CN115128607A - Cross MIMO array radar system and three-dimensional imaging method thereof - Google Patents

Cross MIMO array radar system and three-dimensional imaging method thereof Download PDF

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CN115128607A
CN115128607A CN202210790134.2A CN202210790134A CN115128607A CN 115128607 A CN115128607 A CN 115128607A CN 202210790134 A CN202210790134 A CN 202210790134A CN 115128607 A CN115128607 A CN 115128607A
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tensor
array
cross
mimo
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冯为可
胡晓伟
郭艺夺
蒲涛
路复宇
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Air Force 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
    • 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
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9021—SAR image post-processing techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/285—Receivers
    • G01S7/295—Means for transforming co-ordinates or for evaluating data, e.g. using computers
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/35—Details of non-pulse systems

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  • Radar, Positioning & Navigation (AREA)
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  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention provides a cross MIMO array radar system and a three-dimensional imaging method thereof, wherein the radar system comprises: the system comprises a cross MIMO array, a vector network analyzer, a radio frequency converter, a microcontroller and a computer; the cross MIMO array comprises a plurality of transmitting array elements and a plurality of receiving array elements; the vector network analyzer is used for generating a step frequency continuous wave signal; the radio frequency converter is used for realizing time-sharing transmission and reception of signals; the microcontroller is used for controlling the radio frequency converter; the computer is used for remotely controlling the vector network analyzer and the microcontroller and storing and processing the received data.

Description

Cross MIMO array radar system and three-dimensional imaging method thereof
Technical Field
The invention relates to the technical field of radar detection, in particular to a cross MIMO array radar system and a three-dimensional imaging method thereof.
Background
A Ground-Based Synthetic Aperture Radar (GB-SAR for short) is a monitoring technology for monitoring displacement, deformation and vibration of natural objects and infrastructures, and the precision can reach sub-millimeter. GB-SAR forms a one-dimensional synthetic aperture by sequentially moving a transmitting-receiving antenna on a track, thereby obtaining higher angular resolution. In recent years, students have proposed a method based on a Multiple Input Multiple Output (MIMO) array to reduce the data acquisition period of the GB-SAR, so that Multiple measurements can be performed in a short time, and the real-time performance of monitoring is improved. Shorter data acquisition times also help to reduce the adverse effects of the atmosphere on the displacement estimate.
Because only one-dimensional synthetic aperture is formed, GB-SAR can only obtain a two-dimensional high-resolution image of a target. In this case, the three-dimensional scene is projected onto the two-dimensional plane, resulting in some target information being lost. In general, when monitoring dams, landslides and the like, the GB-SAR requires accurate positioning of an object having a displacement using a Digital Elevation Model (DEM). However, the projection of two-dimensional GB-SAR images onto DEMs is often complex and accurate DEMs are not always known.
Currently, there are two simple methods to obtain two-dimensional synthetic apertures to achieve three-dimensional high resolution imaging. Firstly, a transmitting and receiving antenna is moved on a two-dimensional track; and secondly, moving the one-dimensional MIMO array on the one-dimensional orbit. However, the two methods have the problems of long data acquisition time, large data volume, poor three-dimensional imaging performance and the like.
Disclosure of Invention
The invention aims to overcome at least some of the defects and provides a cross MIMO array radar system and a three-dimensional imaging method thereof, so that three-dimensional high-resolution imaging and displacement estimation of a target are realized, and meanwhile, the data acquisition time is shortened, the data volume is reduced, and the three-dimensional imaging performance is improved.
In order to solve the technical problems, the invention adopts the following technical scheme:
a cross MIMO array radar system comprising:
the system comprises a cross MIMO array, a vector network analyzer, a radio frequency converter, a microcontroller and a computer; wherein the content of the first and second substances,
the cross MIMO array comprises a plurality of transmitting array elements and a plurality of receiving array elements;
the vector network analyzer is used for generating a step frequency continuous wave signal;
the radio frequency converter is used for realizing time-sharing transmission and reception of signals;
the microcontroller is used for controlling the radio frequency converter;
the computer is used for remotely controlling the vector network analyzer and the microcontroller, storing and processing received data, and finally finishing target three-dimensional imaging and displacement estimation.
