CN113109807A - Frequency diversity array radar underground target three-dimensional imaging method based on compressed sensing - Google Patents

Frequency diversity array radar underground target three-dimensional imaging method based on compressed sensing Download PDF

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CN113109807A
CN113109807A CN202110256588.7A CN202110256588A CN113109807A CN 113109807 A CN113109807 A CN 113109807A CN 202110256588 A CN202110256588 A CN 202110256588A CN 113109807 A CN113109807 A CN 113109807A
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CN113109807B (en
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刘庆华
周辰
廖可非
王海涛
晋良念
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Guilin University of Electronic 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
    • 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
    • G01S13/885—Radar or analogous systems specially adapted for specific applications for ground probing
    • 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
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/411—Identification of targets based on measurements of radar reflectivity
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/414—Discriminating targets with respect to background clutter
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/418—Theoretical aspects
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/30—Assessment of water resources

Abstract

The invention discloses a target three-dimensional imaging method under a frequency diversity array radar based on compressed sensing, which comprises the steps of using two FDA radars to transmit signals to a region to be detected and receive echo data, then using band-pass filters with different central frequencies to carry out filtering processing, carrying out sampling value at fixed time and recording the sampling value as a vector, then establishing a rectangular coordinate system for the region to be detected, carrying out grid division on the detection region, calculating the propagation delay of each pair of array elements in the two arrays relative to the grid, establishing a dictionary and a corresponding scene reflection coefficient by using the delay of each grid, re-stacking all the divided dictionaries and scene reflection coefficients, reconstructing the scene reflection coefficients by using an orthogonal matching tracking algorithm, and finally splitting and re-splicing the scene reflection coefficients to obtain a three-dimensional imaging result so as to reduce the number of required echo sampling points, the pressure of data acquisition is reduced, the imaging result is more stable, and the underground target position can be more intuitively distinguished.

