Layered medium parameter estimation method based on hyperbola fitting

Abstract

The invention belongs to the technical field of ground penetrating radars, and particularly relates to a layered medium parameter estimation method based on hyperbolic fitting. The layered medium parameter estimation method based on hyperbola fitting specifically comprises the following steps: step 1, establishing a multilayer medium hyperbola constraint equation, and obtaining a ground penetrating radar theoretical measurement time constraint equation based on the constraint equation; 2, preprocessing the radar echo signals, extracting feature points, and calculating refraction points generated at the layered interface based on the extracted feature points; and 3, substituting the refraction point calculated in the step 2 into the theoretical measurement time constraint equation of the ground penetrating radar obtained in the step 1, establishing an electromagnetic wave transmission time error model, and realizing parameter estimation of the layered medium by using a nonlinear least square optimized parameter estimation method.

Description

Technical Field

[0001] The present invention belongs to the technical field of ground penetrating radar, and particularly relates to a method for estimating layered medium parameters based on hyperbola fitting. Background Art

[0002] Ground Penetrating Radar (GPR for short) is a non-destructive detection technology that has developed rapidly in recent years and has been widely used in fields such as highway quality inspection, municipal pipeline detection, geological and hydrological monitoring, building damage detection, and military detection. By using ground penetrating radar to estimate the pavement medium parameters, information such as the layer thickness and relative dielectric constant of the measured medium can be obtained. This technology is widely used in the acceptance and damage detection of highways (including airport pavements) and concrete buildings. In these scenarios, the pavement environment is usually a layered medium, and the influence of the interface on the electromagnetic wave propagation path cannot be ignored.

[0003] Regarding the research on hyperbola fitting parameter estimation, most current research regards the layered medium as a single-layer medium, ignoring the change in the electromagnetic wave path, and there is little research on hyperbola fitting for estimating layered medium parameters. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a method for estimating layered medium parameters based on hyperbola fitting. Different from the existing hyperbola fitting methods, the present invention particularly considers the change in the electromagnetic wave propagation path in the layered medium, especially the refraction phenomenon at the layered interface. By calculating these refraction points, the present invention can effectively achieve accurate estimation of the layered medium parameters.

[0005] The technical solution of the present invention is implemented as follows:

[0006] A method for estimating layered medium parameters based on hyperbola fitting, the specific process is as follows:

[0007] Step 1, establish a hyperbola constraint equation for multi-layer media, and obtain a theoretical measurement time constraint equation of the ground penetrating radar based on the constraint equation;

[0008] Step 2, preprocess the radar echo signal and extract feature points, and calculate the refraction points generated at the layered interface based on the extracted feature points;

[0009] Step 3, substitute the refraction points calculated in Step 2 into the theoretical measurement time constraint equation of the ground penetrating radar obtained in Step 1, establish an electromagnetic wave transmission time error model, and use the parameter estimation method of non-linear least squares optimization to achieve the parameter estimation of the layered medium.

[0010] Optionally, the multi-layer dielectric hyperbolic constraint equation of the present invention includes: the hyperbolic constraint equation in air coupling, the hyperbolic constraint equation of the k-th medium, and the hyperbolic constraint equation of the target medium layer.

[0011] Optionally, the hyperbolic constraint equation in air coupling of the present invention is:

[0012]

[0013] where h 0 is the height of the antenna from the ground, represents the refraction point of air and the first layer of dielectric, x i is the position of the antenna, and t represents the two-way propagation time of the electromagnetic wave in air.

[0014] Optionally, the hyperbolic constraint equation of the k-th medium of the present invention is:

[0015]

[0016] where h k represents the thickness of the k-th dielectric layer, v k represents the wave velocity of the k-th dielectric layer, and represent the abscissas of the refraction points of the (k + 1)-th and k-th dielectrics, t k represents the propagation time of the electromagnetic wave in the k-th dielectric layer, k ∈ [1, n - 1], and n is the number of the dielectric layer where the target is located.

[0017] Optionally, the hyperbolic constraint equation of the target medium layer of the present invention is:

[0018]

[0019] where t n represents the propagation time of the electromagnetic wave in the target layer, h n represents the buried depth of the target center, v n represents the wave velocity of the target layer, R represents the radius of the cylindrical object, represents the abscissa of the refraction point of the target layer, x 0 represents the horizontal center position of the target.