A further technical solution is that the cross MIMO array includes M transmitting array elements and N receiving array elements, where M is an integer not less than 2, N is an integer not less than 2, and the number of synthesized virtual array elements is M × N;
in the cross MIMO array, M transmitting array elements are arranged at equal intervals to form a uniform linear transmitting array, N receiving array elements are arranged at equal intervals to form a uniform linear receiving array, the centers of the uniform linear transmitting array and the uniform linear receiving array are overlapped, and a cross MIMO array is formed by cross vertical crossing.
The invention also provides a three-dimensional imaging method of the cross MIMO array radar system, which is realized by adopting any one of the cross MIMO array radar systems, and comprises the following steps:
s101, determining relevant parameters of the radar system according to a scene to be measured and measurement requirements;
s102, controlling a vector network analyzer and a microcontroller through a computer, randomly selecting a receiving and transmitting channel, randomly selecting signal frequency, transmitting and receiving an undersampled echo signal and storing the undersampled echo signal in the computer;
s103, preprocessing echo signals such as time delay, phase correction and gain correction;
s104, establishing a space rectangular coordinate system and a polar coordinate system by using the radar array center to obtain a signal model under the polar coordinate system;
s105, establishing a three-dimensional pseudo polar coordinate system through far field approximation to obtain a tensor signal model under the three-dimensional pseudo polar coordinate system;
s106, establishing a sparse tensor recovery model based on the three-dimensional pseudo polar coordinate system according to a receiving and transmitting channel and a signal frequency corresponding to the undersampled echo signal;
s107, solving the sparse tensor recovery model by using a tensor iterative adaptive algorithm to obtain an imaging scene reflection coefficient tensor, wherein the input parameters of the tensor iterative adaptive algorithm comprise: the under-sampled echo signals, partial Fourier transform matrixes, preset maximum iteration times and conjugate iteration times;
the tensor iterative adaptive algorithm comprises the following steps:
A. initialization: calculating an initial value of the reflection coefficient tensor of the imaging scene and a square value of the initial value of the reflection coefficient tensor of the imaging scene by using the input parameters;
B. estimating iterative tensor factors using a tensor conjugate gradient algorithm, wherein input parameters of the tensor conjugate gradient algorithm include: the undersampled echo signals, the partial Fourier transform matrix, the square value of the reflection coefficient tensor, and the number of conjugate iterations;
C. updating the reflection coefficient tensor and the square value thereof according to the iteration tensor factor, the square value of the reflection coefficient tensor and the partial Fourier transform matrix;
D. and repeating the steps B to C until the preset maximum iteration times is reached, outputting the reflection coefficient tensor, and obtaining a target three-dimensional high-resolution imaging result.
Further, in step S104, the center of the radar array is used as an origin, and the directions of the uniform linear receiving array and the uniform linear transmitting array are the x-axis and the z-axis, respectivelyEstablishing a space rectangular coordinate system x-y-z, wherein the ith receiving array element is located at (x) i 0,0), the jth transmit array element is located at (0,0, z) j ) Where i is 1,2, …, M, j is 1,2, …, N, M is the number of receiving array elements, and N is the number of transmitting array elements;
establishing a polar coordinate system by taking the center of the radar array as an origin
Figure BDA0003729865100000031
Wherein R is the distance from the target to the center of the radar array, theta is the included angle between the target and the y-z plane, namely the azimuth angle,
Figure BDA0003729865100000032
is the included angle between the target and the x-y plane, namely the pitch angle;
the signal model in the polar coordinate system can be expressed as:
Figure BDA0003729865100000033
wherein R is i,j (x, y, z) is the distance from the target at (x, y, z) to the i-j transmit-receive array element, σ (x, y, z) is the reflection coefficient, Ω represents the imaging scene, f q ＝f 0 +(q-1)Δf，q＝1,2,...,Q，f 0 For the initial frequency,. DELTA.f is the frequency step, c is the speed of light, and n (i, j, q) is the noise.
