CN107300694B - Unknown wall parameter estimation method based on electromagnetic wave transmission coefficient - Google Patents
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Abstract
The invention discloses an unknown wall parameter estimation method based on electromagnetic wave transmission coefficients, which comprises the steps of establishing a wall model with three layers of media, wherein a first medium layer and a third medium layer are respectively positioned at two sides of a second medium layer, and the second medium layer is a medium layer to be detected; arranging a transmitting antenna on the first medium layer, arranging a receiving antenna on the third medium layer, wherein the distance from the transmitting antenna to the front surface of the second medium layer is equal to the distance from the receiving antenna to the rear surface of the second medium layer; the transmitting antenna transmits electromagnetic waves, and the receiving antenna receives the electromagnetic waves transmitted by the transmitting antenna; deducing an amplitude attenuation coefficient according to the propagation characteristic of the electromagnetic wave; calculating the propagation delay of the electromagnetic wave; the parameters of the second dielectric layer are estimated according to the amplitude attenuation coefficient and the propagation delay of the electromagnetic waves, and the parameters of the dielectric can be estimated more accurately than those of the dielectric by the traditional method.
Description
Technical Field
The invention belongs to the technical field of through-wall radar imaging, and particularly relates to an unknown wall parameter estimation method based on an electromagnetic wave transmission coefficient.
Background
The ultra-wideband through-wall radar belongs to a nondestructive detection radar and has the characteristics of high distance resolution, strong penetration capability and the like. The electromagnetic wave can penetrate through nonmetal wall media such as a soil wall, a wood wall, a brick wall, a concrete wall and the like, and can be used for detecting and imaging a human body behind the wall or an internal structure of a building. In recent years, the through-wall radar has been widely used in both military and civil applications.
When a through-wall radar is used for detecting a target behind a wall, when electromagnetic waves are incident on the wall, reflection and transmission phenomena occur at the junction of air and the wall. The ability of electromagnetic waves to penetrate through a wall is related to the characteristic parameters of the wall, such as the thickness and dielectric constant of the wall. At present, most imaging algorithms assume known wall parameters and then image targets, but in practical application, the wall parameters cannot be known in advance, and the estimation accuracy of the wall parameters causes problems of positioning deviation, image defocusing, false targets and the like, so that the estimation of the wall parameters is very necessary.
In response to this problem, unknown wall parameters have been studied by scholars. And (3) estimating the thickness and the relative dielectric constant of the wall by taking the geometric model and the signal time delay as entry points. However, the algorithm is completely dependent on the delay estimation, and the accuracy parameter of the estimation result may be limited by the accuracy of the delay estimation. In addition, wall parameters can be predicted through a wall parameter regression method based on a vector machine (SVM), the method is hardly influenced by the number of targets, the length of the wall, sampling intervals and noise, and the prediction accuracy is relatively greatly influenced by the size, the position and the shape of the targets. Therefore, in order to improve the accuracy of target positioning and the imaging quality, it is a critical problem that must be solved to be able to accurately estimate the wall parameters.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides an unknown wall parameter estimation method based on an electromagnetic wave transmission coefficient, which can accurately estimate the wall parameters from the two aspects of the propagation characteristic of the electromagnetic wave penetrating through the wall medium and the propagation delay of the electromagnetic wave.
The technical scheme adopted by the invention is as follows:
an unknown wall parameter estimation method based on an electromagnetic wave transmission coefficient comprises the following steps:
establishing a three-layer medium model, wherein a first medium layer and a third medium layer are respectively positioned at two sides of a second medium layer, the second medium layer is a wall body and is a medium layer to be tested, and the first medium layer and the third medium layer are air;
arranging a transmitting antenna on the first medium layer, arranging a receiving antenna on the third medium layer, wherein the distance from the transmitting antenna to the front surface of the second medium layer is equal to the distance from the receiving antenna to the rear surface of the second medium layer;
the transmitting antenna transmits electromagnetic waves, and the receiving antenna receives the electromagnetic waves transmitted by the transmitting antenna;
deducing an amplitude attenuation coefficient according to the propagation characteristic of the electromagnetic wave;
calculating the propagation delay of the electromagnetic wave, namely the time required for the electromagnetic wave to pass through a wall body;
and estimating parameters of the second dielectric layer, namely wall parameters, according to the amplitude attenuation coefficient and the electromagnetic wave propagation delay.
