CN113109807B - 3D Imaging Method of Underground Targets in Frequency Diversity Array Radar Based on Compressed Sensing - Google Patents

Abstract

The invention discloses a three-dimensional imaging method of a target under a frequency diversity array radar based on compressive sensing. Two FDA radars are used to transmit signals in a region to be measured and receive echo data, and then band-pass filters with different center frequencies are used for filtering processing. The value is sampled at a fixed time and recorded as a vector. Then, a rectangular coordinate system is established for the area to be detected, and the detection area is divided into grids, and the propagation delay of each cell in the two arrays relative to the grid is calculated. The time delay of each grid establishes a dictionary and the corresponding scene reflection coefficients, re-stacks all the divided dictionaries and scene reflection coefficients, uses the orthogonal matching pursuit algorithm to reconstruct the scene reflection coefficients, and finally splits the scene reflection coefficients After re-splicing, three-dimensional imaging results can be obtained, thus reducing the number of echo sampling points required, reducing the pressure of data acquisition, and making the imaging results more stable, and the azimuth of the underground target can be more intuitively distinguished.

Description

3D Imaging Method of Underground Targets in Frequency Diversity Array Radar Based on Compressed Sensing

technical field

The invention relates to the technical field of ground penetrating radar signal processing, in particular to a three-dimensional imaging method for underground targets of frequency diversity array radar based on compressed sensing.

Background technique

Because the frequency diversity array has the advantages of single frequency and simultaneous transmission and reception, the frequency diversity array radar underground target imaging technology has a wide range of application prospects in the military and civil fields. At present, most of the frequency diversity arrays studied by people are aimed at the target in free space, and the target is imaged by signal source localization or back projection. Most of these radar target imaging technologies are the results of a large number of operations using mathematical models, not only the algorithms are not easy to achieve real-time and accuracy requirements, but also cannot be directly applied to the underground environment.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a three-dimensional imaging method of frequency diversity array radar underground target for compressive sensing, which aims to solve the problem that the algorithm adopted by the traditional method in the prior art is not easy to achieve real-time and accuracy requirements, and cannot be directly applied to underground targets. Environmental technical issues.

In order to achieve the above object, a compressive sensing-based frequency diversity array radar three-dimensional imaging method for underground targets adopted in the present invention includes the following steps:

Use two FDA radars that are independent of each other and have a total of N array elements to transmit signals and receive echo data in the area to be measured;

After each array element receives the echo signal, use band-pass filters with different center frequencies for filtering;

The filtered echo signal is sampled at a fixed time t ₀ and recorded as a vector;

The two FDA radars are set in parallel, with the first FDA radar to the second FDA radar as the z-axis positive direction, the first FDA radar to the N/2th array element as the x-axis positive direction, the ground Go to the center of the earth to establish a three-dimensional coordinate system for the positive direction of the y-axis, and use equal steps to divide the area to be detected;

Calculate the propagation delay of each cell in the two arrays relative to each grid, and use the delay of each grid to establish a dictionary and the corresponding scene reflection coefficient;

Restack all z-division dictionaries and scene reflection coefficient matrices;

The scene reflection coefficient is reconstructed by using the orthogonal matching pursuit algorithm, and the scene reflection coefficient is split and re-spliced according to the form of grid division, and the 3D imaging result can be obtained.

In the steps of using two independent FDA radars to transmit signals and receive echo data from the area to be measured:

Two independent FDA radars have a total of N array elements, and the spacing is Z. The value of the spacing should ensure that an effective echo signal can be obtained. 1/R can be used to estimate the echo signal amplitude, where R is the signal propagation for the array element to The farthest propagation path of the area to be detected.

In the steps of sampling the filtered echo signal at a fixed time t ₀ and recording it as a vector:

The selected fixed time must satisfy t ₀ >>max(τ _i ), where τ _i is the two-way delay of the signal reflected by the ith target;

The vector is the sampling value filtered by the band-pass filter with the center frequency f _n of the echo signal received by the m-th array element transmitted by the n-th array element.

In the step of meshing the area to be probed with equal steps:

The area to be detected is divided into grids with equal distance Δd as the step size on each coordinate axis.

In the steps of calculating the propagation delay of each cell in the two arrays relative to each grid:

Each array element consists of two array elements, one array element transmits the signal, and the other array element receives its signal;

The propagation delay of the grid is the delay from the transmitting array element to the receiving array element after the signal is reflected from the grid.

And in the steps of establishing a dictionary and corresponding scene reflection coefficients with the delay of each grid:

The scene reflectance corresponds to a dictionary, with the same form and arrangement, where each element is the reflectance of the mesh at that location.

The beneficial effects of the invention are as follows: calculation is simple, easy to implement, and the number of required echo sampling points is reduced; by using FDA radar for buried target detection, not only the pressure of data acquisition is reduced, but also the required calculation amount is greatly reduced, At the same time, the imaging results are more stable, and the azimuth of the underground target can be distinguished more intuitively.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

FIG. 1 is a flow chart of the steps of the compressive sensing-based frequency diversity array radar three-dimensional imaging method for underground targets of the present invention.

