CN114740471A - Array radar foresight imaging method and device based on echo signal completion - Google Patents

Array radar foresight imaging method and device based on echo signal completion Download PDF

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CN114740471A
CN114740471A CN202210295957.8A CN202210295957A CN114740471A CN 114740471 A CN114740471 A CN 114740471A CN 202210295957 A CN202210295957 A CN 202210295957A CN 114740471 A CN114740471 A CN 114740471A
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array
radar
echo
sparse
target
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程永强
曹凯程
刘清萍
刘康
王宏强
刘红彦
黎湘
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National University of Defense Technology
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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 relates to the technical field of radar imaging, and discloses an array radar foresight imaging method and device based on echo signal completion, wherein a sparse array radar imaging system is constructed, and sparse radar arrays are randomly distributed in an array plane of the sparse array radar imaging system; acquiring a target echo and judging whether the target echo is the echo of a sparse uniform radar array, if not, performing three-dimensional fast Fourier transform on the target echo in the sparse array radar imaging system to obtain a target image; if so, completing the target echo by adopting a matrix completing method; carrying out high-resolution solution on the target in each distance unit in the echo signal by using a continuous domain compressed sensing recovery algorithm; and constructing imaging according to the solving result and outputting a target image.

Description

Array radar forward-looking imaging method and device based on echo signal completion
Technical Field
The application relates to the technical field of radar imaging, in particular to a forward-looking imaging method and device of an array radar based on echo signal completion.
Background
The radar high-resolution imaging technology is a remote sensing detection means with wide application, and plays an important role in the aspects of geographical observation, environmental monitoring, safety warning and the like. The range-wise resolution of radar imaging depends on the signal bandwidth, and the azimuth-wise resolution depends on the antenna aperture. The traditional high-resolution imaging radar relies on a synthetic aperture to realize azimuth high-resolution imaging, and the relative motion of the radar and a target is a necessary condition for forming the synthetic aperture. However, in a front-view observation imaging scene, the radar and the target do not rotate relatively, so that the synthetic aperture required by the traditional high-resolution imaging radar cannot be formed, and the imaging quality is difficult to ensure.
Unlike a side-view imaging mode based on a synthetic aperture, the real-aperture array radar can directly image a target under a forward-view observation scene, and the azimuth resolution of the real-aperture array radar depends on the size of an array aperture, and more specifically, depends on the rayleigh diffraction limit corresponding to an equiphase center of an antenna array. The real aperture array radar can image the target through a back projection algorithm, and the method is not limited by the shape of an antenna array and has great flexibility in application. However, this method has the disadvantages of large computation and long time consumption, which greatly limits the imaging efficiency of the real aperture array radar.
By designing a uniform real aperture array and performing far field approximation on electromagnetic waves, the real aperture array radar can perform fast imaging by using a fast Fourier transform method. The imaging quality of the real aperture array imaging method using the fast fourier transform depends on the main lobe width and the side lobe height of the imaging result, and more specifically, depends on the array aperture and the array element spacing. On the one hand, however, it is not possible to increase the radar array aperture indefinitely in practical applications; on the other hand, when the array aperture is fixed, a smaller array element spacing means a larger number of array elements, which greatly increases the complexity of the system, and a larger array element spacing causes higher side lobes and periodic aliasing of the imaging target in the azimuth direction.
Therefore, how to reduce the complexity of the system while obtaining resolution comparable to that of the uniform array radar becomes an urgent technical problem to be solved.
The above is only for the purpose of assisting understanding of the technical aspects of the present invention, and does not represent an admission that the above is prior art.
Disclosure of Invention
The invention mainly aims to provide a forward-looking imaging method and a forward-looking imaging device for an array radar based on echo signal completion, and aims to solve the technical problem that the prior art cannot obtain resolution equivalent to that of a uniform array radar and simultaneously reduce the complexity of a system.
In order to achieve the above object, the present invention provides an array radar forward-looking imaging method based on echo signal completion, the method comprising:
constructing a sparse array radar imaging system, wherein sparse radar arrays are randomly distributed in an array plane of the sparse array radar imaging system;
acquiring a target echo and judging whether the target echo is the echo of a sparse uniform radar array, if not, performing three-dimensional fast Fourier transform on the target echo in the sparse array radar imaging system to obtain a target image;
if so, completing the target echo by adopting a matrix completing method;
carrying out high resolution solution on the target in each distance unit in the echo signal by using a continuous domain compressed sensing recovery algorithm;
and constructing imaging according to the solving result and outputting a target image.
