CN116719023A - Method for estimating dielectric constant under joint constraint of GPR energy focusing and resolution - Google Patents
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Abstract
The invention provides a dielectric constant estimation method under the joint constraint of GPR energy focusing and resolution, which comprises the steps of traversing a dielectric constant value in a certain range, searching a focusing peak value after offset imaging under a corresponding dielectric constant, calculating a ratio error of a distance resolution and a direction resolution, and taking the ratio of the imaging focusing peak value to the relative resolution error as an evaluation index of the estimated dielectric constant. The dielectric constant corresponding to the maximum index value is used as the estimated dielectric constant value of the medium. The invention can improve the estimation efficiency and the estimation accuracy.
Description
Technical Field
The invention belongs to the technical field of ground penetrating radars, and particularly relates to a dielectric constant estimation method under the joint constraint of GPR energy focusing and resolution.
Background
In the detection of the ground penetrating radar, the speed of the electromagnetic wave can change when the electromagnetic wave propagates in the underground medium due to the difference of dielectric constants, so the magnitude of the dielectric constants is important for the accurate imaging of the ground penetrating radar. Particularly for air-coupled ground penetrating radars, such as airborne GPR (Ground Penetrating Radar ), vehicle-mounted GPR and other layered medium experimental scenes, refraction phenomena can occur on the interfaces of the media, so that the propagation paths and propagation speeds of the waves are changed, and the electromagnetic waves are attenuated to different degrees in different media. The relative dielectric constant of the medium directly influences the final imaging focusing capability and the determination of the depth of the target, and if the dielectric constant is inaccurate, defocusing of imaging can occur, and the depth information of the target is inaccurate. Thus, accurate estimation of the dielectric constant is critical for accurate detection of subsurface targets by ground penetrating radar.
The existing methods for measuring the relative dielectric constant of the medium comprise a known target depth method, a point source reflector method and the like, but the methods need to know the target depth in advance and require a target curve to be clear enough, in an actual measurement scene, the known target depth is unrealistic in advance, the depth of the target cannot be obtained in some dangerous areas, and more clutter exists around the echo of the target curve; the common-center point method and the lamellar reflection method are only suitable for receiving and transmitting separated antennas, the application range is limited, and the result error is larger. These methods can only be used under specific conditions and scenarios, and when the conditions are not ideal, the resulting errors obtained become large.
In the ground penetrating radar, the closer the dielectric constant is to the true value, the better the imaging focusing effect is, and the better the imaging resolution is; when the dielectric constant deviates from the true value, defocusing occurs in imaging, energy is not concentrated, and resolution also deviates from the theoretical value. Thus, at true dielectric constants, the imaging focus center amplitude adds up to a maximum, and when the dielectric constants are offset, the focus center amplitude decreases. According to theoretical calculation of the ground penetrating radar in the distance direction and the azimuth direction, the relative resolution, namely the ratio of the distance direction and the azimuth direction is related to the dielectric constant, so that when the dielectric constant is closest to a true value, the error between the actual resolution ratio and the theoretical ratio is minimum, otherwise, the error is increased.
Disclosure of Invention
In order to solve the technical problems, the invention provides a dielectric constant estimation method under the joint constraint of GPR energy focusing and resolution, which is characterized in that a focusing peak value after offset imaging under a corresponding dielectric constant is firstly found by traversing a dielectric constant value in a certain range, then the ratio error of distance resolution and azimuth resolution is calculated, and the ratio of the imaging focusing peak value to the relative resolution error is used as an evaluation index for estimating the dielectric constant. The dielectric constant corresponding to the maximum index value is used as the estimated dielectric constant value of the medium.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a medium dielectric constant estimation method under the joint constraint of GPR energy focusing and resolution ratio comprises the following steps:
step S1: collecting data by using a ground penetrating radar, and preprocessing a received echo time domain signal; in one radar measurement, the time domain signal of the ith sample in the waveform of the echo time domain signal after preprocessing is expressed as x i ；
Step S2: correcting uneven terrain, respectively extracting the arrival time of the maximum signal of each sample for all time domain samples obtained by measuring the air-coupled ground penetrating radar as the arrival time of the emission signal of the ground penetrating radar to the ground, calculating to obtain the average height of the radar, correcting the height of each sample to the average height, and obtaining an echo time domain signal after correction;
step S3: removing ground clutter and noise from the corrected echo time domain signal by using a singular value decomposition method, and removing signals except a target echo;
step S4: the imaging focusing is completed by utilizing a back projection technology, grids are divided into imaging areas, the refraction point and the corresponding time delay of each grid point are repeatedly calculated, and an imaging focusing matrix is obtained;
step S5: estimating dielectric constants of the media, traversing a certain range of dielectric constant values according to experience cognition of the media, finding out corresponding imaging focusing peak values and resolutions in the distance direction and the azimuth direction, searching the maximum value of the ratio of the imaging focusing peak values to the relative resolution error, wherein the corresponding dielectric constants are pre-estimated values, and the relative resolution is the ratio of the distance direction resolution to the azimuth direction resolution.
