Method for determining the radioelectric properties of a stratified medium using a radio frequency detection system

Abstract

Method for determining the radioelectric properties of a stratified medium comprising the steps of: Determining (101) at least one measure of a frequency transfer function of a transmission channel characterizing the medium; Determining (102) a model of said frequency transfer function for a model of the medium composed of at least two layers separated by a plane; Determining (103, 104) an estimation function of a correlation coefficient between the at least one measure of a frequency transfer function and the model of said function; Finding (105) at least one local maximum of the estimation function; Deducing (106) at least one position value of a plane and a value associated with this plane of a variable characterizing the radioelectric property of the medium. Figure 1

Description

Title of the invention: Method for determining the radioelectric properties of a stratified medium using a radio frequency detection system

[0001] The invention relates to the field of non-destructive devices and methods for characterizing the composition of a non-homogeneous material or medium using a radio frequency system. For example, the invention relates in particular to ground-penetrating radars that enable the detection, location, or identification of underground targets. The invention also applies to the characterization of other media, such as the thickness of skin, fat, and muscle of a living being (human or animal), using a radio frequency detection system positioned on the skin surface.

[0002] The invention relates more specifically to a method for determining the radioelectric properties of a stratified non-homogeneous medium such as soil or biological tissues by means of a radio frequency detection system

[0003] Ground-penetrating radar detection methods for buried targets are generally based on algorithms that require, in their parameters, a precise estimation of the dielectric permittivities of the different soil layers. In general, this information is either unknown or is estimated roughly as an average value for the entire soil structure. These approximations can increase uncertainties in the detection and characterization results of underground targets.

[0004] There is therefore a need for a method to accurately estimate the relative permittivities of the different soil layers and their thicknesses in order to subsequently use this information to improve target detection algorithms using ground-penetrating radar.

[0005] In the following text, the invention is described in the context of detecting targets buried in the ground, but the invention applies more generally to targets located in any material, which may be other than soil. The invention also applies to microwave medical imaging for detecting, for example, veins under the skin or the thicknesses of different biological tissues, or to non-destructive microwave testing for estimating the thickness of concrete layers in an industrial structure.

[0006] For all applications which aim to detect elements in a medium or material from a radio frequency detection system, knowledge of the radioelectric properties of the detection medium is important.

[0007] In general, it is interesting to determine the radioelectric properties of an object with unknown properties.

[0008] Indeed, the spatial localization of the targets sought is generally achieved by analyzing the propagation time of the radio signals emitted and received by the radio frequency system, which are then converted into distances using an estimation of the propagation speed of radio waves in the medium. Now, the propagation speed of an electromagnetic wave depends on the radioelectric properties of the medium, and in particular (although not exclusively) on its dielectric permittivity. The radioelectric properties of the medium make it possible to describe the response of this medium to an applied electric field.

[0009] For example, in the case of ground-penetrating radar, the medium through which the electromagnetic waves pass is generally the ground. In the case of applications in the healthcare field, the medium through which the waves pass relates to a set of biological tissues.

[0010] Most of the time, a priori assumptions are made about the actual values ​​of the radioelectric characteristics of the medium, such as the dielectric permittivity. However, the accuracy of these values ​​can be important to obtain sufficient precision for the detection and characterization of targets.

[0011] The invention therefore addresses a general problem of precise characterization of the radioelectric properties of a medium in which an electromagnetic wave propagates, in particular the dielectric permittivity or the permeability.

[0012] In the field of ground penetration radars, there are several methods of detecting the position of a target.

[0013] A known prior art method is hyperbola curve fitting, described, for example, in reference [1]. When a ground-penetrating radar antenna is moved above the ground surface and the penetrating wave encounters buried targets or interfaces between different soil layers, the received signal observed in the time domain has a hyperbolic shape due to the travel times of the reflected waves, which differ depending on the relative position of the radar antennas and the target. Several antenna position configurations can be used to observe this phenomenon. For example, the transmitting (Tx) and receiving (Rx) antennas can move in the same direction, with one remaining in a fixed position relative to the other.Alternatively, the Tx antenna can move symmetrically to the Rx antenna relative to a fixed central point; this configuration is then called "Common Mid Point". Finally, one antenna can be positioned at different locations relative to the second fixed antenna, in a configuration called "Wide Angle Reflection and Refraction".

[0014] All these observation techniques make it possible to obtain a hyperbolic-shaped diagram when observing the received signal in the time domain as a function of an antenna position metric. The vertex of the hyperbola then indicates the effective position of the target (or interface), and the shape of the hyperbola depends on the horizontal pitch and the signal velocity in the material: the higher the velocity, the wider the hyperbola, and vice versa. By analyzing the shape of the hyperbola, one can determine the wave propagation velocity in the medium and thus its electrical permittivity. Fitting the observed signal to a theoretical hyperbola is performed by a similarity analysis, as described, for example, in references [2, 3].