Further, in step S105, the three-dimensional pseudo polar coordinate system is defined as:
α＝2R/c,β＝sinθ/λ c ,
Figure BDA0003729865100000038
wherein λ is c ＝c/f c Is a wavelength f c Is the center frequency;
based on the three-dimensional pseudo-polar coordinates, a tensor signal model is expressed as:
S＝Σ× 1 F 1 × 2 F 2 × 3 F 3
wherein the extract is κ Is the modulo-tensor-matrix product,Sin order to receive the tensor of the signal,Σtensor of reflectance for imaging scene, F 1 、 F 2 、F 3 Is a fourier transform matrix.
In a further technical solution, in step S106, the sparse tensor recovery model is expressed as:
Figure BDA0003729865100000034
wherein, the first and the second end of the pipe are connected with each other,S un to receive the undersampled signal tensor, F 1 un 、F 2 un And F 3 un Is a partial Fourier transform matrix, ε is the noise level, | · | | non-calculation 0 Being the number of non-zero elements in the vector or tensor, tensorYThe Frobenius norm of (a) is defined as:
Figure BDA0003729865100000035
in step S107, in the tensor iterative adaptive algorithm, the step a of calculating the initial value and the square value of the reflection coefficient tensor may be represented as:
Figure BDA0003729865100000036
and
Figure BDA0003729865100000037
wherein the content of the first and second substances,
Figure BDA0003729865100000041
the pseudo-inverse is represented.
In step S107, in the tensor iterative adaptive algorithm, step B estimates an iterative tensor using a tensor conjugate gradient algorithmThe steps of measuring the factor are as follows: 1) initialization:U 0 ＝0，ζ 0 ＝0，R 0 ＝S un ，P 0 ＝0，
Figure BDA0003729865100000045
t is 1; 2) updating:P t ＝R t-1 +ζ t-1 P t-1 ，T 1 ＝Α o-1 e[P t × 1 (F 1 un ) H × 2 (F 2 un ) H × 3 (F 3 un ) H ]，T 2 ＝T 1 × 1 F un 1 × 2 F 2 un × 3 F 3 un ，η t-1 ＝ρ t-1 /∑∑∑P t * e T 2 ，U t ＝U t-1 +η t-1 P t ，R t ＝R t-1 -η t-1 T 2 ，
Figure BDA0003729865100000042
ζ t ＝ρ t /ρ t-1 wherein e represents a Hadamard product; 3) iteration: let T ← T +1, if T ≦ T, return to step 2); otherwise, the iteration is stopped.
Further, in step S107, in the tensor iterative adaptive algorithm, the updating of the reflection coefficient tensor and the square value thereof in step C may be represented as:
Figure BDA0003729865100000043
and
Figure BDA0003729865100000044
compared with the prior art, the invention has the beneficial effects that:
the invention provides a cross MIMO array radar system, a three-dimensional imaging method thereof, a computer readable storage medium and computer equipment, which can meet the requirements of three-dimensional high-resolution imaging and displacement estimation on a target.
The advantages of the invention include:
(1) the sampling time is fast, the spatial sampling is realized by switching the receiving and transmitting channels, and the aperture is synthesized without moving an antenna;
(2) under the condition of a sparse scene, data sampling time and data memory amount can be greatly reduced by undersampling;
(3) by adopting a tensor iteration adaptive algorithm, the resolution of target three-dimensional imaging can be improved, and the side lobe level can be reduced;
(4) three-dimensional imaging can provide more target information than two-dimensional imaging, thereby realizing accurate positioning of a displacement target.
