of the azimuth dimension2The included angle between them;
(4) establishing a sparse optimization problem for solving a target three-dimensional reconstruction coordinate by using the preprocessed ISAR echo and the expression of the three-dimensional reconstruction coordinates x, y and z:
Figure FDA0003336968850000012
wherein argmax (·) represents taking function independent variable maximum operation, | | | · | | | represents vector modulo operation, | | · | | | | survival2Is represented by2Norm, s is the preprocessed echo signal, a (α) is a parameterized redundant dictionary, α is a set of dictionary atoms, [ α ═ α [ [ α ]1，α2,…,αi,…,αN]N is the number of dictionary atoms, alphai＝[xp,yq,zr]TIs the ith parameter vector, x, in the parameterized redundant dictionarypIs the p-th parameter, y, in the set of distance-dimensional parametersqIs the q parameter, z, of the set of orientation-dimensional parameters of the scattering pointrIs the r-th parameter in the height dimension parameter set,
Figure FDA0003336968850000021
is the target three-dimensional reconstruction coordinate, eta is the estimated signal amplitude, and epsilon is the signal residual error;
(5) solving rarity by adopting orthogonal matching pursuit OMP algorithmObtaining a three-dimensional reconstruction coordinate vector of the target by sparse optimization
Figure FDA0003336968850000022
Performing three-dimensional reconstruction of ISAR target, wherein
Figure FDA0003336968850000023
Is the three-dimensional reconstructed coordinate vector of the kth scattering point of the object,
Figure FDA0003336968850000024
m is the number of scattering points of the target, (. C)TIs a transposition operation in which the phase of the input signal is inverted,
Figure FDA0003336968850000025
and
Figure FDA0003336968850000026
is the three-dimensional reconstructed coordinates of the k-th scattering point.
2. The method of claim 1, wherein: (1) the echo signal is sequentially subjected to line-demodulating and frequency modulation, translation compensation and fast time dimension Fourier transform, and the realization formula is as follows:
(1a) the original signal is processed by de-line frequency modulation and translational compensation according to the following formula:
Figure FDA0003336968850000027
wherein S isif(fi,tm) For the echo signal after the demodulation and the translational compensation, RΔ＝Ri-Rref，RiIs the distance, R, from any scattering point of the target to the radarrefIs the distance from the target reference point to the radar, A is the signal amplitude, TpIs the pulse width, fiIs the signal distance dimension frequency, gamma is the fast time dimension frequency, fdIs the Doppler frequency, gammadIs the Doppler frequency modulation rateC is the speed of light, fcIs the carrier frequency, tmIs a slow time;
(1b) echo signal S after line-breaking frequency modulation and translational compensation processingif(fi,tm) Fast time dimension Fourier transform is carried out to obtain preprocessed ISAR echo signals
Figure FDA0003336968850000028
Figure FDA0003336968850000029
Wherein the content of the first and second substances,
Figure FDA00033369688500000210
is a fast time.