[0015] This method is very common for calibrating data from a ground-penetrating radar (GPR), but it has several major drawbacks. The method's accuracy remains low due to the difficulty of fitting a theoretical curve to an experimental observation subject to uncertainty. Increasing the accuracy requires acquiring a larger number of observations, which implies moving the antennas for each observation. Antenna movement can be avoided by using several spatially distributed Tx and Rx antennas, but in this case, the accuracy of the fitting technique is low. The method is also poorly suited to detecting stratified layers in a non-homogeneous medium, because the different reflections produce overlapping hyperbolas, making fitting more difficult.This situation requires the implementation of complex algorithms, as illustrated by reference [4].

[0016] Another known type of method concerns migration methods, such as those presented, for example, in reference [5]. These methods seek to reduce the inaccuracy of the hyperbola fitting method due to observational uncertainties in the received signal. This is a form of mathematical processing whose main purpose is to increase the accuracy of the hyperbolic traces of targets and interfaces. Theoretically, this process makes it possible to reduce the hyperbolas acquired by the radar to a single localization point. However, implementing this technique proves difficult when applied to potentially noisy experimental data. There is a wide variety of different migration methods, including hyperbolic summation, Kirchhoff migration, inverse projection focusing, phase-shift migration, and a>-k migration [5].

[0017] The main parameter required to reduce the hyperbola to a point corresponds to the dielectric properties of the soil as taught in reference [6]. This makes the migration process a means of increasing the accuracy of the curve fitting, since the process only works correctly if the applied ground transmission velocity is accurate. Thus, migration methods use an average estimate of the relative permittivity of a material for a given depth given. One drawback of these methods is their relative imprecision when the material is composed of several layers with different permittivities.

[0018] Reference [6] proposes a method applied to the detection of buried targets. It proposes testing different average permittivity values ​​for a given acquisition. The selected permittivity is the one that minimizes the surface area of ​​the detected target. Consequently, this method is not generic and is not applicable in the absence of a target, for example, in the case of a stratified inhomogeneous material. Furthermore, the metric of the apparent surface area of ​​the target is imprecise and is only suitable for targets of simple shape, whose apparent surface area varies monotonically with the absolute error in the assumed permittivity.

[0019] Other known methods aim to solve the problem of determining the radioelectric properties of a medium using a radio frequency detection system. Examples include patent applications and patents WO2020180191, EP3164672, WO2022091456, FR3041108 and FR3142553.

[0020] All these methods have drawbacks; some are invasive and destructive, others require prior knowledge of the medium's geometry, and still others are not applicable to inhomogeneous media. Generally, these methods offer solutions for processing radar data in the time domain.

[0021] There is a need for a method to accurately characterize the radioelectric properties of a medium using a radio frequency detection system that overcomes the limitations of prior art methods. In particular, the proposed method must be relatively simple to be compatible with implementation in a resource-constrained embedded system.

[0022] A new characterization method is proposed which operates in the frequency domain and which has reduced complexity compared to prior art methods.

[0023] The method according to the invention is particularly suitable for the characterization of stratified media composed of several layers separated by planes, each layer having different radioelectric properties or more generally of media that can be modeled, even approximately, by such a stratified structure.

[0024] The invention relates to a method for determining the radioelectric properties of a stratified medium comprising the steps of: - To determine, using a radio frequency detection system comprising at least one transmitter and one receiver, for each pair associating a receiver and a transmitter, at least one measurement of a frequency transfer function of a transmission channel characterizing the medium, - Determine a model of said frequency transfer function for a model of the medium composed of at least two layers separated by a plane, the model of the transfer function being a function of at least one variable characterizing a radioelectric property of the medium and at least one variable characterizing the position of the plane relative to the detection system, - Determine an estimation function for a correlation coefficient between at least one measurement of a frequency transfer function and the model of said function, - Search for at least one local maximum of the estimation function on the domain defined by at least one variable characterizing the position of the plane and at least one variable characterizing a radioelectric property of the medium, - Deduce at least one position value of a plane and a value associated with this plane of the variable characterizing the radioelectric property of the medium.

[0025] According to a particular aspect of the invention, the plane is parallel to the surface of the medium, the detection system is arranged parallel to the surface of the medium and at least one variable characterizing the position of the plane includes the depth of the plane.