Optionally, the step of constructing a sparse array radar imaging system, in which sparse radar arrays are randomly distributed in an array plane of the sparse array radar imaging system, includes:
constructing a sparse array radar imaging system, wherein an array plane of the radar imaging system comprises M columns and N rows of receiving and transmitting array element positions, the sparse radar array is randomly distributed in the array plane, and a position vector of each receiving and transmitting array element can be expressed as
Figure BDA0003563314340000021
The position vector of the scattering point of the object can be expressed as
Figure BDA0003563314340000022
Optionally, the acquiring a target echo and determining whether the target echo is an echo of a sparse uniform radar array, and if not, performing three-dimensional fast fourier transform on the target echo in the sparse array radar imaging system to obtain a target image includes:
acquiring a target echo, and judging whether the target echo is an echo of a sparse uniform radar array;
if not, deducing the echo of the sparse uniform radar array to be located at (x)m,0,zn) The target echo received by the array element is written as:
Figure BDA0003563314340000031
where o (-) is the scattering distribution function of the target,
Figure BDA0003563314340000032
is a space wave number vector;
and carrying out three-dimensional fast Fourier transform on the target echo to obtain a target image.
Optionally, the step of performing a three-dimensional fast fourier transform on the target echo to obtain a target image includes:
approximating the target echo based on far field conditions yields:
Figure BDA0003563314340000033
wherein k is0＝2π/λ0Denotes the central wave number, λ0Wavelength, s, corresponding to the center frequencycTo relate toA separation variable k, xmAnd znA function of (a);
for the three separation variables k, xmAnd znPerforming three-dimensional fast Fourier transform to obtain a target image, namely:
Figure BDA0003563314340000034
optionally, if so, a step of completing the target echo by using a matrix completing method includes:
completing the sparse radar array signal by adopting a matrix completion method, and setting Sp∈Sc N×MFor echo signals scThe p-th slice after range-wise pulse compression, i.e.
Figure BDA0003563314340000035
Definition of S'p＝Sp(omega) is a corresponding signal of the sparse radar array, omega is a sparse array element position index, and the problem of block Hankel matrix completion in the presence of noise can be written as follows:
Figure BDA0003563314340000036
wherein | · | purple*Is a kernel norm of the matrix, | | · | | non-calculationFIs the Frobenius norm,
Figure BDA0003563314340000037
under-sampler for reference omega, YEFor signals S passing through a uniform radar arraypConstructed block Hankel matrix, XEIs signal S 'through a sparse radar array'pConstructing a block Hankel matrix;
for the block Hankel matrix YEAnd Hankel matrix YnSolving is carried out by solving for each YnRadar array signal with complementary mean values of anti-angle elements of matrixNumber (n).
Optionally, before the step of performing high-resolution solution on the target in each range unit in the echo signal by using a continuous domain compressed sensing recovery algorithm, the method further includes:
the pair of echo signals scThe formula for doing the distance-wise pulse-compressed p-th slice can be written as:
Figure BDA0003563314340000041
wherein
Figure BDA0003563314340000042
o (l) is the scattering coefficient of the first scattering point of the object,
Figure BDA0003563314340000043
is composed of
Figure BDA0003563314340000044
In matrix form, then the observation matrix can be written as:
Y＝Sp+W
wherein W is observation noise;
solving for SpThe regularized objective function of (a) is written as:
Figure BDA0003563314340000045
optionally, the step of performing high resolution solution on the target in each range unit in the echo signal by using a continuous domain compressive sensing recovery algorithm includes:
for the SpThe regularized objective function of (a) is solved by the following semi-positive problem:
Figure BDA0003563314340000046
the position of the scattering point passes through the pair of echo signals scSolving a formula of a p slice after the distance pulse compression:
Figure BDA0003563314340000047
coefficient passing
Figure BDA0003563314340000048
And (6) calculating.