Drawings
Fig. 1 is a schematic structural diagram of a cross MIMO array radar system according to an embodiment of the present invention;
fig. 2 is a point spread function of a cross MIMO array radar system according to an embodiment of the present invention for a target located at (10,0, 0);
fig. 3 is a schematic imaging geometry diagram of a cross MIMO array radar system according to an embodiment of the present invention;
FIG. 4 is a compressive sampling model of the reflection coefficient tensors of an imaging scene according to an embodiment of the present invention;
FIG. 5 shows the BP algorithm three-dimensional imaging results of two corner reflectors located at (0,6.5,0) m and (1,9.5,0.5) m according to an embodiment of the present invention;
FIG. 6 shows three-dimensional imaging results of 3D FPFA algorithm for two corner reflectors located at (0,6.5,0) m and (1,9.5,0.5) m according to an embodiment of the present invention;
FIG. 7 shows the three-dimensional imaging results of the T-IAA algorithm for two corner reflectors located at (0,6.5,0) m and (1,9.5,0.5) m according to the present invention;
fig. 8 shows the displacement estimation result of the corner reflector by different algorithms according to the embodiment of the present invention.
Icon: 1-transmitting array element, 2-receiving array element, 3-vector network analyzer, 4-radio frequency converter, 5-microcontroller and 6-computer.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The embodiment of the invention provides a cross MIMO array radar system, which comprises a cross MIMO array, a vector network analyzer 3, a radio frequency converter 4, a microcontroller 5 and a computer 6, as shown in FIG. 1. Specifically, wherein:
the cross MIMO array comprises a plurality of transmitting array elements 1 and a plurality of receiving array elements 2, wherein each transmitting array element 1 forms a uniform linear transmitting array, each receiving array element 2 forms a uniform linear receiving array, and the synthesized virtual array elements form an equivalent uniform planar array.
The vector network analyzer 3 is used to generate a step frequency continuous wave signal.
The radio frequency converter 4 is used for realizing time-sharing transmission and reception of signals.
The microcontroller 5 is used to control the rf converter 4.
And the computer 6 is used for remotely controlling the vector network analyzer 3 and the microcontroller 5, storing and processing the received data, and finally finishing target three-dimensional imaging and displacement estimation.
Step S101, in the cross MIMO array radar system provided in this embodiment, the ith receiving antenna is located at (x) i 0,0), the jth transmit antenna is located at (0,0, z) j ) Where i is 1,2, …,16, j is 1,2, …,16, the signal frequency is 4.75-5.25 GHz, the frequency number is Q201, the distance resolution is 0.3m, the array element spacing of the transmitting array and the receiving array is 5cm and 6cm, respectively, the resolution of the system in x direction is about 0.067rad, the resolution in z direction is about 0.080rad, and the point spread function of the system for the target located at (10,0,0) is shown in fig. 2.
Step S104 ofThe rectangular coordinate system and the polar coordinate system of the space established at the center of the radar array are shown in FIG. 3, and are located at (x) 0 ,y 0 ,z 0 ) The distance between the ith-j receiving and transmitting array element and the target is as follows:
Figure BDA0003729865100000051
thus, (x) 0 ,y 0 ,z 0 ) The echo signal of the target at the ith-j transceiving channels and the qth frequency can be expressed as:
Figure BDA0003729865100000052
wherein, f q ＝f 0 +(q-1)Δf，q＝1,2,...,Q，f 0 Is the initial frequency, Δ f is the frequency step, σ 0 For the target reflection coefficient, c is the speed of light, and n (i, j, q) is the noise.
The sum of the echo signals of all targets in the imaged scene can be expressed as:
Figure BDA0003729865100000061
wherein R is i,j (x, y, z) is the distance from the target at (x, y, z) to the i-j th transceiving array element, σ (x, y, z) is the reflection coefficient thereof, and Ω represents the imaging scene.