[0026] According to a particular aspect of the invention, the plane is not parallel to the surface of the medium, the detection system is arranged parallel to the surface of the medium or inclined with respect to the surface of the medium and at least one variable characterizing the position of the plane includes the depth of the plane with respect to a point of the detection system and the angle of inclination of the plane with respect to the surface of the medium or with respect to the detection system.

[0027] According to a particular aspect of the invention, the steps of determining at least one measure of the frequency transfer function and of determining a model of said transfer function are carried out for each pair associating a transmitting antenna and a receiving antenna of the detection system, the method further comprising the determination of a correlation coefficient between said measurement and said model for each of said pairs, the estimation function being calculated from all the correlation coefficients.

[0028] According to a particular aspect of the invention, the amplitude and phase of the frequency transfer function model depend on the distance between a transmitting antenna and a point in the plane and on the distance between the point in the plane and a receiving antenna.

[0029] According to a particular aspect of the invention, the correlation coefficient estimation function is determined as an average of the correlation coefficients for all pairs and for one or more discrete frequency values.

[0030] According to a particular aspect of the invention, each correlation coefficient is weighted by a predefined weighting coefficient.

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[0042] According to a particular aspect of the invention, each weighting coefficient is inversely proportional to the number of pairs that have the same geometric arrangement between the transmitting antenna, the point in the plane and the receiving antenna as that of the pair associated with the correlation coefficient. According to a particular aspect of the invention, at least one variable characterizing a radioelectric property of the medium is taken from: the real part or the imaginary part of the dielectric permittivity or of the permeability. According to a particular aspect of the invention, the correlation coefficient is determined by an equalization method of type ZF, MMSE or MRC. In one embodiment, the method includes a step of replacing, in the estimation function, the depth variable with an electrical depth variable _r~7 , where e'r is the real part of the permittivity zel ~ zNcf dielectric. In one embodiment, the method further includes the application of a Dix-type algorithm to determine the respective permittivities of the medium layers from the estimated permittivities. According to one particular aspect of the invention, the stratified medium is the ground and the detection system is a ground-penetrating radar. The invention also relates to a device for determining radioelectric properties of layers of a stratified medium comprising a radio frequency detection system including at least one transmitting antenna and one receiving antenna and a processing unit, the device being configured to implement the method according to the invention. The invention also relates to a computer program comprising code instructions which lead the device according to the invention to execute the steps of the method according to the invention. The invention also relates to a computer-readable medium on which the computer program according to the invention is recorded. Other features and advantages of the present invention will become more apparent from the following description in relation to the following attached drawings. [Fig. 1] represents a flowchart detailing the steps for implementing a method for determining the radioelectric properties of a medium according to an embodiment of the invention, [Fig.2] schematically illustrates an example of a radio frequency detection system, suitable for implementing the invention, [Fig.3] illustrates a schematic diagram of a stratified medium model,

[0044] [Fig.4a] represents an illustration of permittivity estimation by focusing in the domain (e'r,z),

[0045] [Fig.4b] represents an illustration of permittivity estimation by focusing in the domain (e'r,zei),

[0046] [Fig. 5a] illustrates an example of the application of the invention to a laminate floor,

[0047] [Fig.5b] illustrates a focusing result for the example of [Fig.4a],

[0048] [Fig.6] represents a schematic diagram of a stratified medium model with a plane inclined relative to the ground surface,

[0049] [Fig.7] represents a diagram illustrating an alternative embodiment of the invention,

[0050] [Fig.8a] represents a focusing result obtained via the method according to the invention without the application of weighting coefficients in the calculation of the overall estimation function,

[0051] [Fig.8b] represents a focusing result obtained via the method according to the invention with application of weighting coefficients in the calculation of the overall estimation function,

[0052] [Fig.9] represents a comparative diagram of the maximum of the estimation function global as a function of the real part of the dielectric permittivity for the two variants of figures 8a and 8b,

[0053] [Fig. 10] schematically illustrates an example of a system suitable for implementing the invention.

[0054] Fig. 1 represents a flowchart of a method for determining radioelectric properties of a stratified medium according to an embodiment of the invention.

[0055] In the following description, the method is described for a non-limiting example intended for determining the permittivity of a medium such as soil using a radio frequency detection system such as ground-penetrating radar. However, the invention is not limited to the determination of permittivity but extends to the determination of any radioelectric property characterizing a medium, such as permeability.

[0056] Similarly, the invention is not limited to the use of a ground-penetrating radar device but extends to any radio frequency detection device.

[0057] The method begins in step 101 with a set of frequency transfer function measurements using a radio frequency detection device.

[0058] The radio frequency detection system comprises a transmitter capable of transmitting a radio frequency signal via at least one transmitting antenna Tx and a receiver capable of receiving this radio frequency signal via at least one receiving antenna Rx. Several versions of the transmitted signal are observed and depend on the positions of the Tx and Rx antennas.