[0020] Optionally, the electromagnetic wave transmission time error model in step three of the present invention is:

[0021]

[0022] where f(x 0 , x i , x p , v k , h k) represents the theoretical measurement time constraint equation of the ground penetrating radar, t data represents the actually measured time, h k represents the thickness of the k-th layer of the medium layer, x i represents the position of the antenna, x 0 represents the horizontal center position of the target, represents the horizontal coordinate of the electromagnetic wave refraction point of the k-th layer of the medium layer; v k represents the wave velocity of the k-th layer of the medium layer;

[0023] The goal of the optimization problem is to find the parameter vector p to minimize E(p) and estimate the relative dielectric constant of the background.

[0024] Optionally, the preprocessing in the present invention is: mean filtering and binarization processing.

[0025] Optionally, the extraction of feature points in the present invention is:

[0026] For each horizontal position, eliminate the rows with all zero values and retain the region containing valid information;

[0027] For the region containing valid information, calculate the absolute value of each pixel value, find the row index corresponding to the largest absolute value, and the largest absolute value represents the most significant feature point at this horizontal position.

[0028] Optionally, when the dielectric constant is increasing in the present invention, calculate the coordinates of the refraction point x p according to the following quartic equation:

[0029]

[0030] where, is the intersection of the line connecting the imaging point of the k-th layer of the medium and the i-th antenna with the x-axis,, represents the abscissa of the refraction point of the k-th layer of the medium, represents the abscissa of the refraction point of the k-1-th layer, x 0 represents the horizontal center position of the target, h i represents the thickness of the medium layer.

[0031] Optionally, when the dielectric constant is decreasing in the present invention, calculate the coordinates of the refraction point x p according to the following quartic equation:

[0032]

[0033] where, is the intersection of the line connecting the imaging point of the k-th layer of the medium and the i-th antenna with the x-axis,, represents the abscissa of the refraction point of the k-th layer of the medium, represents the abscissa of the refraction point of the k-1-th layer, x0 represents the target horizontal center position, h i represents the thickness of the dielectric layer.

[0034] The beneficial effects of the present invention are as follows:

[0035] The present invention particularly considers the change in the propagation path of electromagnetic waves in layered media, especially the refraction phenomenon at the layered interface, establishes a hyperbolic constraint equation for multi-layer media to constrain the layer thickness and relative dielectric parameters of each layer of the dielectric; preprocesses the radar echo signal and extracts feature points, calculates the refraction points generated at the layered interface, and then establishes an electromagnetic wave transmission time error model, and uses the parameter estimation method of non-linear least squares optimization to achieve the parameter estimation of the layered media. After verification by simulation experiments, this method has higher accuracy compared with the traditional hyperbolic medium parameter estimation method under the same model, and belongs to an efficient ground-penetrating method. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0037] Figure 1 is a model diagram of the hyperbolic constraint equation of the layered medium of the method of the present invention;

[0038] Figure 2 is a simulation model diagram of the multi-layer medium established by the method of the present invention;

[0039] Figure 3 is a hyperbolic fitting curve diagram of the multi-layer medium of the method of the present invention.

[0040] Specific implementation process

[0041] The embodiments of the present invention will be described in detail below with reference to the drawings.

[0042] It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other; and, based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present disclosure.

[0043] It should be noted that the following description relates to various aspects of embodiments within the scope of the appended claims. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is illustrative only. Based on this disclosure, those skilled in the art should understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of the aspects set forth herein can be used to implement an apparatus and / or practice a method. Additionally, this apparatus and / or method can be implemented using other structures and / or functionality in addition to one or more of the aspects set forth herein.

[0044] An embodiment of the present application provides a method for estimating parameters of layered media based on hyperbola fitting. This embodiment is based on the Ricker wavelet and is implemented through the following steps:

[0045] Step 1: Based on the hyperbola constraint equation of multi-layer media, obtain the theoretical measurement time constraint equation of the ground penetrating radar; as Figure 1 shown, the specific process is as follows:

[0046] Step 101: Hyperbola constraint equation for double-layer media;

[0047] Based on the analysis of the electromagnetic wave trajectory, the dependence relationship between the fitted hyperbola geometry and the estimated parameters can be defined. The distance from the antenna center at any position x i to the cylindrical object is denoted as z i , the antenna moves close to the ground, and the distance when it is exactly on the axis of the cylindrical object is z 0 , R is the radius, the height of the first layer of medium is h 1 , the wave velocity is The burial depth of the center of the second-layer target is h 2 , the wave velocity is The horizontal center position of the target is x 0 , x p is the horizontal coordinate of the electromagnetic wave refraction point.