3. The method of claim 1, wherein: (2) the three-dimensional reconstruction coordinate system X ' -Y ' -Z ' is constructed as follows:
(2a) calculating a unit vector i (t) of the radar sight line directionm) Wherein, tmIs a slow time;
(2b) unit vector i (t) according to radar sight directionm) Calculating tmA radar sight line direction unit vector i (0) at time 0;
(2c) unit vector i (t) according to radar sight directionm) Calculating a unit vector i (t) of the radar sight line directionm) First derivative of
Figure FDA0003336968850000031
(2d) First derivative of unit vector according to radar sight direction
Figure FDA0003336968850000032
Calculating tmFirst derivative of unit vector of radar sight line direction at 0 moment
Figure FDA0003336968850000033
(2e) First derivative of unit vector according to radar sight direction
Figure FDA0003336968850000034
Calculating a unit vector i (t) of the radar sight line directionm) Second derivative of (2)
Figure FDA0003336968850000035
(2f) Second derivative of unit vector according to radar sight direction
Figure FDA0003336968850000036
Calculating tmSecond derivative of unit vector of radar sight line direction at 0 moment
Figure FDA0003336968850000037
(2g) According to at tmUnit vector i (0), first derivative of radar gaze direction at time 0
Figure FDA0003336968850000038
And second derivative
Figure FDA0003336968850000039
Obtaining an echo s (t) of a slow time dimension of a scattering pointm)：
Figure FDA00033369688500000310
Wherein A is signal amplitude, r is a vector from any scattering point to the center of the scattering point, v is the motion speed of the radar, and rCRIs tmThe distance from the radar to the center of the scattering point at time 0,
Figure FDA00033369688500000311
is at tmPosition of radar under geodetic coordinate system at time 0Vector rR(tm) O (t) is a second order leadm) Is tmThe higher order terms of (1);
(2h) the directions of the three-dimensional reconstruction coordinate system X ' -Y ' -Z ' obtained according to (2g) are:
Figure FDA00033369688500000312
wherein n is1Is the direction of X' coordinate axis in the three-dimensional reconstruction coordinate system, namely the distance dimension direction vector; n is2Is the direction of the Y' coordinate axis in the three-dimensional reconstruction coordinate system, namely the direction vector of the orientation dimension; n is3The direction of the coordinate axis Z' in the three-dimensional reconstruction coordinate system is the vector of the height dimension.
4. The method of claim 1, wherein: (3) the three-dimensional reconstruction coordinate system X ' -Y ' -Z ' is utilized to construct the expressions of the three-dimensional reconstruction coordinates X, Y and Z of the scattering point under the three-dimensional reconstruction coordinate system, and the following are realized:
(3a) according to the three-dimensional reconstruction coordinate system X ' -Y ' -Z ', constructing an expression of a distance dimensional coordinate X and an orientation dimensional coordinate Y of the scattering point in the three-dimensional reconstruction coordinate system:
Figure FDA0003336968850000041
wherein R isΔThe distance of the vector from the scattering point to the center of the scattering point projected along the distance dimension direction;
(3b) is provided with
Figure FDA0003336968850000042
For the intermediate direction vector, a vector n of scattering points in the intermediate direction is constructed4Expression of the projected length w:
Figure FDA0003336968850000043
wherein the content of the first and second substances,
Figure FDA0003336968850000044
is at tmPosition vector r of radar under geodetic coordinate system at 0 momentR(tm) A second derivative of;
(3c) vector n in the middle direction according to the scattering point4And (3) constructing an expression of a height dimension coordinate z of the scattering point in a three-dimensional reconstruction coordinate system by using the expression of the projection length w:
Figure FDA0003336968850000045
where θ is the intermediate direction vector n4And the direction vector direction n of the azimuth dimension2The included angle therebetween.
5. The method of claim 1, wherein: (4) the sparse optimization problem of constructing and solving a target three-dimensional reconstruction coordinate is established, and the following is realized:
(4a) constructing a scattering point slow time dimension echo signal s' (t) related to three-dimensional reconstruction coordinates by using expressions of the three-dimensional reconstruction coordinates x, y and zm) Expression (c):
Figure FDA0003336968850000051
where A is the signal amplitude, c is the speed of light, fcIs the carrier frequency, tmIs the slow time, v is the speed of movement of the radar, rCRIs tmThe distance from the radar to the center of the scattering point at time 0,
Figure FDA0003336968850000052
is at tmPosition vector r of radar under geodetic coordinate system at 0 momentR(tm) O (t) is a second order leadm) Is tmThe higher order terms of (1);