[0059] According to one embodiment, these different versions of the received signal are obtained from several Tx antennas located at fixed positions and several Rx antennas located at fixed positions, according to a configuration of the radio frequency detection device called "Multiple Input Multiple Output (MIMO)".

[0060] Figure 2 schematically illustrates an example of such a radio frequency detection system in the form of a ground penetration radar having five transmitting antennas and four receiving antennas.

[0061] Alternatively, the different measurements can also be obtained by carrying out successive transmissions, and by moving the Tx or Rx antennas between each transmission.

[0062] Thus, a measurement is obtained for each pair associating a transmitting antenna Tx with a receiving antenna Rx for a given position of these two antennas.

[0063] The invention also applies to the case where a single antenna is used for both transmission and reception and is connected to the transmitter and receiver via a separation device such as a coupler.

[0064] The separation between the signals transmitted via each pair of Tx and Rx antennas is achieved in the time domain through successive transmissions, but it can also be achieved by any conventional multiple access method, such as frequency separation or by codes.

[0065] We now consider the general case of a system composed of M transmitting antennas and N receiving antennas, or more generally, of M different transmitting antenna positions and N different receiving antenna positions. M and N are two strictly positive integers.

[0066] The radio frequency detection system further includes an estimation module configured to determine, from the signal transmitted via the Tx antenna in position m and received via the Rx antenna in position n, a complex transfer function Hmn(f) for different values ​​of frequencies f.

[0067] Several methods for obtaining the transfer function Hmn(f) and for choosing a signal to be transmitted exist in the state of the art and are known techniques in the field of channel estimation or radio sounding.

[0068] References [9],

[10] and

[11] give examples of such methods.

[0069] The transfer function Hmn(f) depends on the composition of the medium traversed by the signal, and in particular the spatial distribution of the radioelectric properties of the medium, and in the case of the presence of targets, the position and Radar Equivalent Area (SER) of the targets.

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[0081] At the end of step 101, we therefore have a measurement of transfer function Hmn(f) for several frequency values ​​and for each pair (m,n) associating a transmitting antenna and a receiving antenna for which a measurement has been carried out. In step 102, a theoretical model of the frequency transfer function is then determined which takes into account the radioelectric properties of the medium through which the signal passes. The chosen model is suitable for a stratified medium composed of at least two layers, each layer separated by a plane P located at a depth zp, each layer being made of a homogeneous medium. For example, the chosen model can consider a homogeneous medium with a permittivity of real part e'r and negligible imaginary part. The transfer function between the emitter m and the receiver n, for this stratified medium model, is modeled by the following equation (1): ---------(1) rm and rn are respectively the positions of the transmitting antenna and the antenna of reception, Gm and Gn are the respective gains of the transmitting and receiving antennas; c is the speed of light in a vacuum. P) and P) represent respectively the distances, according to a specular reflection geometry, between the transmitting antenna m and the receiving antenna n via the plane P, respectively between the bridge rm and the plane P and between the point rn and the plane P. In the case where the radar antennas are aligned along the (O x) axis, with xm being the abscissa of the transmitting antenna m and xn the abscissa of the receiving antenna n, the Distances are calculated using the following relationship: Thus the spatial dimensions of the detection problem thus posed are reduced to the depth along the z-axis. The model given by equation (1) considers on the one hand the phase shift linked to the geometry of the scene for rectilinear propagation and on the other hand an amplitude given by the radar equation from the literature (see reference [7]). Without departing from the scope of the invention, other models can be developed to replace that of equation (1) insofar as they take into account at least one radioelectric property of the medium, for example the permittivity e'r.

