Method for estimating permittivity of medium under joint constraints of gpr energy focusing and resolution

Abstract

The application provides a medium dielectric constant estimation method under GPR energy focusing and resolution joint constraint, through traversing a range of dielectric constant values, firstly, a focusing peak after migration imaging under a corresponding dielectric constant is found, then a ratio error of distance direction resolution and azimuth direction resolution is calculated, a ratio of the imaging focusing peak and the relative resolution error is taken as an evaluation index of the estimated dielectric constant, and when the index value is maximum, the corresponding dielectric constant is taken as the dielectric constant estimation value of the medium. The application can improve estimation efficiency and estimation accuracy.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of ground penetrating radar, and particularly relates to a medium dielectric constant estimation method under joint constraints of GPR energy focusing and resolution. BACKGROUND

[0002] In ground penetrating radar detection, due to the difference in dielectric constant, the speed of electromagnetic wave changes when propagating in the underground medium, and therefore, the size of the dielectric constant is crucial for the accurate imaging of the ground penetrating radar. Especially for air-coupled ground penetrating radar, such as airborne GPR (Ground Penetrating Radar), vehicle-mounted GPR and other layered medium experimental scenes, electromagnetic waves will be refracted at the medium interface, resulting in changes in the propagation path and speed of the wave, and causing different degrees of attenuation of electromagnetic waves in different media. The relative dielectric constant of the medium directly affects the final imaging focusing ability and the determination of the target depth, and if the dielectric constant is not accurate, the imaging will appear out of focus, and the depth information of the target will also be inaccurate. Therefore, accurate estimation of the dielectric constant is crucial for accurate detection of underground targets by ground penetrating radar.

[0003] The existing methods for measuring the relative dielectric constant of the medium include the known target depth method, the point source reflector method, etc., but such methods require prior knowledge of the target depth and require the target curve to be clear enough. In actual measurement scenarios, it is not realistic to know the target depth in advance, and in some dangerous areas, it is impossible to obtain the depth of the target, and there are many clutter around the target curve echo. The common center point method and the layered reflection method are only applicable to the transceiver separation antenna, the scope of application is limited, and the result error is large. These methods can only be used under specific conditions and scenes, and when the conditions are not ideal, the error of the obtained results will be large.

[0004] In ground penetrating radar, the closer the dielectric constant is to the true value, the better the imaging focusing effect and the better the imaging resolution; when the dielectric constant deviates from the true value, the imaging will appear out of focus, the energy is not concentrated, and the resolution also deviates from the theoretical value. Therefore, under the true dielectric constant, the imaging focusing center amplitude accumulation is maximum, and when the dielectric constant deviates, the focusing center amplitude decreases. According to the theoretical calculation in the range direction and the azimuth direction of the ground penetrating radar, the relative resolution, i.e. the ratio of the two, is related to the dielectric constant, and therefore, when the dielectric constant is closest to the true value, the actual resolution ratio should have the smallest error with the theoretical ratio, otherwise, the error will increase. SUMMARY

[0005] To solve the above technical problems, the present application provides a medium dielectric constant estimation method under the joint constraint of GPR energy focusing and resolution, which first finds the focusing peak after migration imaging under a certain range of dielectric constant values by traversing the dielectric constant values, then calculates the error ratio of the distance resolution and the azimuth resolution, and takes the ratio of the imaging focusing peak and the relative resolution error as the evaluation index of the estimated dielectric constant. The dielectric constant corresponding to the maximum index value is taken as the estimated value of the dielectric constant of the medium.

[0006] To achieve the above purpose, the present application adopts the following technical solutions:

[0007] A medium dielectric constant estimation method under the joint constraint of GPR energy focusing and resolution, comprising the following steps:

[0008] Step S1: Collecting data using ground penetrating radar, pre-processing the received echo time domain signal; in a radar measurement, the time domain signal of the i th sample in the waveform of the above pre-processed echo time domain signal is represented as x i ;

[0009] Step S2: Correcting uneven terrain, extracting the time of arrival of the maximum value signal of each sample as the time of arrival of the ground penetrating radar transmission signal to the ground for all time domain samples obtained by the air-coupled ground penetrating radar measurement, and calculating the average height of the radar to correct the height of each sample to the average height to obtain the corrected echo time domain signal;