The reflection coefficient of the target at (x, y, z) can be estimated by Back Projection (BP) algorithm, as follows:
Figure BDA0003729865100000062
in FIG. 3, it is assumed that
Figure BDA0003729865100000063
Is the distance from the center of the radar array to the target, θ 0 As Op and y-z plane clampsThe angle of the corner is such that,
Figure BDA0003729865100000064
is the angle between Op and the x-y plane, x can be obtained 0 ＝R 0 sinθ 0 And
Figure BDA00037298651000000614
according to the cosine theorem, the distance between the i-j th transceiving array element and the far-field target can be approximately expressed as:
Figure BDA0003729865100000065
thus, the BP algorithm is used to estimate the relative amounts of (R, θ,
Figure BDA0003729865100000066
) The reflection coefficient of the target can be simplified as follows:
Figure BDA0003729865100000067
wherein f is c Is a center frequency, λ c ＝c/f c Is a function of the wavelength of the light,
Figure BDA0003729865100000068
is limited by:
Figure BDA0003729865100000069
where Δ R ═ c/2B is the range resolution, B is the signal bandwidth, L x And L z The synthetic aperture lengths of the system in the x-direction and z-direction, respectively.
When | ψ i,j,q When | satisfies the following condition, the phase term
Figure BDA00037298651000000610
Negligible:
Figure BDA00037298651000000611
at this time, for the radar system constructed, (R, θ,
Figure BDA00037298651000000612
) The reflection coefficient of the target can be estimated approximately as:
Figure BDA00037298651000000613
it can be seen that the exponential terms in the above equation constitute the kernel of the three-dimensional fourier transform.
Therefore, in step S105, the three-dimensional pseudo-polar coordinates (α, β, γ) are defined as:
α＝2R/c,β＝sinθ/λ c ,
Figure BDA0003729865100000071
based on the pseudo polar coordinate system, the received signal tensor model can be expressed as:
S＝Σ× 1 F 1 × 2 F 2 × 3 F 3
wherein the extract is κ Is the modulo-tensor-matrix product,Sin order to receive the tensor of the signal,Σtensor of reflectance for imaging scene, F 1 、 F 2 、F 3 Is a fourier transform matrix.
At this time, the Three-dimensional Far-field Pseudo-polar coordinate Algorithm (Three-dimensional Far-field Pseudo-polar Format Algorithm, abbreviated as 3D FPFA) can be used to estimate the reflection coefficient tensor of the imaging scene, which is expressed as:
Figure BDA0003729865100000072
wherein, (. cndot.) H Is a conjugate transpose of the original image,
Figure BDA0003729865100000073
representing a three-dimensional fourier transform.
And step S106, when the imaging scene is sparse, namely only a few strong targets exist, a sparse tensor recovery model can be established, and a tensor compression sensing method is adopted to carry out three-dimensional imaging, so that the side lobe level is reduced, and higher resolution is obtained.
Figure BDA0003729865100000074
Wherein epsilon is the noise level, | · | | non-calculation 0 Being the number of non-zero elements in the vector or tensor, tensorYThe Frobenius norm of (a) is defined as:
Figure BDA0003729865100000075
one advantage of imaging with the tensor compressed sensing method is that: high quality imaging results are obtained even under data undersampling conditions, which helps to reduce data acquisition time and data memory volume. For the constructed radar system, in order to reduce the number of transceiving channels, a data acquisition program is used for controlling a radio frequency converter to randomly gate part of transceiving channels, and in order to reduce the number of frequencies, the data acquisition program is used for controlling a vector network analyzer to randomly generate part of frequencies.
The undersampled signal model (i.e., the compressive sampling model of the reflection coefficient tensor) is shown in FIG. 4, whereS un For the received undersampled signal tensor, F 1 un 、F 2 un And F 3 un Is a partial fourier transform matrix. Then, a three-dimensional high resolution image of the target can be obtained by solving the following sparse tensor recovery model.