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[0093] For example, equation (1) can be replaced by the following equation (Ibis) in which the coefficient is replaced by e'r. JgÂ.c kl m„ 1 (Ibis) ------L±_2!----— e-i2rrf^ W) Indeed, equation (1) provides a transfer function model suitable for a plane located at a depth zp in a homogeneous medium with a real part permittivity kr and a negligible imaginary part. Its phase is calculated by considering the delay accumulated by the wave for rectilinear propagation between the Tx antenna and the scatterer, and then between the scatterer and the Rx antenna. Its amplitude is given by the radar equation (see reference [7]). Observation of experimental results tends to show that the model given by equation (1) is not always optimal with regard to the modeling of amplitude. A physical explanation for the adaptation proposed by equation (Ibis) is that the radar cross-section (RCS) is assumed to be independent of the radioelectric properties of the medium. However, it is estimated that the RCS of a given object evolves inversely proportionally to the permittivity kr of the medium. The model of equation (Ibis) allows for improved focusing, as explained later. Figure 3 shows a schematic diagram of this model in a transverse (Ox,z) plane. A group of 8 antennas (M=N=8) is arranged in a plane that corresponds, for example, to the surface of a soil. Figure 3 shows a first plane 301 corresponding to a separation between two soil layers with different permittivities and a second plane 302 corresponding to a test plane located at an arbitrary depth z according to the model described previously. In step 103, a correlation coefficient is determined between the measurement carried out in step 101 and the model determined in step 102, for each pair of antennas. For example, the correlation coefficient is determined using relation (3) which represents a Zero Forcing (ZF) type equalization. (3) ( J ? Zp, S r) — , ,2 d * represents the complex conjugation operator Alternatively, the correlation coefficient can be obtained via another equalization formula, such as Minimum Mean Square Error (MMSE) or Maximum Ratio Combining (MRC). The correlation coefficient depends on at least the frequency, at least one spatial coordinate, and at least one radio frequency property, and is representative of a correlation between the measured transfer function Hmn(f) and the model W tm(f, Zp- 8 rj'

[0095] Steps 101, 102, 103 are iterated for each pair associating a transmitting antenna of index m and a receiving antenna of index n.

[0096] In step 104, a global estimation function of the correlation coefficient is then determined for all observations made by the radio frequency detection system.

[0097] Considering that the transfer functions are observed over a set of L discrete frequencies fb as well as for the different bi-static angles from M positions rm of the emitter and N positions rn of the receiver, the global estimation function is obtained by performing a consistent summation of the different observations as represented by equation (4):

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[0099] In step 105, at least one maximum of the global estimation function, or more precisely its absolute value when this function is complex, is then sought. The search is carried out in the multidimensional space consisting of the spatial variables and the variables characterizing the radioelectric properties that form the domain of definition of this function.

[0100] This approach is based on the principle that the values ​​of radioelectric properties that best correspond to the physical reality of the field provide correlation coefficient values ​​that are consistent between different frequencies and different configurations of observations, maximizing the magnitude of the consistent sum of equation (4).

[0101] This maximization of the modulus of the coherent sum of the correlation coefficients for values ​​of variables that correspond to an observed physical reality is also called the "focusing principle".

[0102] In step 106 of the method, at least one radioelectric property value associated with a spatial position of a plane P is deduced.

[0103] For example, for the example of equations (3) and (4), we obtain a position value and a dielectric permittivity value associated with this position which are defined by equation (5):

[0104] = argmax| A(z^ 8r) | (5) r

[0105] Argmax represents the mathematical function argument of the maximum, which provides the values ​​of the variables for which a function reaches its maximum.

[0106] Given the a priori model given by equation (1), the vector Zpax provides information on the position of the plane providing the largest Radar Equivalent Area in the observed space and g*™* provides information on the most representative value of the real part of the average dielectric permittivity in the part of the medium traversed by the electromagnetic wave between the transmitting antennas and the receiving antennas via the plane located at the depth z1^.

[0107] Advantageously, step 106 is not limited to the search for a single maximum but can be extended to the search for several local maxima of the function | A ( zp, Er ) | corresponding to several planes separating several layers of the stratified medium.

[0108] For example, we seek the R vertices of the continuous function |A(ZpEr)| exhibiting the highest values. The coordinates of each local maximum provide both the spatial position of a significant scatterer associated with a plane and the value of the radioelectric property most representative of the medium traversed by the electromagnetic wave between the transmitting and receiving antennas via this plane.

[0109] In one embodiment of the invention, the search for the maximum (step 105) can be performed in a subdomain of the domain of definition of the function | A ( Zp 8r ) j. Thus, for example, the search for the maximum can be limited to a subset of given spatial positions, for example, points located beyond a certain depth in the case of ground-penetrating radar. Similarly, the search for radioelectric property values ​​can be limited to a predefined interval.

[0110] In one embodiment of the invention, Dix's algorithm described in reference [8] is used to estimate the average permittivities of several soil layers.

[0111] Indeed, the average values ​​of permittivities estimated by the method of [Fig.1] correspond to the portion of the ground between the antenna array and the scattering planes associated with the detected maxima.

[0112] To obtain the permittivity per layer from the average permittivity, Dix's algorithm, which is based on root mean square velocities, is applied. This method allows the average permittivities to be decomposed into permittivities per layer.