Figure 2 is a schematic diagram of the location of two arrays of the present invention.

FIG. 3 is a schematic diagram of a 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 an information map of the ball target buried target of the present invention.

FIG. 7 is a three-dimensional imaging result diagram of a spherical target of the present invention.

FIG. 8 is an information diagram of a buried target of a cylindrical target of the present invention.

FIG. 9 is a result diagram of three-dimensional imaging of a cylindrical target of the present invention.

Detailed ways

The following describes in detail the embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary, and are intended to explain the present invention and should not be construed as limiting the present invention.

In the description of the present invention, it should be understood that the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", The orientations or positional relationships indicated by "horizontal", "top", "bottom", "inside", "outside", etc. are based on the orientations or positional relationships shown in the accompanying drawings, which are only for the convenience of describing the present invention and simplifying the description, rather than Indication or implication that the referred device or element must have a particular orientation, be constructed and operate in a particular orientation, is not to be construed as a limitation of the invention. In addition, in the description of the present invention, "plurality" means two or more, unless otherwise expressly and specifically defined.

Referring to FIG. 1, the present invention provides a three-dimensional imaging method for an underground target of a frequency diversity array radar based on compressed sensing, including the following steps:

S1: Use two FDA radars that are independent of each other and have a total of N array elements to transmit signals and receive echo data in the area to be measured;

S2: After each array element receives the echo signal, use bandpass filters with different center frequencies for filtering;

S3: Sampling and taking the value of the echo signal after filtering at a fixed time, and recording it as a vector;

S4: Two FDA radars are set in parallel, with the first FDA radar to the second FDA radar as the positive direction of the z-axis, and the first to the N/2th array element of the first FDA radar as the positive direction of the x-axis , the ground to the center of the earth is the positive direction of the y-axis to establish a three-dimensional coordinate system, and the area to be detected is meshed with equal steps;

S5: Calculate the propagation delay of each cell in the two arrays relative to each grid, and use the delay of each grid to establish a dictionary and corresponding scene reflection coefficients;

S6: Re-stack all z-axis divided dictionaries and scene reflection coefficient matrices;

S7: Use the orthogonal matching pursuit algorithm to reconstruct the scene reflection coefficient, and split and re-splicing the scene reflection coefficient according to the form when dividing the grid, so as to obtain the three-dimensional imaging result.

Specifically, please refer to Figure 2. Two FDA radars with a total of N independent array elements are used to transmit signals and receive echo data in the area to be measured. The distance between the two arrays is Z, and the transmitted signals of the two FDA radars are expressed as:

s _n (t)=sin(2πf _n t)n=1,2,…,N

Among them, f _n =f ₀ +(n-1)·Δf, (n=1,2,...,N) is the transmit frequency of the nth array element, f ₀ is the fundamental frequency of the FDA array, and n is the array element , Δf is the frequency offset.

At this time, in the underground scene of q targets, the signal received by the mth receiving array element is expressed as:

Among them, β(R) is the attenuation coefficient of the electromagnetic wave during the propagation process, a(i) is the reflection coefficient of the ith target, and τ _i is the two-way delay of the signal reflected by the ith target.

Please refer to Figure 3. After each array element receives the echo signal, it uses band-pass filters with different center frequencies for filtering. The center frequencies of the band-pass filters are:

f _n =f ₀ +(n-1)·Δf,n=1,2,...,N

The filtered echo signal is sampled at a fixed time t ₀ , and the selected fixed time must satisfy t ₀ >>max(τ _i ), where τ _i is the round-trip delay of the signal reflected by the ith target. And record it as a vector r=[r ₁₁ r ₁₂ ... r _nm ] ^T , where r _nm is the echo signal transmitted by the nth array element and received by the mth array element after bandpass filtering with the center frequency _fn The sampled value filtered by the filter, its expression is:

Please refer to Figure 4. Take the first FDA radar to the second FDA radar as the z-axis positive direction, the first FDA radar to the N/2th array element as the x-axis positive direction, the ground to the ground The center is the positive direction of the y-axis to establish a three-dimensional index system, and the area to be detected is divided into grids with equal distance Δd as the step size on each coordinate axis.

Take its xoy plane at each z-axis division point and calculate the propagation delay of each cell in the two arrays relative to the grid, and use the delay of each grid on this plane to establish a dictionary [Ψ _nm ] _z and the corresponding scene The reflection coefficient [S _nm ] _z , the dictionary and scene reflection coefficients are expressed as:

为发射信号在各个网格点的延迟，v是电磁波在地下介质中的传播速度，R_nmz表示在三维网格中第n个阵元发射被第m个阵元接收的信号到网格的总距离。Among them, [Ψ _nm ] _z =[g(1,1) _z ,g(1,2) _z ,...,g(P,Q) _z ] is the zth division point by the nth emission array element and the dictionary of the received signal of the mth array element, P is the number of pixels along the x-axis, Q is the number of pixels along the y-axis,

is the delay of the transmitted signal at each grid point, v is the propagation speed of the electromagnetic wave in the underground medium, and R _nmz represents the total amount of the signal received by the n-th array element transmitted by the m-th array element to the grid in the three-dimensional grid. distance.