Further, the preprocessing in step S1 includes compensating for system delay, removing the direct wave signal to remove the fixed background and filtering out multiple reflections.
Further, the step S2 includes calculating a distance z between the ground penetrating radar and the ground at each sample i Each sample is movedSo that the ground is corrected to the same level, wherein +.>Is the average value of all distances; the time domain echo signal after correction is expressed as:
x(m,n)＝g(m,n)+o(m,n)+n(m,n) (4)
where x (m, n) is the corrected time domain echo signal, g (m, n) represents the reflected echo of the ground, o (m, n) represents the reflected signal of the subsurface target, and n (m, n) represents noise and other clutter in the environment.
Further, the step S4 includes finding amplitude { a } of the corresponding imaging point on all A-scan data of the antenna according to the obtained time delay 1 ,a 2 ,...,a L Adding the amplitude values to obtain an amplitude added value of the imaging pointThe imaging focusing matrix of the whole imaging area after delay and amplitude accumulation is expressed as A (M, N), the dividing grid of the imaging area is M multiplied by N, L is the acquisition channel number of the antenna on one measuring line, and A (x) m ,y n ) For imaging grid points (x m ,y n ) An amplitude accumulated value at.
Further, the step S5 includes the steps of:
the first step: calculating resolution: the detection resolution of the ground penetrating radar comprises a distance resolution and a azimuth resolution;
(1) The range resolution of a radar is typically defined as:
where c is the propagation velocity of the electromagnetic wave in vacuum, ε r The relative dielectric constant of the medium, B is the effective bandwidth of the radar;
(2) The azimuth resolution calculation process is as follows:
the law of refraction of electromagnetic waves is as follows:
wherein ,for the beam width of the antenna in air, +.>Epsilon for the beam width of the antenna in the subsurface medium r Is the relative dielectric constant of the medium;
the beam width of the antenna in air is:
wherein ,λ0 For the wavelength of the antenna in the air, byDetermining f 0 The center frequency of the antenna work is the aperture of the antenna;
combining equation (6) and equation (7) yields an antenna beam width in the subsurface medium of:
the synthetic aperture length of the antenna after the change is:
wherein R is an inclined distance;
the electromagnetic wave velocity entering the underground medium is:
the azimuth resolution of the radar is:
substituting equation (8), equation (9), and equation (10) into equation (11) yields the radar with an azimuthal resolution in the medium of:
therefore, the ratio of the distance resolution to the azimuth resolution is:
and a second step of: searching for an imaging focus peak:
searching for peaks of the imaging focus matrix a (M, N), expressed as:
A(p)＝max(max(A p (M,N))) (10)
wherein ,Ap (M, N) is a focusing imaging matrix with a dielectric constant p, A p Is the corresponding focus peak;
and a third step of: calculating the ratio of the resolution in the distance direction and the azimuth direction:
the ratio of the distance resolution to the azimuth resolution is denoted as the relative resolution, and when the dielectric constant is p, the theoretical ratio is expressed as:
obtaining the actual relative resolution of k through actual measurement data processing;
fourth step: calculating the ratio of the imaging focus peak to the relative resolution error, expressed as:
wherein ,k0 The numerical value of the ratio coefficient of the two theoretical resolutions is determined by external conditions and experimental experience;
fifth step: search mu p I.e. the dielectric constant pre-estimated value is p|max (mu) p )。
The beneficial effects are that:
(1) The invention provides a method for estimating the dielectric constant of an underground medium under the joint constraint of signal focusing and resolution, when the signal focusing and resolution are close to the actual dielectric constant, the image focusing peak value is maximum, the relative resolution error is minimum, the result of the ratio of the two is larger than that of other dielectric constants, and the estimation accuracy of the dielectric constant can be shown.