[0113] Thus, the permittivity 'A»] of the Cn layer is determined from the average permittivities edco-»«] between the antenna array and the Cn layer and between the antenna array and the layer by means of the following relations:

[0114] A. / —. -\2(6)

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[0116] Zo-O

[0117] In another embodiment, the global estimation function A( Xp, Zp, <A) est modifiée de sorte à introduire un changement de variable. En effet, pour faciliter la recherche de maxima dans un espace multidimensionnel, il est pertinent de modifier la variable de profondeur z en la remplaçant par une variable de profondeur électrique _ [~7. zel“

[0118] Figures 4a and 4b illustrate, by way of example, the advantage of such a change of variable.

[0119] Figure 4a represents the value of the function A ( Xp, Zp, ) represented by its maximum value according to the dimension x in the plane (e'r,z).

[0120] The [Fig.4b] represents the same value in the (e'r,zel) plane.

[0121] It can be noted that the focusing task is significantly better defined in the (e'r,zei) plane. This is due to the fact that the physical metric being analyzed is fundamentally temporal in nature, being homogeneous to a delay, and not spatial in nature. Thus, a better quantified function is obtained when observed on a regular grid in the (e'r,zei) plane, compared to the (e'r,z) plane.

[0122] In figures 4a and 4b two maxima are observed for the values ​​(e'r,zei) = (5, 2.10m) and (6,4.50 m).

[0123] Figures 5a and 5b illustrate an example of the result of the method according to the invention applied to the detection of planes and characterization of soil layers.

[0124] Fig. 5a schematically illustrates an example of stratified soil composed of three layers: a first layer of asphalt 501 with permittivity era = 9 between depths z0 = 0 m and zl = 0.15 m, a second layer 502 of fill material with permittivity ermr = 20 between depths zl = 0.15 m and z2 = 1.95 m and a third layer 503 of generic soil with permittivity ersg = 15, from depth z2 = 1.95 m.

[0125] The results of the method according to the invention are illustrated in [Fig. 5b]. A first plane PI is detected at a depth of 21 cm, close to the actual depth of 15 cm of the first interface between the first two layers 501 and 502. A second plane P2 is detected at a depth of 2.04 m, close to the actual depth of 1.95 m of the second interface between the last two layers 502 and 503. The average permittivities detected by the algorithm for the media located above these two planes are 8.6 and 18.3, respectively. After application of Dix's algorithm, the permittivities obtained for the first two layers are 8.6 and 20.0, respectively.

[0126] In one embodiment of the invention, the transfer function model of equations (1), (1bis) and (2) is provided for a plane parallel to the ground surface and to the plane

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[0140] The radar can be modified to be adapted for detecting planes inclined or oblique to the ground surface. To achieve this, we define an angle α formed by plane P with a horizontal plane parallel to the ground surface. This principle is illustrated in [Fig. 6]. In this configuration, the elevation zp no longer represents the constant depth of the plane, but the depth of the plane vertically from a fixed point in the antenna array R, for example, the center of the antenna array, with abscissa xc. For example, we can set xc=0 without loss of generality. The distances Apn(rm, P) and A'p'ir^ P) introduced into the model of equation (Ibis) are then calculated using the following relations: Apn(rmP) = + Apm(r^ P) = ^-x^f + x^2 (8) The following variables are introduced: mn mJzp (9) z'm-{xn-x'myana z"m = - x^atia+zp ( 10) x'm = 2zpCosasina + x,„(l - 2wn2a) (11) z 'm = 2cosa(z.pCosa - xmsinaj (12) "rj represents the coordinates of the image point of the transmitting antenna" 'm' m! index m by axial symmetry via the plane P and z™") represents the coordinates of the specular reflection point between the transmitting antenna of index m and the receiving antenna of index n via the plane P. If a=0 we get back to the distances calculated via equation (2). Figure [Fig. 6] illustrates the specular reflection paths on an oblique plane P with inclination a=30°. Using equations (7) and (8) to calculate the distances Apn(rtn, P) and Ap”(r„, P) in the evaluation of the transfer function WmAf) given by equation (1) or (Ibis), we obtain a global estimation function A„m(Zp, a, e ) with three variables: the elevation of the plane oblique to the vertical of a fixed point of the antenna array, the angle that the oblique plane forms with the horizontal plane parallel to the ground surface and of the plane formed by the detector, and the dielectric permittivity of the medium. The method for finding the maxima of this function described previously is then applied identically to determine the coordinates of the oblique plane (Zp, a) and the radioelectric properties of the medium s'r.

[0141] The method according to the invention is also suitable and directly applicable in the case where the medium consists of horizontal layers, but where the plane formed by the detector is inclined or oblique with respect to the surface of the medium. One application of this scenario is when the radio frequency detector is positioned in a plane inclined with respect to the surface of the medium. For example, in the field of ground-penetrating radar, the radar can be tilted at the front of a vehicle so as to illuminate a portion of the ground obliquely.