In addition, in order to achieve the above object, the present invention further provides an array radar forward-looking imaging device based on echo signal completion, where the device includes:
the system construction module is used for constructing a sparse array radar imaging system, and sparse radar arrays are randomly distributed in an array plane of the sparse array radar imaging system;
the non-sparse derivation module is used for acquiring a target echo and judging whether the target echo is the echo of a sparse uniform radar array, if not, the target echo is subjected to three-dimensional fast Fourier transform in the sparse array radar imaging system to obtain a target image;
the matrix completion module is used for completing the target echo by adopting a matrix completion method if the target echo exists;
the compressed sensing module is used for carrying out high-resolution solution on the target in each distance unit in the echo signal by utilizing a continuous domain compressed sensing recovery algorithm;
and the output module is used for constructing imaging according to the solving result and outputting the target image.
In addition, to achieve the above object, the present invention further provides an array radar forward-looking imaging apparatus based on echo signal completion, the apparatus including: a memory, a processor and an echo signal completion based array radar forward looking imaging program stored on the memory and operable on the processor, the echo signal completion based array radar forward looking imaging program configured to implement the steps of the echo signal completion based array radar forward looking imaging method as described above
In addition, to achieve the above object, the present invention further provides a medium, on which an array radar foresight imaging program based on echo signal completion is stored, and when being executed by a processor, the array radar foresight imaging program based on echo signal completion realizes the steps of the array radar foresight imaging method based on echo signal completion as described above.
According to the method, a sparse array radar imaging system is constructed, and sparse radar arrays are randomly distributed in an array plane of the sparse array radar imaging system; acquiring a target echo and judging whether the target echo is the echo of a sparse uniform radar array, if not, performing three-dimensional fast Fourier transform on the target echo in the sparse array radar imaging system to obtain a target image; if so, completing the target echo by adopting a matrix completing method; carrying out high resolution solution on the target in each distance unit in the echo signal by using a continuous domain compressed sensing recovery algorithm; the imaging is constructed according to the solving result, a target image is output, signals of the sparse array radar are complemented in a matrix complementing mode, the resolution capacity equivalent to that of the uniform array radar is obtained, the complexity of the system is greatly reduced, meanwhile, the imaging target is solved and reconstructed through a two-dimensional atomic norm minimization method, the two-dimensional atomic norm minimization method can be used for solving to obtain an accurate main lobe peak value, the main lobe is theoretically infinite and narrow, the height of side lobes can be greatly reduced, the imaging quality is improved, and the problem that the front imaging quality of the array radar is limited is effectively solved.
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Fig. 1 is a schematic structural diagram of an array radar forward-looking imaging device based on echo signal completion in a hardware operating environment according to an embodiment of the present invention;
FIG. 2 is a schematic flowchart of a forward-looking imaging method of an array radar based on echo signal completion according to a first embodiment of the present invention;
FIG. 3 is a forward-looking imaging scene diagram of an array radar based on continuous domain compressed sensing according to a first embodiment of the forward-looking imaging method of the array radar based on echo signal completion of the invention;
FIG. 4 is a schematic diagram of a uniform array and a sparse array according to a first embodiment of a radar array forward-looking imaging method based on echo signal completion according to the present invention;
fig. 5 shows imaging results of the method, the sparse array echo three-dimensional fast fourier transform and the complementary array echo three-dimensional fast fourier transform according to the first embodiment of the echo signal complementary based array radar forward-looking imaging method.
Detailed Description
It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, fig. 1 is a schematic structural diagram of an array radar forward-looking imaging device based on echo signal completion in a hardware operating environment according to an embodiment of the present invention.
As shown in fig. 1, the array radar forward-looking imaging device based on echo signal completion may include: a processor 1001, such as a Central Processing Unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. The communication bus 1002 is used to implement connection communication among these components. The user interface 1003 may include a Display screen (Display), an input unit such as a Keyboard (Keyboard), and the optional user interface 1003 may also include a standard wired interface, a wireless interface. The network interface 1004 may optionally include a standard wired interface, a Wireless interface (e.g., a Wireless-Fidelity (WI-FI) interface). The Memory 1005 may be a Random Access Memory (RAM) Memory, or a Non-Volatile Memory (NVM), such as a disk Memory. The memory 1005 may alternatively be a storage device separate from the processor 1001.