(2) The estimated dielectric constant of the underground medium can provide help for mastering the condition of the underground medium, and can improve the ascertaining rate of an underground target and the accuracy of the depth information of the target when used for subsequent processing.
(3) The dielectric constant pre-estimation method based on focusing and resolution provided by the invention has high calculation efficiency, reduces the search range for the accurate estimation of the subsequent dielectric constant, and can improve the estimation efficiency and the estimation accuracy.
(4) The dielectric constant estimation method provided by the invention has wide application scene range, no antenna mode limit, no experimental scene limit and the like, and is simultaneously suitable for the ground penetrating radar and the space coupling ground penetrating radar.
Drawings
FIG. 1 is a flow chart of a method for estimating dielectric permittivity under joint constraint of GPR energy focusing and resolution of the present invention.
Detailed Description
In order to further clarify the technical solution, the gist of the present invention and the advantages thereof, the following details of the procedure for carrying out the present invention are provided.
The invention relates to a method for estimating dielectric constant under the joint constraint of GPR energy focusing and resolutionIn the estimation of dielectric constant byThe implementation shows that after traversing a range of values of dielectric constant,the dielectric constant value corresponding to the maximum value is taken. Wherein A represents an imaging focusing matrix, deltad and Deltar are respectively the theoretical range-wise resolution and the azimuth-wise resolution of the radar, k is the ratio of the measured data range-wise resolution to the azimuth-wise resolution, and k 0 For two theoretical resolution ratio coefficients, p is an estimate of the dielectric constant, and max (·) represents the maximum value.
As shown in fig. 1, a method for estimating dielectric permittivity under joint constraint of GPR energy focusing and resolution according to the present invention includes the steps of:
step S1: and acquiring data by using a ground penetrating radar, and preprocessing a received echo time domain signal, wherein the preprocessing comprises compensating system delay, removing a direct wave signal, removing a fixed background, filtering multiple reflections and the like. In one radar measurement, the time domain signal of the ith sample in the waveform of the echo time domain signal after preprocessing is expressed as x i 。
Step S2: and correcting uneven terrain, and respectively extracting the arrival time of the maximum signal of each sample for all time domain samples obtained by measuring the air-coupled ground penetrating radar as the arrival time of the ground penetrating radar transmitting signal. Calculating the distance z between the ground penetrating radar and the ground at each sample i Each sample is moved(/>Is the average of all distances) so that the ground is corrected to the same horizontal plane. The echo time domain signal after correction is expressed as:
x(m,n)＝g(m,n)+o(m,n)+n(m,n) (4)
where x (m, n) is the corrected echo time domain signal, g (m, n) represents the reflected echo of the ground, o (m, n) represents the reflected signal of the subsurface target, and n (m, n) represents noise and other clutter in the environment.
For a ground-coupled ground-penetrating radar, no terrain correction is required, and this step can be skipped.
Step S3: and removing ground clutter and noise from the corrected echo time domain signal by using a singular value decomposition method, and removing signals except the target echo so as to reduce the influence on subsequent processing.
Step S4: the back projection technology is used for completing imaging focusing, the idea of delay-summation is mainly used for dividing the imaging area into grids, and the refraction point and the corresponding time delay of each grid point are repeatedly calculated. Finding amplitude value { a } of corresponding imaging point on all A-scan data of antenna according to obtained time delay 1 ,a 2 ,…,a L Adding the amplitudes to obtain an amplitude added value of the imaging pointThe imaging focus matrix after delay and amplitude accumulation of the entire imaging region is denoted as a (M, N).
The grid division of the imaging area is M multiplied by N, L is the acquisition channel number of the antenna on one measuring line, A (x) m ,y n ) For imaging grid points (x m ,y n ) An amplitude accumulated value at.