Figure BDA0003729865100000076
Step S107, a Tensor Iterative Adaptive algorithm (T-IAA for short) is used for solving the sparse Tensor recovery model, and the specific algorithm execution steps are shown in Table 1.
TABLE 1 tensor iterative adaptive algorithm
Figure BDA0003729865100000077
1) Initialization:
Figure BDA0003729865100000081
o is 1, wherein
Figure BDA0003729865100000082
To represent
Pseudo-inverse;
2) estimating: to be provided withS un 、F 1 un 、F 2 un 、F 3 un AndΑ o-1 estimate for input by tensor conjugate gradient algorithmU o-1 ，
The iteration number of the tensor conjugate gradient algorithm is T;
3) updating:
Figure BDA0003729865100000083
and
Figure BDA0003729865100000084
wherein e represents
A Hadamard product;
4) iteration: let O ← O +1, if O is less than or equal to O, return to step 2); otherwise, the iteration is stopped.
Figure BDA0003729865100000085
The specific implementation steps of the tensor conjugate gradient algorithm are shown in table 2.
TABLE 2 tensor conjugate gradient algorithm
Figure BDA0003729865100000086
The cross MIMO array radar system provided by the embodiment of the invention is adopted to image two three-plane corner reflectors with the sizes of 40cm and 30cm respectively and the positions of (0,6.5,0) m and (1,9.5,0.5) m respectively, and three-dimensional imaging results obtained by a BP algorithm, a 3D FPFA algorithm and a T-IAA algorithm only using 1/8 undersampled data are respectively shown in figures 5, 6 and 7. As shown in fig. 5 and 6, the BP algorithm and the 3D FPFA algorithm can obtain similar imaging results, but both have high-level side lobes and poor imaging quality. As shown in fig. 7, under the condition of randomly selecting 64 pairs of transceiving channels and 101 frequencies, the T-IAA algorithm can still obtain high-resolution imaging results, which is superior to the BP algorithm and the 3D FPFA algorithm. In addition, the running time of the BP algorithm, the running time of the 3D FPFA algorithm and the running time of the T-IAA algorithm are respectively 7.76s, 0.12s and 1.50s, which shows that the BP algorithm is the most time-consuming, and the 3D FPFA algorithm can effectively reduce the calculation time. The T-IAA algorithm only uses 1/8 undersampled data, so that the data acquisition time can be reduced, and the data volume can be reduced. The three-sided corner reflector with the size of 40cm is moved, the step length of each movement is 1mm, and displacement estimation results obtained by using a BP algorithm, a 3D FPFA algorithm and a T-IAA algorithm are shown in FIG. 8. It can be seen that the BP algorithm, the 3D FPFA algorithm and the T-IAA algorithm can achieve accurate estimation of target displacement.
In particular, in some preferred embodiments of the present invention, there is further provided a computer device, including a memory and a processor, where the memory stores a computer program, and the processor implements the steps of the three-dimensional imaging method of the cross MIMO array radar system in any one of the above embodiments when executing the computer program.
In other preferred embodiments of the present invention, a computer-readable storage medium is further provided, on which a computer program is stored, and the computer program is executed by a processor to implement the steps of the three-dimensional imaging method for the cross MIMO array radar system in any of the above embodiments. It will be understood by those skilled in the art that all or part of the processes of the method according to the above embodiments may be implemented by a computer program, which may be stored in a non-volatile computer-readable storage medium, and when executed, the computer program may include the processes of the embodiments of the method for three-dimensional imaging of a cross MIMO array radar system, and will not be described again here.
Although the invention has been described herein with reference to a number of illustrative embodiments thereof, it should be understood that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the spirit and scope of the principles of this disclosure. More specifically, various variations and modifications are possible in the component parts and/or arrangements of the subject combination arrangement within the scope of the disclosure, the drawings and the appended claims. In addition to variations and modifications in the component parts and/or arrangements, other uses will also be apparent to those skilled in the art.