[0010] Step S3: Removing the ground clutter and noise from the above corrected echo time domain signal using the singular value decomposition method to remove the signals other than the target echo;

[0011] Step S4: Completing imaging focusing using the back projection technology, dividing the imaging area into grids, repeatedly calculating the refraction point and the corresponding time delay of each grid point, and obtaining the imaging focusing matrix;

[0012] Step S5: Estimating the dielectric constant of the medium, traversing a certain range of dielectric constant values according to the experience and cognition of the medium, finding the corresponding imaging focusing peak and the resolution in the distance direction and the azimuth direction, searching for the maximum value of the ratio of the imaging focusing peak and the relative resolution error, and the corresponding dielectric constant is the estimated value. The relative resolution is the ratio of the distance resolution and the azimuth resolution.

[0013] Further, the pre-processing in step S1 includes compensating for system delay, removing direct wave signals to remove fixed background and filter out multiple reflections.

[0014] Further, the step S2 includes calculating the distance between the ground penetrating radar and the ground at each sample as z i , and moving each sample This aligns the ground with the same horizontal plane, where The mean value for all distances is given; the corrected time-domain echo signal is represented as:

[0015] x(m,n)=g(m,n)+o(m,n)+n(m,n) (4)

[0016] Where x(m,n) is the corrected time-domain echo signal, g(m,n) represents the reflected echo from the ground, o(m,n) represents the reflected signal from the underground target, and n(m,n) represents noise and other clutter in the environment.

[0017] Further, step S4 includes finding the amplitude value {a1, a2, ..., a...} of the corresponding imaging point on all A-scan data of the antenna based on the obtained time delay. L The sum of these amplitude values ​​yields the cumulative amplitude value for that imaging point. The imaging focusing matrix after delay and amplitude accumulation of the entire imaging area is represented as A(M,N), the imaging area is divided into grids of M×N, and L is the number of acquisition channels of the antenna on a single measurement line. A(x m ,y n ) is the imaging grid point (x) m ,y n The cumulative amplitude value at point ).

[0018] Further, step S5 includes the following steps:

[0019] Step 1: Calculate the resolution: The detection resolution of ground penetrating radar includes range resolution and azimuth resolution;

[0020] (1) The range resolution of radar is usually defined as:

[0021]

[0022] Where c is the speed of electromagnetic wave propagation in vacuum, ε r Where is the relative permittivity of the medium, and B is the effective bandwidth of the radar;

[0023] (2) The calculation process for azimuth resolution is as follows:

[0024] The law of refraction of electromagnetic waves is as follows:

[0025]

[0026] in, This refers to the antenna's beamwidth in the air. ε is the beamwidth of the antenna in the underground medium. r is the relative permittivity of the medium;

[0027] The beam width of the antenna in air is:

[0028]

[0029] where λ0 is the wavelength of the antenna in air, determined by f0 is the center frequency of the antenna, and D is the aperture of the antenna.

[0030] Combining equation (6) and equation (7), the beam width of the antenna in the underground medium is:

[0031]

[0032] The synthetic aperture length of the antenna after the change is:

[0033]

[0034] where R is the slant range.

[0035] The speed of the electromagnetic wave entering the underground medium is:

[0036]

[0037] The azimuth resolution of the radar is:

[0038]

[0039] Substituting equation (8), equation (9), and equation (10) into equation (11), the azimuth resolution of the radar in the medium is:

[0040]

[0041] Therefore, the ratio of the range resolution to the azimuth resolution is:

[0042]

[0043] Second step: search for the imaging focus peak value:

[0044] Search for the peak value of the imaging focus matrix A(M, N), denoted as:

[0045] A(p) = max(max(A p (M, N))) (10)

[0046] where A p (M, N) is the focus imaging matrix when the dielectric constant is p, and A p is the corresponding focus peak value.

[0047] Third step: calculate the ratio of the resolution in the range and the azimuth:

[0048] The ratio of range resolution to azimuth resolution is denoted as relative resolution. When the dielectric constant is p, the theoretical ratio is expressed as:

[0049]

[0050] The actual relative resolution k was obtained through processing the measured data.

[0051] Step 4: Calculate the ratio of the image focusing peak value to the relative resolution error, expressed as:

[0052]

[0053] Where k0 is a coefficient for the ratio of two theoretical resolutions, the value of which is determined by external conditions and experimental experience;

[0054] Step 5: Search μ p The maximum value, i.e., the estimated value of the dielectric constant, is p|max(μ). p ).