Those skilled in the art will appreciate that the configuration shown in fig. 1 does not constitute a limitation of an array radar forward-looking imaging apparatus based on echo signal completion, and may include more or fewer components than those shown, or some components in combination, or a different arrangement of components.
As shown in fig. 1, a memory 1005, which is a storage medium, may include therein an operating system, a data storage module, a network communication module, a user interface module, and an array radar forward-looking imaging program based on echo signal completion.
In the array radar forward-looking imaging device based on echo signal completion shown in fig. 1, the network interface 1004 is mainly used for data communication with a network server; the user interface 1003 is mainly used for data interaction with a user; the processor 1001 and the memory 1005 of the array radar forward-looking imaging device based on echo signal completion can be arranged in the array radar forward-looking imaging device based on echo signal completion, and the array radar forward-looking imaging device based on echo signal completion calls an array radar forward-looking imaging program based on echo signal completion stored in the memory 1005 through the processor 1001 and executes the array radar forward-looking imaging method based on echo signal completion provided by the embodiment of the invention.
The embodiment of the invention provides an array radar forward-looking imaging method based on echo signal completion, and referring to fig. 2, fig. 2 is a schematic flow chart of a first embodiment of the array radar forward-looking imaging method based on echo signal completion.
In this embodiment, the array radar forward-looking imaging method based on echo signal completion includes the following steps:
step S10: constructing a sparse array radar imaging system, wherein sparse radar arrays are randomly distributed in an array plane of the sparse array radar imaging system.
It should be noted that, referring to fig. 3, it is assumed that the array plane of the radar imaging system includes M columns of N rows of positions of the transmit-receive array elements, the sparse radar array is randomly distributed in the array plane, and the position vector of each transmit-receive array element can be represented as
Figure BDA0003563314340000071
The position vector of the scattering point of the object can be expressed as
Figure BDA0003563314340000072
Further, the sparse array radar imaging system is constructed, and the sparse radar arrays are randomly distributed in the sparse array radar imagingA step in the array plane of the system comprising: constructing a sparse array radar imaging system, wherein an array plane of the radar imaging system comprises M columns and N rows of receiving and transmitting array element positions, the sparse radar array is randomly distributed in the array plane, and a position vector of each receiving and transmitting array element can be expressed as
Figure BDA0003563314340000081
The position vector of the scattering point of the object can be expressed as
Figure BDA0003563314340000082
Step S20: and acquiring a target echo and judging whether the target echo is the echo of the sparse uniform radar array, if not, performing three-dimensional fast Fourier transform on the target echo in the sparse array radar imaging system to obtain a target image.
In a specific implementation, target echoes are acquired. Echoes of a non-sparse uniform radar array are first derived. Neglecting amplitude attenuation in signal propagation, then lie in (x)m,0,zn) The target echo received by the array element can be written as:
Figure BDA0003563314340000083
where o (-) is the scattering distribution function of the target,
Figure BDA0003563314340000084
is a spatial wavenumber vector. Is located at (0, y)0A reference signal with amplitude 1 at 0) can be written as
Figure BDA0003563314340000085
The echo signal after correcting for the reference distance can be written as
Figure BDA0003563314340000086
Wherein y'1＝y′-y0And is provided with
Figure BDA0003563314340000087
The above formula is based on plane wave approximation under far field conditions, i.e. satisfying y0＞＞xm,znX, z. k 2 pi/λ is the spatial wavenumber and λ is the wavelength. Bringing formula (4) into formula (3) gives:
Figure BDA0003563314340000088
wherein k is0＝2π/λ0Denotes the central wave number, λ0The wavelength corresponding to the center frequency. In the formula (5), scAbout three separate variables k, xmAnd znThe function of (a), therefore, three-dimensional fast fourier transform can be performed on three variables to obtain a target image, namely:
Figure BDA0003563314340000091
however, equation (6) is derived based on a non-sparse uniform radar array. When the radar array is sparse, equation (6) cannot be directly applied.