Claims (10)

1. A cross MIMO array radar system, characterized by: the method comprises the following steps: the system comprises a cross MIMO array, a vector network analyzer, a radio frequency converter, a microcontroller and a computer; the cross MIMO array comprises a plurality of transmitting array elements and a plurality of receiving array elements; the vector network analyzer is used for generating a step frequency continuous wave signal; the radio frequency converter is used for realizing time-sharing transmission and reception of signals; the microcontroller is used for controlling the radio frequency converter; the computer is used for remotely controlling the vector network analyzer and the microcontroller, storing and processing received data, and finally finishing target three-dimensional imaging and displacement estimation.
2. The cross MIMO array radar system of claim 1, wherein: the cross MIMO array comprises M transmitting array elements and N receiving array elements, wherein M is an integer not less than 2, N is an integer not less than 2, and the number of the synthesized virtual array elements is M multiplied by N; in the cross MIMO array, M transmitting array elements are arranged at equal intervals to form a uniform linear transmitting array, N receiving array elements are arranged at equal intervals to form a uniform linear receiving array, the centers of the uniform linear transmitting array and the uniform linear receiving array are superposed, and the uniform linear transmitting array and the uniform linear receiving array are vertically crossed in a cross manner to form the cross MIMO array.
3. A three-dimensional imaging method based on the cross MIMO array radar system of any one of claims 1-2, wherein: the method comprises the following steps:
s101, determining relevant parameters of the radar system according to a scene to be measured and measurement requirements;
s102, controlling a vector network analyzer and a microcontroller through a computer, randomly selecting a receiving and transmitting channel, randomly selecting signal frequency, transmitting and receiving an undersampled echo signal and storing the undersampled echo signal in the computer;
s103, preprocessing echo signals such as time delay, phase correction and gain correction;
s104, establishing a space rectangular coordinate system and a polar coordinate system by using the radar array center to obtain a signal model under the polar coordinate system;
s105, establishing a three-dimensional pseudo polar coordinate system through far field approximation to obtain a tensor signal model under the three-dimensional pseudo polar coordinate system;
s106, establishing a sparse tensor recovery model based on the three-dimensional pseudo polar coordinate system according to a receiving-transmitting channel and a signal frequency corresponding to the under-sampled echo signal;
s107, solving the sparse tensor recovery model by using a tensor iterative adaptive algorithm to obtain an imaging scene reflection coefficient tensor, wherein the input parameters of the tensor iterative adaptive algorithm comprise: the under-sampled echo signals, partial Fourier transform matrixes, preset maximum iteration times and conjugate iteration times;
the tensor iterative adaptive algorithm comprises the following steps:
A. initialization: calculating an initial value of the imaging scene reflection coefficient tensor and a square value thereof by using the input parameters;
B. estimating iterative tensor factors using a tensor conjugate gradient algorithm, wherein input parameters of the tensor conjugate gradient algorithm include: the undersampled echo signals, the partial Fourier transform matrix, the square value of the reflection coefficient tensor, and the number of conjugate iterations;
C. updating the reflection coefficient tensor and the square value thereof according to the iteration tensor factor, the square value of the reflection coefficient tensor and the partial Fourier transform matrix;
D. and repeating the steps B to C until the preset maximum iteration times is reached, outputting the reflection coefficient tensor, and obtaining a target three-dimensional high-resolution imaging result.