[0048] When the propagation path of the electromagnetic wave in the first layer of medium is x 1 and a triangle will be formed. According to the Pythagorean theorem, we get:

[0049]

[0050] where x i represents the antenna center at any position.

[0051] Also, because Substituting the above into the equation and simplifying, we obtain the hyperbola constraint equation for the first layer of medium:

[0052]

[0053] In the second-layer medium, the electromagnetic wave continues to propagate downward to the imaging point, and the path is denoted as z i , and at this time, a new triangle will be formed for the propagation path. According to the Pythagorean theorem, we can obtain:

[0054] (z 0 +R) 2 +(x p -x 0 ) 2 =(zi+R) 2 (3)

[0055] Also, because Substituting the above into the equation and arranging, we obtain the hyperbolic constraint equation for the second-layer medium:

[0056]

[0057] At the same time, because Substituting the above into the equation and arranging, we get:

[0058]

[0059] Step 102: Hyperbolic constraint equation for multi-layer media;

[0060] The n-layer medium model is composed of n + 1 layers of media, and there are dielectric constant differences between the media. Assuming that the distance between the transmitting antenna and the receiving antenna can be ignored, that is, the transceiver is integrated, and the antenna moves horizontally. The electromagnetic wave propagates in the underground homogeneous medium, is refracted through multiple layers of media and finally reaches the target, and the electromagnetic wave signal is reflected back to the receiving antenna after being reflected by the target. According to the analysis of the electromagnetic wave trajectory, a hyperbolic geometric model can be established and the dependence relationship between the model parameters and the estimated values can be determined.

[0061] The center of the antenna is at any position x i , R is the radius of the cylindrical object (i.e., the target), and the antenna is at a certain height h from the ground 0 , represents the refraction point between the air and the first-layer medium. According to Fermat's principle, the electromagnetic wave propagates in a straight line in the air to form a triangle, and its propagation path is x. According to the Pythagorean theorem, we obtain:

[0062]

[0063] Also, because where c is the speed of light in a vacuum. Substituting the above into the equation and arranging, we obtain the hyperbolic constraint equation for air coupling:

[0064]

[0065] In the non-target medium layer, the electromagnetic wave continues to propagate downward, and the propagation path is x k , the height of the k-th layer of medium is h k , and the wave velocity is ε rk which is the relative permittivity of the k-th layer of medium. There is a refraction phenomenon of the electromagnetic wave at each stratified interface, is the horizontal coordinate of the refraction point of the electromagnetic wave in the k-th layer, where k ∈ [1, n - 1]. In this case, the propagation path of the electromagnetic wave will form a new triangle in each layer. According to the Pythagorean theorem, we can get:

[0066]

[0067] Also, because Substituting the above formula and arranging it, we can obtain the hyperbolic constraint equation of the k-th medium:

[0068]

[0069] In the target medium layer, the electromagnetic wave continues to propagate downward, and the buried depth of the target center is h n , and the wave velocity is ε n which is the permittivity of the n-th layer of medium. The propagation path of the electromagnetic wave is x n , and the horizontal center position of the target is x 0 . At this time, the propagation path will form a new triangle in the target layer. According to the Pythagorean theorem, we can get:

[0070]

[0071] Also, because Substituting the above formula and arranging it, we can obtain the hyperbolic constraint equation of the target medium layer:

[0072]

[0073] Step 103: According to the hyperbolic constraint equation (7) in the case of air coupling, the hyperbolic constraint equation (9) of the k-th medium, and the hyperbolic constraint equation (11) of the target medium layer, obtain the theoretical measurement time constraint equation of the ground penetrating radar.

[0074] In this step, the theoretical detection time of the ground penetrating radar is: the propagation time t of the electromagnetic wave in the case of air coupling, the propagation time t k of the electromagnetic wave in the n - 1 layers of medium 0 , x i , x p , v k , h k) In this equation, the horizontal coordinate x of the electromagnetic wave refraction point p is an unknown quantity and needs to be obtained through Step 2.