Further, the step of acquiring a target echo and judging whether the target echo is an echo of a sparse uniform radar array, and if not, performing three-dimensional fast fourier transform on the target echo in the sparse array radar imaging system to obtain a target image includes: acquiring a target echo, and judging whether the target echo is an echo of a sparse uniform radar array; if not, deducing the echo of the sparse uniform radar array to be located at (x)m,0,zn) The target echo received by the array element is written as:
Figure BDA0003563314340000092
where o (-) is the scattering distribution function of the target,
Figure BDA0003563314340000093
is a space wave number vector; and carrying out three-dimensional fast Fourier transform on the target echo to obtain a target image.
Further, the step of performing three-dimensional fast fourier transform on the target echo to obtain a target image includes:
approximating the target echo based on far field conditions yields:
Figure BDA0003563314340000094
wherein k is0＝2π/λ0Denotes the central wave number, λ0Wavelength, s, corresponding to the center frequencycAbout three separate variables k, xmAnd znA function of (a); for the three separation variables k, xmAnd znPerforming three-dimensional fast Fourier transform to obtain a target image, namely:
Figure BDA0003563314340000095
step S30: and if so, completing the target echo by adopting a matrix completing method.
In a specific implementation, the sparse radar array echo signal is completed. Based on the Toeplitz matrix characteristic and the Hankel matrix characteristic of the uniform array echo signal, a matrix completion method can be adopted to complete the sparse radar array signal. Let Sp∈sc N×MFor echo signals scThe p-th slice after range-wise pulse compression, i.e.
Figure BDA0003563314340000101
Referring to FIG. 4, S 'is defined'p＝SpAnd (omega) is a corresponding signal of the sparse radar array, and omega is a sparse array element position index. Then S'pCan be regarded as SpAccording to the result of the undersampling of omega, the missing array elements can be recovered by solving a relaxation kernel norm optimization problem. The block Hankel matrix completion problem in the presence of noise can be written as:
Figure BDA0003563314340000102
wherein | · | purple*Is the kernel norm of the matrix, | ·| luminanceFIs the Frobenius norm,
Figure BDA0003563314340000103
under-sampler for reference omega, YEFor signals S passing through a uniform radar arraypConstructed block Hankel matrix, XEIs signal S 'through a sparse radar array'pAnd constructing a block Hankel matrix. The form of the block Hankel matrix can be written as:
Figure BDA0003563314340000104
wherein Y isnIs a Hankel matrix which is formed by signals corresponding to the n-th row radar array, i.e.
Figure BDA0003563314340000105
Solving a block Hankel matrix YEAnd Hankel matrix YnThe completed radar array signal can then be passed through each YnThe mean of the anti-angle elements of the matrix is obtained. By the method, the sparse radar array echo signals can be completed.
Further, if yes, a matrix completion method is adopted to complete the target echo, and the method includes: method for carrying out matrix completion on sparse radar array signalNumber is complemented, S is setp∈Sc N×MFor echo signals scThe p slice after range-wise pulse compression, i.e.
Figure BDA0003563314340000106
Definition of S'p＝Sp(omega) is a corresponding signal of the sparse radar array, omega is a sparse array element position index, and the problem of block Hankel matrix completion in the presence of noise can be written as follows:
Figure BDA0003563314340000111
wherein | · | charging*Is the kernel norm of the matrix, | ·| luminanceFIs the Frobenius norm,
Figure BDA0003563314340000112
under-sampler for reference omega, YEFor signals S passing through a uniform radar arraypConstructed block Hankel matrix, XEIs signal S 'through a sparse radar array'pConstructing a block Hankel matrix; for the block Hankel matrix YEAnd Hankel matrix YnSolving is carried out by solving for each YnThe mean of the anti-angle elements of the matrix yields the completed radar array signal.
Step S40: and carrying out high-resolution solution on the target in each distance unit in the echo signal by using a continuous domain compressed sensing recovery algorithm.