4. The cross MIMO array radar system three-dimensional imaging method of claim 3, wherein: in step S104, a spatial rectangular coordinate system x-y-z is established with the center of the radar array as an origin and the directions of the uniform linear receiving array and the uniform linear transmitting array as an x-axis and a z-axis, respectively, where the ith receiving array element is located at (x-y-z) i 0,0), the jth transmit array element is located at (0,0, z) j ) Where i is 1,2, …, M, j is 1,2, …, N, M is the number of receiving array elements, and N is the number of transmitting array elements;
establishing a polar coordinate system by taking the center of the radar array as an origin
Figure FDA0003729865090000023
Wherein R is the distance from the target to the center of the radar array, theta is the included angle between the target and the y-z plane, namely the azimuth angle,
Figure FDA0003729865090000024
is the included angle between the target and the x-y plane, namely the pitch angle;
the signal model in the polar coordinate system can be expressed as:
Figure FDA0003729865090000021
wherein R is i,j (x, y, z) is the distance from the target at (x, y, z) to the i-j th transceiving array element, σ (x, y, z) is the reflection coefficient thereof, Ω represents the imaging scene, f q ＝f 0 +(q-1)Δf，q＝1,2,...,Q，f 0 For the initial frequency,. DELTA.f is the frequency step, c is the speed of light, and n (i, j, q) is the noise.
5. The cross MIMO array radar system three-dimensional imaging method of claim 3, wherein: in step S105, the three-dimensional pseudo polar coordinate system is defined as:
α＝2R/c,β＝sinθ/λ c ,
Figure FDA0003729865090000022
wherein λ is c ＝c/f c Is a wavelength, f c Is the center frequency.
6. The cross MIMO array radar system three-dimensional imaging method according to claim 3, wherein: in step S105, based on the three-dimensional pseudo polar coordinates, a tensor signal model is expressed as:
S＝Σ× 1 F 1 × 2 F 2 × 3 F 3
wherein the extract is κ Is the modulo-tensor-matrix product,Sin order to receive the tensor of the signal,Σtensor of reflectance for imaging scene, F 1 、F 2 、F 3 Is a fourier transform matrix.
7. The cross MIMO array radar system three-dimensional imaging method according to claim 3, wherein: in step S106, the sparse tensor recovery model is expressed as:
Figure FDA0003729865090000031
wherein the content of the first and second substances,S ·n to receive the undersampled signal tensor, F 1 un 、F 2 un And F 3 un Is a partial Fourier transform matrix, ε is the noise level, | · | | non-calculation 0 Being the number of non-zero elements in the vector or tensor, tensorYThe Frobenius norm of (a) is defined as:
Figure FDA0003729865090000032
8. the cross MIMO array radar system three-dimensional imaging method of claim 3, wherein: in step S107, in the tensor iterative adaptive algorithm, the calculation of the initial value of the reflection coefficient tensor and the square value thereof in step a may be represented as:
Figure FDA0003729865090000033
and
Figure FDA0003729865090000034
wherein the content of the first and second substances,
Figure FDA0003729865090000035
the pseudo-inverse is represented.
9. The cross MIMO array radar system three-dimensional imaging method of claim 3, wherein: in step S107, in the tensor iterative adaptive algorithm, the step B of estimating the iterative tensor factor by using the tensor conjugate gradient algorithm includes: 1) initialization:U 0 ＝0，ζ 0 ＝0，R 0 ＝S un ，P 0 ＝0，
Figure FDA0003729865090000036
t is 1; 2) updating:P t ＝R t-1 +ζ t-1 P t-1 ，T 1 ＝Α o-1 e[P t × 1 (F 1 un ) H × 2 (F 2 un ) H × 3 (F 3 un ) H ]，T 2 ＝T 1 × 1 F un 1 × 2 F 2 un × 3 F 3 un ，η t-1 ＝ρ t-1 /∑∑∑P t * eT 2 ，U t ＝U t-1 +η t-1 P t ，R t ＝R t-1 -η t-1 T 2 ，
Figure FDA0003729865090000037
ζ t ＝ρ t /ρ t-1 wherein e represents a Hadamard product; 3) iteration: let T ← T +1, if T ≦ T, return to step 2); otherwise, the iteration is stopped.
10. The cross MIMO array radar system three-dimensional imaging method of claim 3, wherein: in step S107, in the tensor iterative adaptive algorithm, updating the reflection coefficient tensor and the square value thereof in step C may be represented as:
Figure FDA0003729865090000038
and
Figure FDA0003729865090000039
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