Description

Frequency diversity array radar underground target three-dimensional imaging method based on compressed sensing
Technical Field
The invention relates to the technical field of ground penetrating radar signal processing, in particular to a frequency diversity array radar underground target three-dimensional imaging method based on compressed sensing.
Background
Due to the advantages of single frequency and simultaneous transceiving of the frequency diversity array, the frequency diversity array radar underground target imaging technology has wide application prospect in the military and civil fields. Most of the frequency diversity arrays studied at present are directed to targets in free space, and target imaging is performed through signal source positioning or back projection. Most of the radar target imaging technologies are results obtained by utilizing mathematical models to carry out a large amount of operations, so that the algorithm is not easy to realize the requirements on real-time performance and accuracy, and cannot be directly applied to underground environments.
Disclosure of Invention
The invention aims to provide a frequency diversity array radar underground target three-dimensional imaging method for compressed sensing, and aims to solve the technical problems that an algorithm adopted by a traditional method in the prior art is not easy to realize real-time and accuracy requirements, and cannot be directly suitable for an underground environment.
In order to achieve the above object, the present invention provides a frequency diversity array radar underground target three-dimensional imaging method based on compressed sensing, which comprises the following steps:
two independent FDA radars are used for transmitting signals to the area to be detected and receiving echo data;
after each array element receives an echo signal, performing filtering processing by using band-pass filters with different central frequencies;
the echo signal after filtering processing is carried out for a fixed time t0Sampling and taking values, and recording the values as vectors;
establishing a three-dimensional coordinate system between the two arrays, and performing grid division on the region to be detected by using equal step length;
calculating the propagation delay of each pair of array elements in the two arrays relative to each grid, and establishing a dictionary and a corresponding scene reflection coefficient by using the delay of each grid;
restacking all the dictionaries divided by the z axis and the scene reflection coefficient matrixes;
and reconstructing the scene reflection coefficient by using an orthogonal matching pursuit algorithm, and splitting and splicing the scene reflection coefficient according to the form of grid division to obtain a three-dimensional imaging result.
The method comprises the following steps of using two independent FDA radars to transmit signals to a region to be detected and receive echo data:
the two independent FDA radars have N array elements in total, the distance is Z, the distance value is required to ensure that effective echo signals can be obtained, the amplitude of the echo signals can be estimated by 1/R, wherein R is the farthest propagation path from the array elements to the area to be detected.
The echo signal after filtering processing is carried out for a fixed time t0Sampling value taking is carried out, and the sampling value is recorded as a vector:
the selected fixed time must satisfy t0＞＞max(τi) In which τ isiIs the two-way time delay of the signal after the reflection of the ith target;
the vector is received by the m-th array element transmitted by the n-th array element, and the echo signal has a center frequency fnThe band-pass filter filters the sampled values.
Establishing a three-dimensional coordinate system between the two arrays, and performing grid division on the region to be detected by using equal step length:
and taking the first FDA radar to the second FDA radar as the positive direction of a z axis, the first array element to the Nth array element of the first FDA radar as the positive direction of an x axis, the ground to the geocenter as the positive direction of a y axis to establish a three-dimensional coordinate system, and performing grid division on the regions to be detected by taking the equal distance delta d as step length on each coordinate axis.
In the step of calculating the propagation delay of each pair of array elements in the two arrays relative to each grid:
each pair of array elements consists of two array elements, one array element transmits signals, and the other array element receives the signals;
the propagation delay of the grid is the delay from the transmission of the signal from the transmitting array element to the receiving array element after the reflection of the signal from the grid.
And establishing a dictionary and a corresponding scene reflection coefficient by using the time delay of each grid:
the scene reflection coefficient corresponds to the dictionary and has the same form and arrangement, wherein each element is the reflection coefficient of the grid at the position.
The beneficial effects of the invention are as follows: the method has the advantages that the calculation is simple, the realization is easy, the required echo sampling point number is reduced, the buried target detection is carried out by using the FDA radar, the data acquisition pressure is reduced, the required calculation amount is greatly reduced, meanwhile, the imaging result is more stable, and the underground target azimuth can be more intuitively distinguished.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of steps of a compressed sensing-based frequency diversity array radar underground target three-dimensional imaging method of the invention.
Fig. 2 is a schematic illustration of the position of two arrays of the present invention.
Figure 3 is a schematic diagram of the bandpass filter of the present invention.
Fig. 4 is a schematic diagram of the meshing of the present invention.
FIG. 5 is a flow chart of the steps of the orthogonal matching pursuit algorithm of the present invention.
Fig. 6 is a diagram of spherical target buried target information of the present invention.
Fig. 7 is a diagram of the results of three-dimensional imaging of a ball target of the present invention.
Fig. 8 is a cylindrical target buried target information diagram of the present invention.
Fig. 9 is a diagram of the results of three-dimensional imaging of a cylindrical target of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
In the description of the present invention, it is to be understood that the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on the orientations or positional relationships illustrated in the drawings, and are used merely for convenience in describing the present invention and for simplicity in description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, are not to be construed as limiting the present invention. Further, in the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
Referring to fig. 1, the present invention provides a frequency diversity array radar underground target three-bit imaging method based on compressed sensing, including the following steps:
s1: two independent FDA radars are used for transmitting signals to the area to be detected and receiving echo data;
s2: after each array element receives an echo signal, performing filtering processing by using band-pass filters with different central frequencies;
s3: sampling the echo signals after filtering processing at fixed time, and recording the sampled values as vectors;
s4: establishing a three-dimensional coordinate system between the two arrays, and performing grid division on the region to be detected by using equal step length;