[0055] Beneficial effects:

[0056] (1) This invention proposes a method for estimating the dielectric constant of underground media under the joint constraints of signal focusing and resolution. When the image focusing peak is close to the true dielectric constant, the relative resolution error is the smallest. The ratio of the two is larger than that of other dielectric constants, which better reflects the accuracy of the dielectric constant estimation.

[0057] (2) The dielectric constant of the underground medium estimated by the present invention can help to understand the underground medium conditions. It can be used for subsequent processing to improve the detection rate of underground targets and improve the accuracy of target depth information.

[0058] (3) The dielectric constant pre-estimation method based on focusing and resolution proposed in this invention has high computational efficiency, which narrows the search range for subsequent accurate estimation of dielectric constant and can improve estimation efficiency and accuracy.

[0059] (4) The dielectric constant estimation method proposed in this invention has a wide range of applicable scenarios, with no antenna mode restrictions or experimental scenario restrictions, and is applicable to both ground-coupled ground-penetrating radar and air-coupled ground-penetrating radar. Attached Figure Description

[0060] Figure 1 This is a flowchart of the dielectric constant estimation method for dielectric materials under the combined constraints of GPR energy focusing and resolution of the present invention. Detailed Implementation

[0061] To further clarify the technical solution, key points of implementation, and advantages of the present invention, the implementation steps of the present invention are described in detail below.

[0062] The medium dielectric constant estimation method under the joint constraint of GPR energy focusing and resolution of the application is used for dielectric constant estimation, and is realized by representing the dielectric constant after traversing a certain range of values, taking the maximum value when the dielectric constant value corresponding to the maximum value. Wherein A represents the imaging focusing matrix, Δd and Δr are the theoretical range resolution and azimuth resolution of the radar respectively, k is the ratio of the measured data range resolution to the azimuth resolution, k0 is the ratio coefficient of the two theoretical resolutions, p is the estimated value of the dielectric constant, and max(·) represents taking the maximum value.

[0063] As Figure 1 shown, the medium dielectric constant estimation method under the joint constraint of GPR energy focusing and resolution of the application includes the following steps:

[0064] Step S1: using ground penetrating radar to collect data, pre-processing the received echo time domain signal, the pre-processing includes compensating system delay, removing direct wave signal to remove fixed background, filtering multiple reflections, etc. In a radar measurement, the time domain signal of the i-th sample in the waveform of the echo time domain signal after the above pre-processing is represented as x i .

[0065] Step S2: correcting uneven terrain, for all time domain samples obtained by air-coupled ground penetrating radar measurement, extracting the time of arrival of the maximum value signal of each sample as the time of arrival of the ground penetrating radar transmission signal to the ground. The distance between the ground penetrating radar and the ground at each sample is calculated as z i , then each sample is moved ( to the mean value of all distances), so that the ground is corrected to the same horizontal plane. The corrected echo time domain signal is represented as:

[0066] x(m,n)=g(m,n)+o(m,n)+n(m,n) (4)

[0067] Wherein 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 underground target, and n(m,n) represents the noise and other clutter in the environment.

[0068] For ground-coupled ground penetrating radar, terrain correction is not required, and this step can be skipped.

[0069] Step S3: using singular value decomposition method on the above corrected echo time domain signal to remove ground clutter and noise, remove signals other than target echoes, and reduce the influence on subsequent processing.

[0070] Step S4: Imaging and focusing are achieved using back projection technology. This mainly utilizes the delay-summation approach, dividing the imaging area into a grid and repeatedly calculating the refraction point and corresponding time delay for each grid point. Based on the obtained time delay, the amplitude value {a1, a2, ..., a...} of the corresponding imaging point on all A-scan data from the antenna is found. L The sum of these amplitude values ​​yields the cumulative amplitude value for that imaging point. The imaging focusing matrix of the entire imaging area after delay and amplitude accumulation is represented as A(M,N).

[0071] The imaging area is divided into M×N grids, where L is the number of acquisition channels of the antenna on a single measurement line, and A(x) m ,y n ) is the imaging grid point (x) m ,y n The cumulative amplitude value at point ).