[0075] Step 2: Preprocess the radar echo signal and extract feature points, and calculate the refraction point x generated at the layered interface based on the extracted feature points p ; The specific process is as follows:

[0076] Step 201: Mean filtering and image binarization processing of the radar echo signal;

[0077] During the detection process of the ground penetrating radar, when the electromagnetic wave propagates downward, the receiver first receives the direct wave signal. The direct wave is generated by the signal directly transmitted by the radar reaching the receiver without being reflected by underground objects, and it is the signal with the strongest amplitude. Since the energy and amplitude of the direct wave usually far exceed those of the reflected wave of underground objects, it will have a significant impact on the measurement results. By distinguishing the direct wave from the reflected wave of underground targets, the interference of the direct wave can be effectively eliminated.

[0078] Among the methods for eliminating the direct wave, mean filtering is one of the most common and commonly used methods. The basic principle of the mean filtering method is to first calculate the mean of the echo data of all measurement points, and then subtract this mean from the echo data collected at each measurement point position. Assuming there are a total of N measurement points, the mean filtering method can be expressed as:

[0079]

[0080] In the formula, X i,j is the data after mean filtering.

[0081] In the embodiment, a statistical-based method is used to process the ground penetrating radar image obtained after mean filtering. First, calculate the mean (μ) and standard deviation (σ) of the entire image to characterize the central tendency and distribution range of the image data. Secondly, set an adaptive threshold according to the mean and standard deviation, and this threshold is determined by adding a certain multiple of the standard deviation to the mean. To further process the image, a logical mask is created, which identifies all pixel points higher than the adaptive threshold. Finally, initialize a binary image with the same size as the original image, and set the positions corresponding to the true pixel points in the mask to 1, and the remaining positions remain 0. In this way, a binarized image is obtained, where the pixel points higher than the threshold are retained, and the pixel points lower than the threshold are set as the background.

[0082] Step 202: Extract features from the binarized ground penetrating radar image;

[0083] In this embodiment, a feature point extraction method based on energy field analysis is used to identify key underground structure features from the binarized ground penetrating radar image.

[0084] For each horizontal position, check whether the corresponding row vector contains non - zero values to ensure that only the regions containing valid information are processed. For the regions containing valid information, calculate the absolute value of each pixel value, and find the maximum energy value and its corresponding row index. This maximum energy value represents the most significant feature point at that horizontal position:

[0085]

[0086] where s 1 and s 2 represent the data before and after feature extraction, respectively.

[0087] Finally, store the coordinates of each feature point and the corresponding energy value into the feature point array. By this method, the key underground structure feature points can be extracted from the ground - penetrating radar image, providing important information for subsequent image analysis and interpretation.

[0088] Step 203: Refraction point calculation;

[0089] In a layered medium, when considering the path of light from one point to another, the refraction phenomenon of light at the interface between different media needs to be considered, and the light path is solved by numerical methods, that is, the refraction point is solved. When the radar moves on the surface of the layered medium, the electromagnetic wave passes through multiple underground media. Due to the different speeds of electromagnetic waves in the two media, the refraction phenomenon will occur at the medium interface. According to Snell's law of refraction, we can get:

[0090]

[0091] where α represents the incident angle of the electromagnetic wave, β represents the refraction angle of the electromagnetic wave, ε 1 represents the relative permittivity in the first layer of the medium, ε 2 represents the relative permittivity in the second layer of the medium. After squaring, we get the following formula, and it is represented by ε rm :

[0092]

[0093] The height of the first layer of the medium is h 1 and the wave speed is The buried depth of the center of the second - layer target is h 2 and the wave speed is The horizontal center position of the target is x 0 , x p is the horizontal coordinate of the electromagnetic wave refraction point, x i is the abscissa of the antenna corresponding to the extracted feature point (i.e., the abscissa of the feature point). The coordinates of the refraction point are unknowns, and through geometric relationships, we can get:

[0094]

[0095] At the same time, using the Mast refraction point approximation method, for the double-layer dielectric geometric model, the coordinates of the refraction point can be approximately obtained by the following formula:

[0096]

[0097] In the formula, x l is the intersection point of the line connecting the imaging point and the i-th antenna with the x-axis.

[0098] By ε rm Combining the above two formulas to obtain a quartic equation about x p Solving this quartic equation to obtain the coordinates of x p

[0099]

[0100] However, as the horizontal coordinate spacing between the antenna and the imaging point increases, the position of the refraction point obtained by the approximation method gradually deviates from the true value. In order to reduce the influence brought by the sharp increase of the refraction point approximation calculation error, the imaging point is taken as the new reference origin, and the antennas are symmetrically arranged on both sides of the imaging point to reduce the error in the refraction point calculation.