[0142] In another embodiment of the invention, the overall estimation function given by equation (4) is modified by assigning a variable weight to each correlation coefficient. Equation (4) then becomes:

[0143] A ( Fp, S r) — ( ^nm ( ff ^P' kr )

[0144] y(m, n, 1) is a weighting coefficient which can take different values ​​for each observation associated with a frequency and a pair of antennas.

[0145] For example, the following weighting function makes it possible to disregard observations made by the transmitting antenna with index m=l, in the case where these observations are deemed erroneous:

[0146] y(m, n, l) = 0, if m= 1

[0147] y (m, n,l) = 1, if m * 1

[0148] Fig. 7 illustrates an example of determining the weighting coefficients for an application case to the detection of horizontal planes, i.e. parallel to the plane formed by the radar antennas, for example the plane parallel to the ground surface.

[0149] Fig. 7 schematically illustrates such a configuration for an example of 8 ArA 8 antennas. It can be noted that several pairs of antennas (transmit / receive) perform a similar observation of the P-plane in the sense that the Fonde path emitted by the transmitting antenna towards the P-plane, and then reflected back to the receiving antenna, is the same for several pairs of antennas.

[0150] The following pairs of antennas thus have the same observation of the P-plane and can be grouped into 8 groups G1-G8: G1: (Ab A0; (A2, A2); (A3, A3); (A4, A4); (A5, A5); (A6, A6); (A7, A7); (A8, A8) G2: (Ab A2); (A2, A3); (A3, A4); (A4, A5); (A5, A6); (A6, A7); (A7, A8); (A2, AO; (A3, A2); (A4, A3); (A5, A4); (A6, A5); (A7, A6); (A8, A7); G3: (Ab A3); (A2, A4); (A3, A5); (A4, A6); (A5, A7); (A6, A8); (A3, AJ; (A4, A2); (A5, A3); (A6, A4); (A7, A5); (A8, Ag); G4: (Ab A4); (A2, A5); (A3, A6); (A4, A7); (A5, A8); (A4, AJ; (A5, A2); (A6, A3); (A7, A4); (A8, A5) G5: (Ab AJ; (A2, A6); (A3, A7); (A4, A8); (A5, AJ; (A6, AJ; (A7, AJ; (A8, AJ; G6: (Ab AJ; (A2, AJ; (A3, A8); (A6, AJ; (A7, AJ; (A8, A3); G7: (Ab A7); (A2, AJ; (A7, AJ; (A8, AJ; G8: (Ab AJ; (A8, AJ;

[0151] An example of a weighting choice is to balance the contribution of each type of observation by counting the pairs corresponding to each type of observation and allocating to each pair a weight inversely proportional to the number of similar pairs.

[0152] More generally, the weighting coefficient y of each group of antenna pairs having the same observation of the P-plane is equal to y = k / Np, where Np is the number of antenna pairs having the same observation of the P-plane and k is a strictly positive number. The values ​​of Np for each group are given below: G1 :NP= 8 G2: Np = 14 G3: Np = 12 G4: Np = 10 G5: Np = 8 G6: Np = 6 G7: Np = 4 G8: Np = 2

[0153] To normalize the absolute value of the correlation function with respect to the unweighted case, the value of k is chosen, for example, such that k = MxN / Ng, where Ng represents the number of groups of antenna pairs, i.e., a weighting coefficient equal to y = (MxN) / (Npx Ng). In the example in [Fig. 7], Ng = 8.

[0154] Using the example from [Fig.7], the following weights are allocated to the eight groups defined above: G1: y = 64 / (8*8) = 1 G2: y = 64 / (14*8) = 4 / 7 G3: y = 64 / (12*8) = 2 / 3 G4: y = 64 / (10*8) = 4 / 5 G5: y = 64 / (8*8) = 1 G6: y = 64 / (6*8) = 4 / 3 G7: y = 64 / (4*8) = 2 G8: y = 64 / (2*8) = 4

[0155] In other words, each weighting coefficient is inversely proportional to the number of antenna pairs that have the same geometric arrangement, For example, the same cumulative distance between the transmitting antenna, the point in the plane, and the receiving antenna as that of the pair associated with the correlation coefficient. Another example of a geometric arrangement that allows comparison of antenna pairs is the angle of incidence formed between the normal to the plane and the path of the transmitting antenna at the point in the plane.

[0156] Figures 8a and 8b present a focusing result applied to a measurement consisting of detecting a horizontal plane at a depth of 1.40m and evaluating the permittivity of the material constituting the corresponding layer formed of sand.

[0157] Figure 8a shows the result without weighting coefficients in the calculation of the overall estimation function (equation 4). Figure 8b shows the same result by applying the weighting coefficients described above to the overall estimation function (equation 13).