Further, the specific derivation of the amplitude attenuation coefficient derived from the propagation characteristics of the electromagnetic wave is as follows:
the electromagnetic wave is emitted by a transmitting antenna in the first dielectric layer, sequentially passes through the first dielectric layer, the second dielectric layer and the third dielectric layer, and is finally received by a receiving antenna in the third dielectric layer, and the total field quantity in the first dielectric layer, the second dielectric layer and the third dielectric layer is represented by the following formulas (1), (2) and (3):
Wherein EnRepresenting the electric field strength, H, in the first, second and third dielectric layersnRepresents the magnetic field intensity in the first, second and third medium layers, and n is 1,2, 3;
Enirepresenting the amplitude of the incident wave in the first, second and third dielectric layers, EnrTable 1,2,3, the amplitude of the reflected wave in the first, second and third dielectric layers; x, y and z represent three-dimensional space coordinates of the three-layer medium model; d is the thickness of the second dielectric layer, and j is an imaginary unit;
k0representing wavenumbers in the first dielectric layer and the third dielectric layer, η0Representing the wave impedance in the first and third dielectric layers,k, η represent the wave number and wave impedance in the second dielectric layer respectively, ε、εrreplacing the dielectric constant and relative dielectric constant, ε, in the second dielectric layer0E instead of the dielectric constant in the first and third dielectric layers0εr;ωRepresenting the angular frequency of the transmitted signal; mu.s0The permeability of the first medium layer and the third medium layer, and the permeability of the second medium layer, are not considered, i.e., the permeability of the wall body itself, i.e., μ ═ μ0;
The boundary conditions for z-0 and z-d are:
E1|z=0=E2|z=0,H1|z=0=H2|z=0(4)
E2|z=d=E3|z=d,H2|z=d=H3|z=d(5)
namely, expressed as:
when z is 0:
when z is d:
the transmission coefficient can be expressed as:
wherein: e1iIs the incident wave field strength of the first medium layer, E3tThe transmitted wave field strength of the third dielectric layer, P, Q being the real and imaginary parts of the transmission coefficient;
from this, the amplitude attenuation coefficient S can be calculated as:
wherein A istRepresenting the amplitude of the transmitted wave, AiRepresenting the incident wave amplitude.
Further, calculating the propagation delay of the electromagnetic wave specifically includes:
the propagation time t of the electromagnetic wave from the transmitting antenna to the receiving antenna is obtained according to the equation (12),
where c represents the propagation velocity of the electromagnetic wave, v represents the propagation velocity of the electromagnetic wave in the wall, and l represents the distance from the transmitting antenna to the front surface of the wall and the distance from the receiving antenna to the rear surface of the wall.
Further, the estimating of the parameters of the second dielectric layer according to the amplitude attenuation coefficient and the propagation delay of the electromagnetic wave specifically comprises:
solving the system of equations according to equation (13) to obtain the estimated wall parameter values,
the invention has the beneficial effects that: according to the invention, from the propagation characteristic of the electromagnetic wave penetrating through the medium, the transmission coefficient of the electromagnetic wave penetrating through the wall is deduced according to the field quantity and the boundary condition of each medium, and the amplitude attenuation coefficient is further obtained. Then, according to the propagation delay principle of electromagnetic waves, the nonlinear relation between the propagation delay and the wall body parameters can be obtained, and finally, the transcendental equation set is solved by utilizing a Newton iteration method, so that the medium parameters can be estimated more accurately than the traditional method.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of an electromagnetic wave through-wall model;
FIG. 2 is a time domain plot of a transmit signal minus a first order Gaussian signal;
FIG. 3 is a frequency domain plot of a negative first order Gaussian signal of a transmit signal;
FIG. 4 is a graph of the effect of media thickness on transmitted signal;
FIG. 5 is a graph of the effect of relative permittivity on transmitted signal;
FIG. 6 is a time domain plot of the transmitted signal and the incident signal for three different walls.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, and the scope of the present invention will be more clearly and clearly defined.
And carrying out simulation experiments according to the model, wherein the emission signal is a negative first-order Gaussian signal, a time domain graph and a frequency domain graph are shown in figures 2-3, and a time domain waveform graph of the transmission signal can be obtained through the simulation experiments and is shown in figures 4-5. FIG. 4 shows the effect of wall thickness on the transmitted signal when the relative dielectric constant is 4, and it can be seen that the greater the thickness, the more severe the electromagnetic wave attenuation, and the greater the time delay; fig. 5 shows the effect of the relative dielectric constant on the transmission signal when the wall thickness is 0.20m, and it can be seen that the greater the relative dielectric constant, the more the electromagnetic wave is attenuated, and the greater the time delay, i.e. there is a non-linear relationship between the wall thickness and the relative dielectric constant and the transmission signal.