[0101] To solve the refraction point of the k-th layer of medium, it is necessary to relate to the refraction point of the k-1-th layer, where k ∈ [1, n]. According to Snell's law of refraction, we can get:

[0102]

[0103] In the formula, α represents the incident angle of the electromagnetic wave, β represents the refraction angle of the electromagnetic wave, and ε rk represents the relative permittivity in the k-th layer of medium. When k = 1, ε r0 represents the relative permittivity of the speed of light c in air. Squaring the above formula, the obtained expression is represented by ε rm as:

[0104]

[0105] During the solution process, the coordinates of the refraction point are used as unknowns. Through geometric relationships, we can get:

[0106]

[0107] At the same time, the Mast refraction point approximation method is adopted and extended to the refraction point approximation method for multi-layer media:

[0108] ​

[0109] In the formula, is the intersection point of the line connecting the imaging point and the refraction point on the (k - 1)-th layer with the x-axis. When k = 1, represents the position of the antenna, that is, x i .

[0110] By ε rm simultaneously, a quartic equation in one variable about x p is obtained. Solving this quartic equation in one variable gives the coordinates of x p .

[0111]

[0112] Among them, and represent the refraction points on the k-th layer and the (k - 1)-th layer, h i represents the thickness of the i-th layer, represents the intersection point of the line connecting the imaging point and the refraction point on the (k - 1)-th layer with the x-axis, x 0 represents the target horizontal center position.

[0113] The above method is applicable to the case where the dielectric constant increases. At the same time, as the abscissa spacing between the antenna and the imaging point becomes larger, the position of the refraction point obtained by the approximate method gradually deviates from the true value. To reduce the influence brought by the sharp increase in the approximate calculation error of the refraction point, the imaging point is taken as the new reference origin, and the antennas are symmetrically arranged on both sides of the imaging point to reduce the error in the calculation of the refraction point.

[0114] When the dielectric constant decreases, the approximate solution method for the refraction point proposed by Liu is used,

[0115]

[0116] simultaneously to obtain the calculation equation for the refraction point when the dielectric constant decreases

[0117]

[0118] Step 3: Substitute the refraction point calculated in Step 2 into the theoretical measurement time constraint equation of the ground penetrating radar obtained in Step 1, and use the parameter estimation method of nonlinear least squares optimization to realize the parameter estimation of the layered medium. The specific implementation of this step is as follows:

[0119] Use the parameter estimation method based on nonlinear least squares optimization, aiming to adjust the model parameters through an optimization algorithm to best fit the given data set:

[0120]

[0121] Among them, f(x 0 , xi , x p , v k , h k ) represents the time constraint equation for the theoretical measurement of ground penetrating radar, t data represents the actually measured time, and the vector P includes the thickness of the dielectric layer and the relative dielectric constant parameter.

[0122] The goal of the optimization problem is to find the parameter vector p that minimizes E(p), and by finding the hyperbola that best fits the feature extraction graph, the relative dielectric constant of the background can be estimated:

[0123]

[0124] The present invention proposes a method for estimating the parameters of layered media based on hyperbola fitting. Using the hyperbola fitting method for layered media, first, the image is binarized and feature points are extracted, the refraction points generated at the layered interface are calculated, and then the parameter estimation of the layered media is realized based on the parameter estimation method of nonlinear least squares optimization. Finally, it is verified through simulation software, as Figure 2 shown in the established simulation model diagram of multi-layer media.

[0125] Thus, a method for estimating the parameters of layered media based on hyperbola fitting is completed. Embodiment

[0126] In order to verify the method for estimating the parameters of layered media based on hyperbola fitting proposed by the present invention, simulation experiments are designed for analysis. As Figure 2-3 shown, the simulation uses gprMax software to establish different dielectric models, and the simulation parameters are as shown in Table 1.

[0127] Table 1 Simulation parameter settings

[0128]

[0129] Under the above model, the method invented is tested, and the parameter estimation results are as shown in Table 2.