s5: calculating the propagation delay of each pair of array elements in the two arrays relative to each grid, and establishing a dictionary and a corresponding scene reflection coefficient by using the delay of each grid;
s6: restacking all the dictionaries divided by the z axis and the scene reflection coefficient matrixes;
s7: and reconstructing the scene reflection coefficient by using an orthogonal matching pursuit algorithm, and splitting and splicing the scene reflection coefficient according to the form of grid division to obtain a three-dimensional imaging result.
Specifically, referring to fig. 2, two FDA radars having N array elements which are mutually independent are used to transmit signals to a region to be measured and receive echo data, the distance between the two arrays is Z, and the transmission signals of the two FDA radars are represented as:
sn(t)＝sin(2πfnt)n＝1,2,…,N
wherein f isn＝f0N-1. Δ f, (N-1, 2, …, N) is the transmission frequency of the nth array element, f0The base frequency of the FDA array, n is the number of the array element, and Δ f is the frequency offset.
At this time, in the underground scenario of q targets, the signal received by the mth receiving array element is represented as:
Figure BDA0002967621970000041
wherein, beta (R) is attenuation coefficient of electromagnetic wave in propagation process, a (i) is reflection coefficient of ith target, and tauiIs the two-way time delay of the signal after the ith target reflection.
Referring to fig. 3, after each array element receives an echo signal, a bandpass filter with different center frequencies is used for filtering, where the center frequencies of the bandpass filters are:
fn＝f0+(n-1)·Δf,n＝1,2,…,N
the echo signal after filtering processing is carried out for a fixed time t0Sampling value is carried out, and the selected fixed time must meet t0＞＞max(τi) In which τ isiIs the two-way time delay of the signal after the ith target reflection. And recorded as the vector r ═ r11 r12… rnm]TWherein r isnmFor transmitting the m-th array elementThe central frequency of echo signal received by array element is fnThe band-pass filter of (2) has an expression of:
Figure BDA0002967621970000042
referring to fig. 4, a three-dimensional index system is established with the first FDA radar to the second FDA radar as the positive z-axis direction, the first array element to the nth array element of the first FDA radar as the positive x-axis direction, and the ground to the geocenter as the positive y-axis direction, and the areas to be detected are gridded on each coordinate axis by taking the equal distance Δ d as the step length.
Taking its xoy plane at each z-axis division point and calculating the propagation delay of each pair of array elements in two arrays relative to the grid, and using the delay of each grid in the plane to establish dictionary [ psi [ ]nm]zAnd corresponding scene reflection coefficient [ S ]nm]zDictionary and scene reflection coefficients are expressed as:
Figure BDA0002967621970000051
wherein [ Ψ [ ]nm]z＝[g(1,1)z,g(1,2)z,…,g(P,Q)z]A dictionary of signals received by the nth transmit and mth array elements for the z-th division point, P being the number of points along the x-axis pixel, Q being the number of points along the y-axis pixel,
Figure BDA0002967621970000052
for the delay of the transmitted signal at each grid point, v is the propagation velocity of the electromagnetic wave in the subsurface medium, RnmzRepresenting the total distance from the nth array element in the three-dimensional grid to transmit the signal received by the mth array element to the grid.
All the dictionaries divided by the z axis and the scene reflection coefficients are stacked again, and the stacked dictionaries and the stacked scene reflection coefficients are psi respectively3DAnd S3DThe stacking mode is as follows:
Figure BDA0002967621970000053
wherein [ Ψ [ ]]zAnd [ S ]]zDictionary and scene reflection coefficient constructed for the z-th division point stacked through S5.
Scene reflection coefficient S using orthogonal matching pursuit algorithm3DReconstructing, and reflecting coefficient S of scene according to form of grid division3DAnd splitting and splicing again to obtain a three-dimensional imaging result.
Referring to fig. 5, the specific steps of the orthogonal matching pursuit algorithm are as follows:
s11: inputting a preprocessed and sampled echo signal, a spliced dictionary and total iteration times;
s12: initializing a residual error, supporting an index vector set and iteration times;
s13: calculating the contribution degree of the dictionary to the echo signal;
s14: adding the found most relevant dictionary elements into an index set;
s15: and updating the residual error and the iteration number, outputting the result when the updated iteration number is equal to the total iteration number, and returning to the step S13 if the updated iteration number is not equal to the total iteration number.
Specifically, compared with the prior art, the frequency diversity array radar underground target three-dimensional imaging method based on compressed sensing has the following advantages:
the calculation is simple and easy to realize. Compared with the prior art, the method reduces the number of required echo sampling points, and not only reduces the pressure of data acquisition, but also greatly reduces the required operation amount by using FDA radar to detect the buried target;
the frequency diversity array radar underground target three-dimensional imaging result based on compressed sensing is stable. Compared with the prior art, the method can more intuitively distinguish the underground target direction, and has advantages in the stability of results.
Specific example 1:
referring to FIG. 6, a three-dimensional sand with dimensions of 2.1m 1m 0.6m is first createdGround scene, relative dielectric constant epsilon of sand usedr3, conductivity σ 0.01, relative permeability μ r1, add 4 ideal conductor pellets with a radius of 0.03m to the sand. 2 FDA-MIMO radar arrays consisting of 20 array elements are adopted for ground detection simulation, the initial frequency is 300MHz, the frequency deviation is 60MHz, the array element spacing is 10cm, and the double array spacing is 60 cm. And performing ground penetrating radar simulation by using the gprMax, and obtaining an echo signal. The frequency diversity array radar underground target three-dimensional imaging method based on compressed sensing is applied to imaging, and the imaging result shown in figure 7 can be obtained.
Specific example 2:
referring to FIG. 8, a three-dimensional sand scene with dimensions of 2.1m × 0.6m × 0.6m is created, using sand with a relative permittivity ∈ of the sandr3, conductivity σ 0.01, relative permeability μ r1. A cylinder with the diameter of 5cm is used as a buried target, and the coordinates of the centers of circles of the top surface and the bottom surface of the buried cylinder are (0.8,0.5 and 0.3) and (1.2,0.5 and 0.3) respectively. 2 FDA-MIMO radar arrays consisting of 20 array elements are adopted for ground detection simulation, the initial frequency is 300MHz, the frequency deviation is 60MHz, the array element spacing is 10cm, and the double array spacing is 60 cm. And performing ground penetrating radar simulation by using the gprMax, and obtaining an echo signal. The frequency diversity array radar underground target three-dimensional imaging method based on compressed sensing is applied to imaging, and the imaging result shown in figure 9 can be obtained.
The imaging results of the embodiment 1 and the embodiment 2 show that accurate results can be obtained by three-dimensionally imaging the underground target by using the frequency diversity array radar with compressed sensing, and imaging errors have little influence on the result position.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (6)