The electromagnetic wave is emitted by a transmitting antenna in the first dielectric layer, sequentially passes through the first dielectric layer, the second dielectric layer and the third dielectric layer, and is finally received by a receiving antenna in the third dielectric layer, and the total field quantity in the first dielectric layer, the second dielectric layer and the third dielectric layer is represented by the following formulas (1), (2) and (3):
Wherein EnRepresenting the electric field strength, H, in the first, second and third dielectric layersnRepresents the magnetic field intensity in the first, second and third medium layers, and n is 1,2, 3;
Enirepresenting the amplitude of the incident wave in the first, second and third dielectric layers, EnrTable 1,2,3, the amplitude of the reflected wave in the first, second and third dielectric layers; x, y and z represent three-dimensional space coordinates of the three-layer medium model; d is the thickness of the second dielectric layer, and j is an imaginary unit;
k0representing wavenumbers in the first dielectric layer and the third dielectric layer, η0Representing the wave impedance in the first and third dielectric layers,k, η represent the wave number and wave impedance in the second dielectric layer (wall), respectively, ε、εrsubstitute for the sum of the dielectric constants in the second dielectric layerRelative dielectric constant,. epsilon0E instead of the dielectric constant in the first and third dielectric layers0εr(ii) a ω represents the angular frequency of the transmitted signal; mu.s0The magnetic permeability of the first medium layer and the third medium layer and the magnetic permeability of the second medium layer are determined, and the magnetic permeability of the wall body is not considered, so that the magnetic permeability of the wall body is determined, and therefore, the magnetic permeability of the wall body is determined to be mu0;
The boundary conditions for z-0 and z-d are:
E1|z=0=E2|z=0,H1|z=0=H2|z=0(4)
E2|z=d=E3|z=d,H2|z=d=H3|z=d(5)
namely, expressed as:
when z is 0:
when z is d:
the transmission coefficient can be expressed as:
wherein: e1iIs the incident wave field strength of the first medium layer, E3tThe transmitted wave field strength of the third dielectric layer, P, Q being the real and imaginary parts of the transmission coefficient;
from this, the amplitude attenuation coefficient S can be calculated as:
wherein A istRepresenting the amplitude of the transmitted wave, AiRepresenting the amplitude of the incident wave, it is assumed herein that the propagation of the electromagnetic wave in air is unattenuated, i.e. AiIs a constant value.
From equation (11), the wall thickness, relative dielectric constant and frequency of the transmitted signal cause the amplitude A of the transmitted waveiAnd (4) attenuation. In this context, equation (11) has two variables, namely wall thickness and relative dielectric constant, with the frequency of the excitation source unchanged.
Referring to fig. 1, the propagation time t of the electromagnetic wave from the transmitting antenna to the receiving antenna can be obtained as shown in equation (12):
wherein c represents the propagation velocity of the electromagnetic wave,represents the propagation speed of the electromagnetic wave in the wall body, and l represents the distance from the transmitting antenna to the front surface of the wall body and the distance from the receiving antenna to the rear surface of the wall body.
Step 4, estimating wall parameters, namely solving the relative dielectric constant e of the wallrAnd wall thickness d
Based on the above analysis, the amplitude attenuation coefficient S (. epsilon.)rD) and propagation time t (. epsilon.)rAnd d) both have nonlinear relations with the wall thickness and the relative dielectric constant, as shown in formula (13):
from equation (13), the solution of the equation set is the wall parameter value to be estimated.
The invention utilizes FDTD to carry out modeling simulation, the length and the width of a simulation space are both 2.0m, and the transmitting antenna and the receiving antenna are respectively 0.70m away from the front surface and the rear surface of the wall body. In order to prove the effectiveness of the wall parameter estimation method, three different walls are respectively arranged for simulation experiments, so that simulation data can be obtained. And normalizing the acquired analog data by taking the propagation amplitude of the electromagnetic wave in the air as a reference, and neglecting the attenuation of the electromagnetic wave in a free space. FIG. 6 shows a time domain plot of the transmitted signal and a time domain plot of the incident signal for three different walls. Therefore, the propagation time t of the electromagnetic wave from the transmitting antenna to the receiving antenna and the normalized amplitude of the transmitted wave under different wall bodies can be obtained.
In view of the advantages of strong convergence performance, high operation speed and the like of the Newton iteration method, the method adopts the Newton iteration method to solve the corresponding transcendental equation, and the wall thickness and the relative dielectric constant can be inversely estimated.
Finally, the error analysis is performed on the estimated result of the present invention, as follows.
The wall parameters are estimated by the method, and the obtained result is compared with the estimation result obtained by the cost function method, and the result is shown in table 1.