In a specific implementation, each range cell is solved in a two-dimensional high-resolution manner. Equation (7) can be written in discrete form:
Figure BDA0003563314340000113
wherein
Figure BDA0003563314340000114
The matrix form of formula (11) can be written as
Figure BDA0003563314340000115
Wherein
Figure BDA0003563314340000116
o (l) is the scattering coefficient of the first scattering point of the object,
Figure BDA0003563314340000117
is composed of
Figure BDA0003563314340000118
In the form of a matrix, and
Figure BDA0003563314340000119
then the observation matrix can be written as
Y＝Sp+W (15)
Where W is the observation noise. The atomic norm minimization method is a continuous domain compressed sensing recovery algorithm, and continuous atomic number sequence is defined as
Figure BDA0003563314340000121
Wherein { a (f) }nExp (j (2 pi fn)), N is 1,2, and N is the nth element of a (f). A matrix form of two-dimensional atomic groups can be written as
Figure BDA0003563314340000122
Then the matrix atomic norm of equation (13) can be written as
Figure BDA0003563314340000123
Solving for SpCan be written as
Figure BDA0003563314340000124
And equation (19) can be solved by solving the following semi-definite problem:
Figure BDA0003563314340000125
wherein
Figure BDA0003563314340000126
And
Figure BDA0003563314340000127
called first-order Hermitian Toeplitz matrix, and the first rows of the Hermitian Toeplitz matrix respectively correspond to the first-order Hermitian Toeplitz matrix
Figure BDA0003563314340000128
And
Figure BDA0003563314340000129
after solving equation (20), estimated
Figure BDA00035633143400001210
And
Figure BDA00035633143400001211
and corresponding
Figure BDA00035633143400001212
And
Figure BDA00035633143400001213
can be obtained by first order Vandermonde decomposition, i.e.
Figure BDA00035633143400001214
Since the two-dimensional coordinates of the scattering points are ultimately required, the frequency combination needs to be solved through a pairing process
Figure BDA00035633143400001215
From formula (13):
Figure BDA00035633143400001216
wherein
Figure BDA0003563314340000131
The pseudo-inverse is represented. Definition of
Figure BDA0003563314340000132
If element
Figure BDA0003563314340000133
Is above a certain threshold δ e (0,1), it is said to correspond to a set of frequency combinations
Figure BDA0003563314340000134
The corresponding scattering point positions and coefficients can be expressed by equations (12) and (d), respectively
Figure BDA0003563314340000135
Thus obtaining the product.
Further, before the step of performing high resolution solution on the target in each range unit in the echo signal by using the continuous domain compressive sensing recovery algorithm, the method further includes: the pair of echo signals scThe formula for making the p-th slice after the range-wise pulse compression can be written as:
Figure BDA0003563314340000136
wherein
Figure BDA0003563314340000137
o (l) is the scattering coefficient of the first scattering point of the object,
Figure BDA0003563314340000138
is composed of
Figure BDA0003563314340000139
In matrix form, then the observation matrix can be written as:
Y＝Sp+W
wherein W is observation noise; solving for SpThe regularized objective function of (a) is written as:
Figure BDA00035633143400001310
further, the step of performing high resolution solution on the target in each range unit in the echo signal by using a continuous domain compressive sensing recovery algorithm includes: for the SpThe regularized objective function of (a) is solved by the following semi-positive problem:
Figure BDA00035633143400001311
number scAnd (3) solving a formula of the p slice after the distance pulse compression:
Figure BDA00035633143400001312
coefficient pass calculation
Figure BDA00035633143400001313
And (4) obtaining.
Step S50: and constructing imaging according to the solving result and outputting a target image.
It can be understood that fig. 5 is a numerical simulation imaging result of the method, the sparse array echo three-dimensional fast fourier transform, and the complementary array echo three-dimensional fast fourier transform according to the embodiment. The common working mode of the transmitting and receiving array elements is adopted, the overall aperture of the radar array is 0.35m multiplied by 0.35m, the number of the complete array elements is 16 multiplied by 16, and the number of the sparse array elements is 36, namely, the number of the sparse array elements accounts for about 14 percent of the total number of the array elements. The radar array is used for transmitting step frequency modulation electromagnetic waves, the carrier frequency of a transmitting signal is 34GHz, the bandwidth is 1GHz, the target distance is 100m, and the SNR of an imaging signal is 20 dB. FIG. 5(a) is a three-dimensional imaging target, which includes several scattering points. Fig. 5(b) shows an imaging result of performing three-dimensional fast fourier transform on sparse array echoes, fig. 5(c) shows an imaging result of performing three-dimensional fast fourier transform on complementary array echoes, and fig. 5(d) shows an imaging result based on continuous domain compressive sensing according to the present invention.