Step S5: and estimating the dielectric constant of the medium, traversing a certain range of dielectric constants according to experience cognition of the medium, finding out the corresponding imaging focusing peak value and the resolution in the distance direction and the azimuth direction, searching the maximum value of the ratio of the imaging focusing peak value to the relative resolution error (the relative resolution is the ratio of the distance direction resolution to the azimuth direction resolution), and obtaining the corresponding dielectric constant as a pre-estimated value. The method specifically comprises the following steps.
The first step: calculating resolution:
the detection resolution of the ground penetrating radar includes a range-wise resolution and a azimuth-wise resolution.
(1) The range resolution of a radar is typically defined as:
where c is the propagation velocity of the electromagnetic wave in vacuum, ε r B is the effective bandwidth of the radar, which is the relative permittivity of the medium.
(2) The derivation process of the azimuth resolution is as follows:
in the space-coupling GPR, the electromagnetic wave is refracted when entering the underground medium, so that the beam width of the antenna is changed, and the incident angle and the refraction angle of the electromagnetic wave are respectively the half-wave beam width before and after refraction.
The law of refraction of electromagnetic waves is as follows:
wherein ,for the beam width of the antenna in air, +.>Epsilon for the beam width of the antenna in the subsurface medium r Is the relative dielectric constant of the medium.
The beam width of the antenna in air is:
wherein ,λ0 For the wavelength of the antenna in the air, byDetermining f 0 The center frequency of the antenna is the working center frequency, and D is the caliber of the antenna.
Combining equation (6) and equation (7) can result in an antenna beam width in the subsurface medium of:
the synthetic aperture length of the antenna after the change is:
wherein R is the slant distance.
The electromagnetic wave velocity entering the underground medium is:
the azimuth resolution of the radar is:
substituting equation (8), equation (9), and equation (10) into equation (11) yields a radar in-medium azimuth resolution of:
therefore, the ratio of the distance resolution to the azimuth resolution is:
so when the dielectric constant is close to the true value, the error between the actual resolution ratio and the theoretical ratio is very small; when the dielectric constant deviates from the true value, the ratio error of the resolution becomes large.
And a second step of: searching for an imaging focus peak:
searching for peaks of the imaging focus matrix a (M, N), expressed as:
A(p)＝max(A p (M,N)) (10)
wherein ,Ap (M, N) is a focusing imaging matrix with a dielectric constant p, A p Is the corresponding focus peak.
When the dielectric constant is a true value, the focusing effect is best, and the corresponding focusing center amplitude value is the largest; when the dielectric constant deviates from the true value, defocus occurs in imaging, and the amplitude value becomes small.
And a third step of: calculating the ratio of the resolution in the distance direction and the azimuth direction:
the ratio of the distance resolution to the azimuth resolution is denoted as the relative resolution, and when the dielectric constant is p, the theoretical ratio is expressed as:
the actual relative resolution is k through actual measurement data processing.
Fourth step: calculating the ratio of the imaging focus peak to the relative resolution error, expressed as:
wherein ,k0 The numerical values of the two theoretical resolution ratio coefficients are determined by external conditions and experimental experience.
Fifth step: search mu p I.e. the dielectric constant pre-estimated value is p|max (mu) p )。
In summary, the dielectric constant estimation method provided by the invention can provide guarantee for accurate detection of the ground penetrating radar. The focusing maximum value and the resolution are directly obtained from the focusing result, the estimation efficiency is high, and the calculated amount is small; from two aspects, the method improves the accuracy of dielectric constant estimation.
Claims (5)
1. A method for estimating dielectric constant under the joint constraint of GPR energy focusing and resolution is characterized by comprising the following steps:
step S1: collecting data by using a ground penetrating radar, and preprocessing a received echo time domain signal; in one radar measurement, the time domain signal of the ith sample in the preprocessed echo time domain signal waveform is expressed as x i ；
Step S2: correcting uneven terrain, respectively extracting the arrival time of the maximum signal of each sample for all time domain samples obtained by measuring the air-coupled ground penetrating radar as the arrival time of the emission signal of the ground penetrating radar to the ground, calculating to obtain the average height of the radar, correcting the height of each sample to the average height, and obtaining an echo time domain signal after correction;
step S3: removing ground clutter and noise from the corrected echo time domain signal by using a singular value decomposition method, and removing signals except a target echo;
step S4: the imaging focusing is completed by utilizing a back projection technology, grids are divided into imaging areas, the refraction point and the corresponding time delay of each grid point are repeatedly calculated, and an imaging focusing matrix is obtained;
step S5: estimating dielectric constants of the media, traversing a certain range of dielectric constant values according to experience cognition of the media, finding out corresponding focusing peak values and resolutions in a distance direction and a direction, searching the maximum value of the ratio of imaging focusing peak values to relative resolution errors, wherein the corresponding dielectric constants are pre-estimated values, and the relative resolution is the ratio of the distance direction resolution to the direction resolution.