[0072] Step S5: Estimate the dielectric constant of the medium. Based on empirical knowledge of the medium, traverse a certain range of dielectric constants to find the corresponding imaging focus peak and the resolution in the range and azimuth directions. Search for the maximum value of the ratio of the imaging focus peak to the relative resolution error (relative resolution is the ratio of range resolution to azimuth resolution). The corresponding dielectric constant is the pre-estimated value. The above method specifically includes the following steps.

[0073] Step 1: Calculate the resolution:

[0074] Ground penetrating radar has two detection resolutions: range resolution and azimuth resolution.

[0075] (1) The range resolution of radar is usually defined as:

[0076]

[0077] Where c is the speed of electromagnetic wave propagation in vacuum, ε r Let B be the relative permittivity of the medium, and B be the effective bandwidth of the radar.

[0078] (2) The derivation process of the azimuth resolution is as follows:

[0079] In an air-coupled GPR, electromagnetic waves are refracted when they enter the underground medium, causing the antenna beamwidth to change. The incident angle and the refraction angle of the electromagnetic wave are the half-beamwidths before and after refraction, respectively.

[0080] The law of refraction of electromagnetic waves is as follows:

[0081]

[0082] in, This refers to the antenna's beamwidth in the air. The beam width of the antenna in the underground medium is ε r ε is the relative permittivity of the medium.

[0083] The beam width of the antenna in air is:

[0084]

[0085] where λ0 is the wavelength of the antenna in air, determined by f0 is the center frequency of the antenna, and D is the aperture of the antenna.

[0086] The beam width of the antenna in the underground medium can be obtained by combining equation (6) and equation (7):

[0087]

[0088] The synthetic aperture length of the antenna after the change is:

[0089]

[0090] where R is the slant range.

[0091] The speed of the electromagnetic wave entering the underground medium is:

[0092]

[0093] The azimuth resolution of the radar is:

[0094]

[0095] The azimuth resolution of the radar in the medium can be obtained by substituting equation (8), equation (9), and equation (10) into equation (11):

[0096]

[0097] Therefore, the ratio of the range resolution to the azimuth resolution is:

[0098]

[0099] Therefore, when the permittivity is close to the true value, the error between the actual resolution ratio and the theoretical ratio will be small; when the permittivity deviates from the true value, the error of the resolution ratio will become larger.

[0100] Second step: search for the imaging focus peak value:

[0101] Search for the peak value of the imaging focus matrix A(M, N), denoted as:

[0102] A(p) = max(A p (M, N)) (10)

[0103] wherein A p (M,N) is a focusing imaging matrix when the dielectric constant is p, A p is a corresponding focusing peak value.

[0104] When the dielectric constant is a true value, the focusing effect is the best, and the corresponding focusing center amplitude value is the largest; when the dielectric constant deviates from the true value, defocusing occurs in imaging, and the amplitude value also becomes smaller.

[0105] Step 3: calculate the ratio of the resolution in the range direction and the azimuth direction:

[0106] The ratio of the range direction resolution and the azimuth direction resolution is denoted as the relative resolution, and when the dielectric constant is p, the theoretical ratio is expressed as:

[0107]

[0108] The actual relative resolution k is obtained by processing the measured data.

[0109] Step 4: calculate the ratio of the imaging focusing peak value and the relative resolution error, which is expressed as:

[0110]

[0111] wherein k0 is the ratio coefficient of the two theoretical resolutions, and the numerical value is determined by external conditions and experimental experience.

[0112] Step 5: search for the maximum value of μ p , that is, the estimated value of the dielectric constant is p|max(μ p ).

[0113] In summary, the dielectric constant estimation method provided by the application can provide guarantee for accurate detection of ground penetrating radar. The focusing maximum value and the resolution are directly obtained from the focusing result, the estimation efficiency is high, and the calculation amount is small; the method improves the accuracy of dielectric constant estimation from two aspects.