1. A frequency diversity array radar underground target three-dimensional imaging method based on compressed sensing is characterized by comprising the following steps:
two independent FDA radars are used for transmitting signals to the area to be detected and receiving echo data;
after each array element receives an echo signal, performing filtering processing by using band-pass filters with different central frequencies;
sampling the echo signals after filtering processing at fixed time, and recording the sampled values as vectors;
establishing a three-dimensional coordinate system between the two arrays, and performing grid division on the region to be detected by using equal step length;
calculating the propagation delay of each pair of array elements in the two arrays relative to each grid, and establishing a dictionary and a corresponding scene reflection coefficient by using the delay of each grid;
restacking all the dictionaries divided by the z axis and the scene reflection coefficient matrixes;
and reconstructing the scene reflection coefficient by using an orthogonal matching pursuit algorithm, and splitting and splicing the scene reflection coefficient according to the form of grid division to obtain a three-dimensional imaging result.
2. The method for three-dimensional imaging of underground targets by frequency diversity array radar based on compressed sensing according to claim 1, wherein in the step of transmitting signals and receiving echo data to the area to be measured by using two independent FDA radars:
the two independent FDA radars have N array elements in total, the distance is Z, the distance value is required to ensure that effective echo signals can be obtained, the amplitude of the echo signals can be estimated by 1/R, wherein R is the farthest propagation path from the array elements to the area to be detected.
3. The method for three-dimensional imaging of underground target by frequency diversity array radar based on compressed sensing as claimed in claim 2, wherein the echo signals after filtering processing are processed by a fixed time t0Sampling value taking is carried out, and the sampling value is recorded as a vector:
selected byThe fixed time taken must satisfy t0＞＞max(τi) In which τ isiIs the two-way time delay of the signal after the reflection of the ith target;
the vector is received by the m-th array element transmitted by the n-th array element, and the echo signal has a center frequency fnThe band-pass filter filters the sampled values.
4. The method for three-dimensional imaging of underground targets by frequency diversity array radar based on compressed sensing as claimed in claim 3, wherein in the step of establishing a three-dimensional coordinate system between two arrays and meshing the area to be detected with equal step length:
and taking the first FDA radar to the second FDA radar as the positive direction of a z axis, the first array element to the Nth array element of the first FDA radar as the positive direction of an x axis, the ground to the geocenter as the positive direction of a y axis to establish a three-dimensional coordinate system, and performing grid division on the regions to be detected by taking the equal distance delta d as step length on each coordinate axis.
5. The method for three-dimensional imaging of underground targets by frequency diversity array radar based on compressed sensing as claimed in claim 4, wherein the step of calculating the propagation delay of each pair of array elements in two arrays relative to each grid comprises:
each pair of array elements consists of two array elements, one array element transmits signals, and the other array element receives the signals;
the propagation delay of the grid is the delay from the transmission of the signal from the transmitting array element to the receiving array element after the reflection of the signal from the grid.
6. The method for three-dimensional imaging of underground targets by frequency diversity array radar based on compressed sensing as claimed in claim 5, wherein the step of establishing the dictionary and the corresponding scene reflection coefficients by using the time delay of each grid comprises:
the scene reflection coefficient corresponds to the dictionary and has the same form and arrangement, wherein each element is the reflection coefficient of the grid at the position.
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