2. The method according to claim 1, wherein the preprocessing in step S1 includes compensating for system delay, removing direct wave signal to remove fixed background and filtering multiple reflections.
3. A GPR energy focusing and resolution combination as defined in claim 1The method for estimating dielectric permittivity under the constraint is characterized in that the step S2 comprises calculating the distance z between the ground penetrating radar and the ground at each sample i Each sample is movedSo that the ground is corrected to the same horizontal plane, where z is the average of all distances; the time domain echo signal after correction is expressed as:
x(m,n)＝g(m,n)+o(m,n)+n(m,n) (4)
where x (m, n) is the corrected time domain echo signal, g (m, n) represents the reflected echo of the ground, o (m, n) represents the reflected signal of the subsurface target, and n (m, n) represents noise and other clutter in the environment.
4. A method as claimed in claim 3, wherein said step S4 comprises finding the amplitude { a } of the corresponding imaging point on all a-scan data of the antenna based on the obtained time delay 1 ,a 2 ,...,a L Adding the amplitude values to obtain an amplitude added value of the imaging pointThe imaging focusing matrix of the whole imaging area after delay and amplitude accumulation is expressed as A (M, N), the dividing grid of the imaging area is M multiplied by N, L is the acquisition channel number of the antenna on one measuring line, and A (x) m ,y n ) For imaging grid points (x m ,y n ) An amplitude accumulated value at.
5. The method for estimating the dielectric constant of the medium under the joint constraint of energy focusing and resolution of GPR according to claim 4, wherein said step S5 comprises the steps of:
the first step: calculating resolution: the detection resolution of the ground penetrating radar comprises a distance resolution and a azimuth resolution;
(1) The range resolution of a radar is typically defined as:
where c is the propagation velocity of the electromagnetic wave in vacuum, ε r The relative dielectric constant of the medium, B is the effective bandwidth of the radar;
(2) The azimuth resolution calculation process is as follows:
the law of refraction of electromagnetic waves is as follows:
wherein ,for the beam width of the antenna in air, +.>Epsilon for the beam width of the antenna in the subsurface medium r Is the relative dielectric constant of the medium;
the beam width of the antenna in air is:
wherein ,λ0 For the wavelength of the antenna in the air, byDetermining f 0 The center frequency of the antenna work is the aperture of the antenna;
combining equation (6) and equation (7) yields an antenna beam width in the subsurface medium of:
the synthetic aperture length of the antenna after the change is:
wherein R is an inclined distance;
the electromagnetic wave velocity entering the underground medium is:
the azimuth resolution of the radar is:
substituting equation (8), equation (9), and equation (10) into equation (11) yields the radar with an azimuthal resolution in the medium of:
therefore, the relative resolution, i.e. the ratio of the distance-wise resolution to the azimuth-wise resolution, is:
and a second step of: searching for an imaging focus peak:
searching for peaks of the imaging focus matrix a (M, N), expressed as:
A(p)＝max(A p (M,N)) (10)
wherein ,Ap (M, N) is a focusing imaging matrix with a dielectric constant p, A p Is the corresponding focus peak;
and a third step of: calculating the ratio of the resolution in the distance direction and the azimuth direction:
the ratio of the distance resolution to the azimuth resolution is denoted as the relative resolution, and when the dielectric constant is p, the theoretical ratio is expressed as:
obtaining the actual relative resolution of k through actual measurement data processing;
fourth step: calculating the ratio of the imaging focus peak to the relative resolution error, expressed as:
wherein ,k0 The numerical value of the ratio coefficient of the two theoretical resolutions is determined by external conditions and experimental experience;
fifth step: search mu p I.e. the dielectric constant pre-estimated value is p|max (mu) p )。
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