Claims

1. A method for estimating the dielectric constant of a dielectric material under the joint constraints of GPR energy focusing and resolution, characterized in that, Includes the following steps: Step S1: Use ground-penetrating radar to acquire data and preprocess the received echo time-domain signal; in a single radar measurement, the first... The time-domain signal of each sample is represented as: ; Step S2: Correct uneven terrain. For all time-domain samples obtained by air-coupled ground penetrating radar, extract the arrival time of the maximum signal of each sample as the time when the ground penetrating radar transmitted signal arrives at the ground, and calculate the average height of the radar. Correct the height of each sample to the average height to obtain the corrected echo time-domain signal. Step S3: Use singular value decomposition to remove ground clutter and noise from the corrected echo time-domain signal, and remove signals other than the target echo. Step S4: Use back projection technology to complete image focusing, divide the imaging area into grids, repeatedly calculate the refraction point and corresponding time delay of each grid point, and obtain the image focusing matrix; Step S5: Estimate the dielectric constant of the medium. Based on the experience of the medium, traverse a certain range of dielectric constant values ​​to find the corresponding focusing peak and the resolution in the range and azimuth directions. Search for the maximum value of the ratio of the imaging focusing peak to the relative resolution error. The corresponding dielectric constant is the pre-estimated value. The relative resolution is the ratio of the range resolution to the azimuth resolution.

2. The method for estimating the dielectric constant of a dielectric under the joint constraints of GPR energy focusing and resolution as described in claim 1, characterized in that, The preprocessing in step S1 includes compensating for system delay, removing direct wave signals, removing fixed background, and filtering out multiple reflections.

3. The method for estimating the dielectric constant of a dielectric material under the joint constraints of GPR energy focusing and resolution as described in claim 1, characterized in that, Step S2 includes calculating the distance between the ground-penetrating radar and the ground at each sample location. Then each sample moves This allows the ground to be aligned to the same horizontal plane, where The mean value for all distances is given; the corrected time-domain echo signal is represented as: (4) in, It is the corrected time-domain echo signal. This represents the reflected echo from the ground. This represents the reflected signal from an underground target. This indicates noise and other clutter in the environment.

4. The dielectric constant estimation method for a dielectric material under the joint constraints of GPR energy focusing and resolution as described in claim 3, characterized in that, Step S4 includes finding the amplitude value of the corresponding imaging point on all A-scan data of the antenna based on the obtained time delay. These amplitude values ​​are summed to obtain the cumulative amplitude value for that imaging point. The imaging focusing matrix of the entire imaging region after delay and amplitude accumulation is represented as follows: The imaging region is divided into grids as follows: , This represents the number of acquisition channels the antenna collects along a single measurement line. For imaging grid points The cumulative value of the amplitude at that point.

5. The method for estimating the dielectric constant of a dielectric under the joint constraints of GPR energy focusing and resolution as described in claim 4, characterized in that, Step S5 includes the following steps: Step 1: Calculate the resolution: The detection resolution of ground penetrating radar includes range resolution and azimuth resolution; (1) The range resolution of radar is usually defined as: (5) in, It is the speed at which electromagnetic waves propagate in a vacuum. The relative permittivity of the medium, The effective bandwidth of the radar; (2) The calculation process for azimuth resolution is as follows: The law of refraction of electromagnetic waves is as follows: (6) in, This refers to the antenna's beamwidth in the air. The beamwidth of the antenna in the underground medium. is the relative permittivity of the medium; The beamwidth of the antenna in the air is: (7) in, The wavelength of the antenna in air is given by... Decide, The center frequency at which the antenna operates. The aperture of the antenna; Combining equations (6) and (7), the beamwidth of the antenna in the underground medium is obtained as follows: (8) The synthesized aperture length of the antenna after the change is: (9) in, Slope distance; The velocity of electromagnetic waves entering the underground medium is: (10) The radar's azimuth resolution is: (11) Substituting equations (8), (9), and (10) into equation (11), we obtain the azimuth resolution of the radar in the medium as follows: (12) Therefore, the relative resolution, i.e., the ratio of range resolution to azimuth resolution, is: (13) Step 2: Search for the peak image focus: Search imaging focusing matrix The peak value is expressed as: (14) in, The dielectric constant is The focusing imaging matrix at that time, This corresponds to the peak value of the focus; Step 3: Calculate the ratio of the resolution in the range direction to that in the azimuth direction: The ratio of range resolution to azimuth resolution is denoted as relative resolution, and the dielectric constant is... When the theoretical ratio is: (15) The actual relative resolution was obtained through processing the measured data. ; Step 4: Calculate the ratio of the image focusing peak value to the relative resolution error, expressed as: (16) in, These are the ratio coefficients of two theoretical resolutions, whose values ​​are determined by external conditions and experimental experience. Step 5: Search The maximum value, that is, the estimated value of the dielectric constant is .

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