All z-axis divided dictionaries and scene reflection coefficients are re-stacked. The stacked dictionaries and scene reflection coefficients are Ψ _3D and S _3D respectively, and the stacking methods are as follows:

Ψ _3D = [[Ψ] ₁ [Ψ] ₂ ... [Ψ] _Z ]

Among them, [Ψ] _z and [S] _z are the dictionary and scene reflection coefficients composed of the zth division point stacked by S5.

The scene reflection coefficient S _3D is reconstructed by using the orthogonal matching pursuit algorithm, and the scene reflection coefficient S _3D is split and re-spliced according to the form of grid division, and the three-dimensional imaging result can be obtained.

Please refer to Figure 5. The specific steps of the orthogonal matching pursuit algorithm are:

S11: Input the echo signal of preprocessing sampling, the spliced dictionary and the total number of iterations;

S12: Initialization residual, support index vector set and iteration number;

S13: Calculate the contribution of the dictionary to the echo signal;

S14: Add the most relevant dictionary elements found to the index set;

S15: Update the residual and the number of iterations, when the updated number of iterations is equal to the total number of iterations, output the result, otherwise return to step S13.

Specifically, compared with the prior art, the three-dimensional imaging method for underground targets of frequency diversity array radar based on compressed sensing has the following advantages:

The calculation is simple and easy to implement. Compared with the prior art, the present invention reduces the number of required echo sampling points, and by using FDA radar for buried target detection, not only reduces the pressure of data acquisition, but also greatly reduces the required calculation amount;

The 3D imaging results of the frequency diversity array radar underground target based on compressed sensing are stable. Compared with the prior art, the method of the present invention can more intuitively distinguish the orientation of the underground target, and the method of the present invention also has advantages in the stability of the results.

Specific embodiment 1:

Please refer to Fig. 6. First, create a 3D sand scene with a size of 2.1m×1m×0.6m. The sand used has relative permittivity ε _r =3, electrical conductivity σ = 0.01, and relative magnetic permeability μ _r =1 , add 4 ideal conductor spheres with a radius of 0.03m in the sand. Two FDA-MIMO radar arrays consisting of 20 array elements are used for ground penetrating simulation. The initial frequency is 300MHz, the frequency offset is 60MHz, the distance between the array elements is 10cm, and the interval between the two arrays is 60cm. Use gprMax to simulate ground penetrating radar and get the echo signal. By applying the three-dimensional imaging method of the frequency diversity array radar underground target based on the compressed sensing of the present invention for imaging, the imaging result as shown in FIG. 7 can be obtained.

Specific embodiment 2:

Referring to Figure 8, a three-dimensional sand scene with a size of 2.1m × 0.6m × 0.6m is established. The sand used has a relative permittivity ε _r = 3, an electrical conductivity σ = 0.01, and a relative magnetic permeability μ _r = 1. A cylinder with a diameter of 5 cm was used as the buried target, and the center coordinates of the top and bottom surfaces of the buried cylinder were (0.8, 0.5, 0.3) and (1.2, 0.5, 0.3), respectively. Two FDA-MIMO radar arrays consisting of 20 array elements are used for ground penetrating simulation. The initial frequency is 300MHz, the frequency offset is 60MHz, the distance between the array elements is 10cm, and the interval between the two arrays is 60cm. Use gprMax to simulate ground penetrating radar and get the echo signal. The imaging result shown in FIG. 9 can be obtained by applying the three-dimensional imaging method of the frequency diversity array radar underground target based on the compressed sensing of the present invention for imaging.

The imaging results of Example 1 and Example 2 show that accurate results can be obtained by using compressed sensing frequency diversity array radar to image three-dimensional underground targets, and the imaging error has little effect on the result position.

The above disclosure is only a preferred embodiment of the present invention, and of course, it cannot limit the scope of rights of the present invention. Those of ordinary skill in the art can understand that all or part of the process for realizing the above-mentioned embodiment can be realized according to the rights of the present invention. The equivalent changes required to be made still belong to the scope covered by the invention.

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:

transmitting signals to a region to be detected by using two FDA radars which are independent from each other and have N array elements in total 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;

the two FDA radars are arranged in parallel, a three-dimensional coordinate system is established by taking a first FDA radar to a second FDA radar as the positive direction of a z axis, a first array element to an N/2 array element of the first FDA radar as the positive direction of an x axis, and a ground to geocenter as the positive direction of a y axis, and the areas to be detected are subjected to grid division 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 t ₀ Sampling and taking values, and recording the values as vectors:

the selected fixed time must satisfy t ₀ ＞＞max(τ _i ) In which τ is _i Is 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 f _n The 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 meshing the area to be detected with equal step size:

and performing grid division on the region 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 objects by frequency diversity array radar based on compressed sensing as claimed in claim 5, wherein the step of building the dictionary and the corresponding reflection coefficient of the scene 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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