In the embodiment, a sparse array radar imaging system is constructed, and sparse radar arrays are randomly distributed in an array plane of the sparse array radar imaging system; acquiring a target echo and judging whether the target echo is the echo of a sparse uniform radar array, if not, performing three-dimensional fast Fourier transform on the target echo in the sparse array radar imaging system to obtain a target image; if so, completing the target echo by adopting a matrix completing method; carrying out high-resolution solution on the target in each distance unit in the echo signal by using a continuous domain compressed sensing recovery algorithm; the imaging is constructed according to the solving result, a target image is output, signals of the sparse array radar are complemented in a matrix complementing mode, the resolution capacity equivalent to that of the uniform array radar is obtained, the complexity of the system is greatly reduced, meanwhile, the imaging target is solved and reconstructed through a two-dimensional atomic norm minimization method, the two-dimensional atomic norm minimization method can be used for solving to obtain an accurate main lobe peak value, the main lobe is theoretically infinite and narrow, the height of side lobes can be greatly reduced, the imaging quality is improved, and the problem that the front imaging quality of the array radar is limited is effectively solved.
In addition, an embodiment of the present invention further provides a medium, where an array radar forward-looking imaging program based on echo signal completion is stored on the medium, and when executed by a processor, the array radar forward-looking imaging program based on echo signal completion implements the steps of the array radar forward-looking imaging method based on echo signal completion as described above.
The embodiments or specific implementation manners of the array radar forward-looking imaging device based on echo signal completion according to the present invention may refer to the above method embodiments, and are not described herein again.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or system. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in the process, method, article, or system in which the element is included.
The above-mentioned serial numbers of the embodiments of the present invention are only for description, and do not represent the advantages and disadvantages of the embodiments.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solutions of the present invention or portions thereof contributing to the prior art may be embodied in the form of a software product, where the computer software product is stored in a storage medium (such as a rom/ram, a magnetic disk, and an optical disk), and includes several instructions for enabling a terminal device (such as a mobile phone, a computer, a server, an air conditioner, or a network device) to execute the method according to the embodiments of the present invention.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all equivalent structures or equivalent processes performed by the present invention or directly or indirectly applied to other related technical fields are also included in the scope of the present invention.

Claims (10)

1. A forward-looking imaging method of an array radar based on echo signal completion is characterized by comprising the following steps:
constructing a sparse array radar imaging system, wherein sparse radar arrays are randomly distributed in an array plane of the sparse array radar imaging system;
acquiring a target echo and judging whether the target echo is the echo of a sparse uniform radar array, if not, performing three-dimensional fast Fourier transform on the target echo in the sparse array radar imaging system to obtain a target image;
if so, completing the target echo by adopting a matrix completing method;
carrying out high resolution solution on the target in each distance unit in the echo signal by using a continuous domain compressed sensing recovery algorithm;
and constructing imaging according to the solving result and outputting a target image.
2. The method of claim 1, wherein the step of constructing a sparse array radar imaging system with sparse radar arrays randomly distributed in an array plane of the sparse array radar imaging system comprises:
constructing a sparse array radar imaging system, wherein an array plane of the radar imaging system comprises M columns and N rows of receiving and transmitting array element positions, the sparse radar array is randomly distributed in the array plane, and a position vector of each receiving and transmitting array element can be expressed as
Figure FDA0003563314330000011
The position vector of the scattering point of the object can be expressed as
Figure FDA0003563314330000012
3. The method of claim 2, wherein the step of acquiring a target echo and determining whether the target echo is an echo of a sparse, uniform radar array, and if not, performing a three-dimensional fast fourier transform on the target echo in the sparse array radar imaging system to obtain a target image comprises:
acquiring a target echo, and judging whether the target echo is an echo of a sparse uniform radar array;
if not, deducing the echo of the sparse uniform radar array to be located at (x)m,0,zn) The target echo received by the array element is written as:
Figure FDA0003563314330000013
where o (-) is the target scattering distribution function,
Figure FDA0003563314330000014
is a space wave number vector;
and carrying out three-dimensional fast Fourier transform on the target echo to obtain a target image.