(4b) from the result of (4a), a slow time dimension echo signal s' (t) with respect to the scattering point of the three-dimensional reconstruction coordinates is constructedm) Expression (c):
Figure FDA0003336968850000053
where w is zsin θ + ycos θ, and w is the vector n of scattering points in the middle direction4Y is an expression of an orientation dimensional coordinate under a three-dimensional reconstruction coordinate system, z is an expression of a height dimensional coordinate under the three-dimensional reconstruction coordinate system, and theta is an intermediate direction vector n4And the direction vector direction n of the azimuth dimension2The included angle between them;
(4c) obtaining two-dimensional echo signals of scattering points related to three-dimensional reconstruction coordinates x, y and z according to the result of (4b)
Figure FDA0003336968850000054
Expression (c):
Figure FDA0003336968850000055
wherein the content of the first and second substances,
Figure FDA0003336968850000056
is a fast time, TpIs the pulse width, gamma is the fast time dimension frequency, gammadIs the doppler modulation frequency;
(4d) from two-dimensional echo signals of scattering points with respect to three-dimensional reconstruction coordinates x, y, z
Figure FDA0003336968850000061
To construct dictionary atoms
Figure FDA0003336968850000062
Figure FDA0003336968850000063
Wherein the content of the first and second substances,
Figure FDA0003336968850000064
xpis the distance dimension parameter set x ═ x1,x2,…,xp,…,xP]ΤP is the number of parameters in the distance dimension parameter set, yqIs the set of orientation-dimensional parameters of the scattering points y ═ y1,y2,…,yq,…,yQ]ΤThe Q parameter in (1), Q is the number of parameters in the orientation dimension parameter set, zrIs the height dimension parameter set z ═ z1,z2,…,zr,…,zR]ΤThe middle-R parameter, R is the number of parameters in the height dimension parameter set, | | · | | survival2Is represented by2A norm;
(4e) according to dictionary atoms
Figure FDA0003336968850000065
Establishing a parameterized redundant dictionary a (α):
Figure FDA0003336968850000066
where α is a dictionary atom set, α ═ α1，α2,…,αi,…,αN]Where N is the number of dictionary atoms, αi＝[xp,yq,zr]TIs the ith parameter vector in the parameterized redundant dictionary;
(4f) according to the parameterized redundant dictionary A (alpha), constraint conditions are set:
Figure FDA0003336968850000067
wherein | · | purple sweet2Is represented by2The norm of the number of the first-order-of-arrival,
Figure FDA0003336968850000068
for the preprocessed echo signal, eta is the estimated signal amplitude, and epsilon is the signal residual error;
(4g) establishing a sparse optimization problem according to a parameterized redundant dictionary A (alpha) and constraint conditions:
Figure FDA0003336968850000069
wherein argmax (·) represents taking function argument maximum value operation, | | | · | | | represents vector modulo operation,
Figure FDA0003336968850000071
are the target three-dimensional reconstruction coordinates.
6. The method of claim 1, wherein: (5) the sparse optimization problem is solved by adopting an orthogonal matching pursuit OMP algorithm to obtain the three-dimensional reconstruction coordinates of the target, and the method is realized as follows:
(5a) inputting an ISAR echo signal s and a signal residual error epsilon, and setting the number M of scattering points as iteration times;
(5b) setting an initial residual signal res as s, an initial iteration count k as 1, and a target three-dimensional reconstruction parameter set
Figure FDA0003336968850000072
(5c) Calculating a correlation matrix P (alpha) A from the parameterized redundant dictionary A (alpha)Η(α) xres, wherein (·)ΗRepresents a conjugate transpose;
(5d) obtaining a target three-dimensional reconstruction parameter according to the correlation matrix P (alpha):
Figure FDA0003336968850000073
(5e) updating the target three-dimensional reconstruction parameter set:
Figure FDA0003336968850000074
(5f) calculating the amplitude of the residual signal by least squares
Figure FDA0003336968850000075
(5g) Will be provided with
Figure FDA0003336968850000076
Comparing with the signal residual error epsilon, and comparing k with the iteration number M:
if it is
Figure FDA0003336968850000077
Or k < M, the residual signal is updated:
Figure FDA0003336968850000078
let k be k +1, return (5 c);
if it is
Figure FDA0003336968850000079
And k is more than or equal to M, the iteration is stopped to obtain a target three-dimensional reconstruction parameter set
Figure FDA00033369688500000710
Wherein the content of the first and second substances,
Figure FDA00033369688500000711
m is the number of scattering points,
Figure FDA00033369688500000712
and
Figure FDA00033369688500000713
solving a sparse optimization problem to obtain a three-dimensional reconstruction coordinate of a kth scattering point;
(5h) three-dimensional reconstruction of parameter sets from a target
Figure FDA00033369688500000714
And obtaining a three-dimensional reconstruction image.
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