[0130] Table 2 Relative error of parameter estimation

[0131]

[0132] In summary, the above is only the preferred embodiment of the present invention, and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A layered medium parameter estimation method based on hyperbola fitting, characterized in that: The specific process is: Step 1: Establish a multi-layer medium hyperbolic constraint equation, and obtain a ground penetrating radar theoretical measurement time constraint equation based on the constraint equation; Step 2: preprocessing the radar echo signal and extracting feature points, and calculating the refraction points generated at the layered interface based on the extracted feature points; Step three, substitute the refraction point calculated in step two into the theoretical measurement time constraint equation of ground penetrating radar obtained in step one, establish the electromagnetic wave transmission time error model, and use the parameter estimation method of nonlinear least squares optimization to realize the parameter estimation of layered media.

2. The layered medium parameter estimation method based on hyperbola fitting according to claim 1 is characterized in that: The multi-layer medium hyperbolic constraint equation includes: a hyperbolic constraint equation in the case of empty coupling, a hyperbolic constraint equation of the kth medium, and a hyperbolic constraint equation of the target medium layer.

3. The layered medium parameter estimation method based on hyperbola fitting according to claim 2 is characterized in that: The hyperbolic constraint equation during the empty coupling is: Where h0 is the height of the antenna from the ground, represents the refraction point between the air and the first layer of medium, xx is the position of the antenna, and t represents the two-way propagation time of the electromagnetic wave in the air.

4. The layered medium parameter estimation method based on hyperbola fitting according to claim 2 is characterized in that: The hyperbolic constraint equation of the kth medium is: Among them, h k represents the thickness of the kth dielectric layer, v k represents the wave velocity of the kth dielectric layer, and represents the horizontal coordinate of the refraction point of the k+1th layer medium and the kth layer medium, t k It represents the propagation time of electromagnetic wave in the kth dielectric layer, k∈[1,n-1], and n is the number of dielectric layers where the target is located.

5. The layered medium parameter estimation method based on hyperbola fitting according to claim 2 is characterized in that: The hyperbolic constraint equation of the target dielectric layer is: Among them, t n represents the propagation time of electromagnetic waves in the target layer, h n Indicates the target center burial depth, v n represents the wave velocity of the target layer, R represents the radius of the cylindrical object, represents the horizontal coordinate of the refraction point of the target layer, and x0 represents the horizontal center position of the target.

6. The layered medium parameter estimation method based on hyperbola fitting according to claim 1 is characterized in that: The electromagnetic wave transmission time error model in step 3 is: in, represents the theoretical measurement time constraint equation of ground penetrating radar, t data Indicates the actual measurement time, h k represents the thickness of the kth dielectric layer, x i represents the horizontal coordinate of the antenna, x0 represents the horizontal center position of the target, represents the horizontal coordinate of the refraction point of the electromagnetic wave in the kth dielectric layer; v k represents the wave velocity of the kth dielectric layer; The goal of the optimization problem is to find the parameter vector p that minimizes E(p) and estimates the relative dielectric constant of the background.

7. The layered medium parameter estimation method based on hyperbola fitting according to claim 1 is characterized in that: The preprocessing includes: mean filtering and binarization processing.

8. The layered medium parameter estimation method based on hyperbola fitting according to claim 1 is characterized in that: The extracted feature points are: For each horizontal position, remove the rows with all zero values ​​and keep the area containing valid information; For the area containing valid information, calculate the absolute value of each pixel value, find the maximum absolute value and its corresponding row index, and the maximum absolute value represents the most significant feature point at that horizontal position.

9. The layered medium parameter estimation method based on hyperbola fitting according to claim 1 is characterized in that: When the dielectric constant is increasing, the refraction point x is calculated according to the following univariate quartic equation p Coordinates: in, is the intersection of the k-th layer medium imaging point, the i-th antenna connection line and the x-axis, represents the horizontal coordinate of the refraction point of the k-th layer of medium, represents the horizontal coordinate of the refraction point of the k-1th layer, x0 represents the horizontal center position of the target, h i Indicates the thickness of the dielectric layer.

10. The layered medium parameter estimation method based on hyperbola fitting according to claim 1, characterized in that: When the dielectric constant decreases, the refraction point x is calculated according to the following quartic equation p Coordinates: in, is the intersection of the k-th layer medium imaging point, the i-th antenna connection line and the x-axis, represents the horizontal coordinate of the refraction point of the k-th layer of medium, represents the horizontal coordinate of the refraction point of the k-1th layer, x0 represents the horizontal center position of the target, h i Indicates the thickness of the dielectric layer.

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