Table 1 three wall parameter estimation results
As can be seen from Table 1, for the estimation of the relative dielectric constant of the wall, the result obtained by the method is consistent with the result obtained by the cost function method, but for the estimation of the wall parameters, the result obtained by the method is obviously superior to the result obtained by the cost function method.
According to the estimation results obtained above, single error values of two estimation methods under three different walls can be calculated, and the results are shown in table 3 below:
TABLE 3 error table of estimation results of two methods
Finally, the overall error value of the wall parameters estimated by the method of the invention can be calculated to be 5.44%, and the overall error value of the wall parameters estimated by the cost function method is 9.40%. Compared with a cost function method, the method has the advantage that the overall error value is improved by 3.96%. In conclusion, the invention can accurately estimate the wall parameter value, thereby improving the accuracy of target positioning and the imaging quality.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that are not thought of through the inventive work should be included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope defined by the claims.
Claims (2)
1. An unknown wall parameter estimation method based on an electromagnetic wave transmission coefficient is characterized by comprising the following steps:
establishing a wall model with three layers of media, wherein a first medium layer and a third medium layer are air and are respectively positioned at two sides of a second medium layer, and the second medium layer is a wall and is a medium layer to be detected;
arranging a transmitting antenna on the first medium layer, arranging a receiving antenna on the third medium layer, wherein the distance from the transmitting antenna to the front surface of the second medium layer is equal to the distance from the receiving antenna to the rear surface of the second medium layer;
the transmitting antenna transmits electromagnetic waves, and the receiving antenna receives the electromagnetic waves transmitted by the transmitting antenna;
deducing an amplitude attenuation coefficient according to the propagation characteristics of the electromagnetic waves, specifically, the electromagnetic waves are transmitted by a transmitting antenna in a first dielectric layer, sequentially pass through the first dielectric layer, a second dielectric layer and a third dielectric layer, and are finally received by a receiving antenna in the third dielectric layer, and respectively expressing the total field quantity in the first dielectric layer, the second dielectric layer and the third dielectric layer by the following formulas (1), (2) and (3):
Wherein EnRepresenting the electric field strength, H, in the first, second and third dielectric layersnRepresents the magnetic field intensity in the first, second and third medium layers, and n is 1,2, 3;
Enirepresenting the amplitude of the incident wave in the first, second and third dielectric layers, EnrTable 1,2,3, the amplitude of the reflected wave in the first, second and third dielectric layers; x, y and z represent three-dimensional space coordinates of the three-layer medium model; d is the thickness of the second dielectric layer, and j is an imaginary unit;
k0representing wavenumbers in the first dielectric layer and the third dielectric layer, η0Representing the wave impedance in the first and third dielectric layers,k, η represent the wave number and wave impedance in the second dielectric layer respectively, εrrepresents the dielectric constant and the relative dielectric constant, ε, in the second dielectric layer0Represents the dielectric constant in the first and third dielectric layers, and epsilon ═ epsilon0εr(ii) a ω represents the angular frequency of the transmitted signal; mu.s0Is the magnetic permeability in the first dielectric layer and the third dielectric layer, mu is the magnetic permeability in the second dielectric layer, mu is mu0;
The boundary conditions for z-0 and z-d are:
E1|z=0=E2|z=0,H1|z=0=H2|z=0(4)
E2|z=d=E3|z=d,H2|z=d=H3|z=d(5)
namely, expressed as:
when z is 0:
when z is d:
the transmission coefficient can be expressed as:
wherein: e1iIs the incident wave field strength of the first medium layer, E3tThe transmitted wave field strength of the third dielectric layer, P, Q being the real and imaginary parts of the transmission coefficient;
from this, the amplitude attenuation coefficient S can be calculated as:
wherein A istRepresenting the amplitude of the transmitted wave, AiRepresenting the amplitude of the incident wave;
calculating the propagation delay of the electromagnetic wave, specifically: the propagation time t of the electromagnetic wave from the transmitting antenna to the receiving antenna is obtained according to the equation (12),
wherein c represents the propagation speed of the electromagnetic wave, v represents the propagation speed of the electromagnetic wave in the wall body, and l represents the distance from the transmitting antenna to the front surface of the wall body and the distance from the receiving antenna to the rear surface of the wall body;
estimating the second medium layer parameter, namely the wall body parameter according to the amplitude attenuation coefficient and the electromagnetic wave propagation delay, specifically solving the estimated wall body parameter value according to the equation set solved by the formula (13),
2. the method for estimating the unknown wall parameters based on the transmission coefficients of the electromagnetic waves as claimed in claim 1, wherein: the transmitting antenna and the receiving antenna are respectively 0.07m away from the front surface and the rear surface of the wall body.
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