4. The method of claim 3, wherein the step of performing a three-dimensional fast Fourier transform on the target echoes to obtain a target image comprises:
approximating the target echo based on far field conditions yields:
Figure FDA0003563314330000021
wherein k is0＝2π/λ0Denotes the central wave number, λ0Is the wavelength, s, corresponding to the center frequencycAbout three separate variables k, xmAnd znA function of (a);
for the three separation variables k, xmAnd znPerforming three-dimensional fast Fourier transform to obtain a target image, namely:
Figure FDA0003563314330000022
5. the method of claim 1, wherein if yes, the step of complementing the target echo by using a matrix complementing method comprises:
completing the sparse radar array signal by adopting a matrix completion method, and setting Sp∈Sc N×MFor echo signals scThe p slice after range-wise pulse compression, i.e.
Figure FDA0003563314330000023
Definition of S'p＝Sp(omega) is a corresponding signal of the sparse radar array, omega is a sparse array element position index, and the problem of block Hankel matrix completion in the presence of noise can be written as follows:
min||XE||*,
Figure FDA0003563314330000024
wherein | · | purple*Is the kernel norm of the matrix, | ·| luminanceFIs the Frobenius norm,
Figure FDA0003563314330000025
under-sampler for reference omega, YEFor signals S passing through a uniform radar arraypConstructed block Hankel matrix, XEIs signal S 'through a sparse radar array'pConstructing a block Hankel matrix;
for the block Hankel matrix YEAnd Hankel matrix YnSolving is carried out by solving for each YnThe mean of the anti-angle elements of the matrix yields the completed radar array signal.
6. The method as claimed in claim 5, wherein said step of performing high resolution solution to the target in each range bin in the echo signal using continuous domain compressive sensing restoration algorithm further comprises:
the formula for performing the distance direction pulse compression on the echo signal sc for the p-th slice can be written as follows:
Figure FDA0003563314330000031
wherein
Figure FDA0003563314330000032
o (l) is the scattering coefficient of the first scattering point of the object,
Figure FDA0003563314330000033
is composed of
Figure FDA0003563314330000034
In matrix form, then the observation matrix can be written as:
Y＝Sp+W
wherein W is observation noise;
solving for SpThe regularized objective function of (a) is written as:
Figure FDA0003563314330000035
7. the method as claimed in claim 6, wherein the step of performing high resolution solution on the target in each range bin in the echo signal by using continuous domain compressed sensing recovery algorithm comprises:
for the SpThe regularized objective function of (a) is solved by the following semi-positive definite problem:
Figure FDA0003563314330000036
the position of the scattering point passes through the pair of echo signals scAnd (3) solving a formula of the p slice after the distance pulse compression:
Figure FDA0003563314330000037
coefficient passing
Figure FDA0003563314330000041
And (6) calculating.
8. An array radar forward-looking imaging device based on echo signal completion, the device comprising:
the system construction module is used for constructing a sparse array radar imaging system, and sparse radar arrays are randomly distributed in an array plane of the sparse array radar imaging system;
the non-sparse derivation module is used for acquiring a target echo and judging whether the target echo is the echo of a sparse uniform radar array, if not, the target echo is subjected to three-dimensional fast Fourier transform in the sparse array radar imaging system to obtain a target image;
the matrix completion module is used for completing the target echo by adopting a matrix completion method if the target echo exists;
the compressed sensing module is used for carrying out high-resolution solution on the target in each distance unit in the echo signal by utilizing a continuous domain compressed sensing recovery algorithm;
and the output module is used for constructing imaging according to the solving result and outputting the target image.
9. An array radar forward-looking imaging device based on echo signal completion, the device comprising: a memory, a processor and an echo signal completion based array radar forward looking imaging program stored on the memory and executable on the processor, the echo signal completion based array radar forward looking imaging program configured to implement the steps of the echo signal completion based array radar forward looking imaging method according to any one of claims 1 to 7.
10. A medium having stored thereon a echo signal completion based array radar forward looking imaging program, which when executed by a processor, performs the steps of the echo signal completion based array radar forward looking imaging method as recited in any one of claims 1 to 7.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115421157A (en) * 2022-10-24 2022-12-02 深圳大学 Method and device for constructing radar array based on undirected adjacency graph

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115421157A (en) * 2022-10-24 2022-12-02 深圳大学 Method and device for constructing radar array based on undirected adjacency graph

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