[0158] It is noted that the application of the weighting coefficients according to the positions of the antennas with respect to the plane allows for finer focusing, making it possible to better define the permittivity value optimizing the global estimation function.

[0159] This can also be seen in [Fig. 9], which shows the shape of the maximum according to the depth variable z of the overall estimation function, in the two aforementioned cases, as a function of the real part of the permittivity. Curve 900 shows the results corresponding to [Fig. 8a] (without weighting coefficients). Curve 901 shows the results corresponding to [Fig. 8b] (with weighting coefficients). It can be seen that curve 901 is more centered around its maximum than curve 900. The permittivity value obtained is therefore more precise in the second case.

[0160] Fig. 10 schematically represents a system for determining the radioelectric properties of a medium according to an embodiment of the invention.

[0161] The system 1000 mainly comprises a radio frequency detection device RAD of the type described in [Fig.2] and a processing unit UT configured to implement the method according to the invention from measurements made by the RAD device.

[0162] The processing unit TU can be implemented in software and / or hardware form, in particular by using one or more processor(s) and one or more memory(ies). The processor can be a generic processor, a specific processor, an application-specific integrated circuit (also known as an ASIC for "Application-Specific Integrated Circuit"), or a field-programmable gate array (FPGA for "Field-Programmable Gate Array").

[0163] System 1000 may include a user interface for displaying results produced by the method. References

[0164] [1 ] S. Serkan and V. Borecky, “Estimation methods for obtaining GPR signal velocity,” in Proceedings of the Third International Conférence on ACSEE, Zurich, Switzerland, 2015, pp. 10-11.

[0165] [2] E. Forte and M. Pipan, “Review of multi-offset GPR applications : Data acquisition, processing and analysis,” Signal processing, vol. 132, pp. 210-220, 2017.

[0166] [3] I. Dal Bo, A. Klotzsche et al., “Geophysical imaging of regolith in landscapes along a climate and végétation gradient in the Chilean Coastal cordillera,” Catena, vol. 180, pp. 146-159, 2019.

[0167] [4] Q. Dou, L. Wei, D. R. Magee, and A. G. Cohn, “Real-time hyperbola récognition and fitting in GPR data,” IEEE Transactions on Geoscience and Remote Sensing, vol. 55, no. l,pp. 51-62, 2017.

[0168] [5] C. Ozdemir, S5. Demirci et al., “A review on migration methods in B-scan ground penetrating radar imaging,” Mathematical Problems in Engineering, vol. 2014, 2014.

[0169] [6] Z. Dong, X. Feng et al., “3D migration depth focus velocity analysis of hand-held ground penetrating radar,” Geosciences, vol. 12, no. 4, p. 178, 2022.

[0170] [7] E. F. Knott, I. F. Schaeffer, and M. T. Tulley, Radar Cross Section. SciTech Publishing, 2004.

[0171] [8] C. H. Dix, “Seismic velocities from surface measurements,” Geophysic s , vol. 20, no. 1, pp. 68-86,1955.[9] Demery, D. A., I. D. Parsons, and A. M. D. Turkmani. "Sounding techniques for wideband mobile radio channels: a review." IEEE Proceedings (Communications, Speech and Vision) 138.5 (1991): 437-446.

[0172] [9] Demery, D. A., I. D. Parsons, and A. M. D. Turkmani. "Sounding techniques for wideband mobile radio channels: a review." IEEE Proceedings (Communications, Speech and Vision) 138.5 (1991): 437-446.

[0173]

[10] Laurenson, Dave, and Peter Grant. "A review of radio channel sounding techniques." 2006 14th European Signal Processing Conférence. IEEE, 2006.

[0174]

[11] Ullah, M. Habib, and A. Unggul Priantoro. "A review on multiplexing schemes for MIMO channel sounding." International Journal of Computer Science and Network Security 9.6 (2009): 294-300.

Claims

Demands

1. A method for determining the radioelectric properties of a stratified medium comprising the steps of: - Determining (101), by means of a radio frequency detection system comprising at least one transmitter and one receiver, for each pair associating a receiver and a transmitter, at least one measurement of a frequency transfer function of a transmission channel characterizing the medium, - Determining (102) a model of said frequency transfer function for a model of the medium composed of at least two layers separated by a plane, the model of the transfer function being a function of at least one variable characterizing a radioelectric property of the medium and at least one variable characterizing the position of the plane relative to the detection system, - Determining (103, 104) an estimation function of a correlation coefficient between the at least one measurement of a frequency transfer function and the model of said function,- Search (105) for at least one local maximum of the estimation function on the domain defined by at least one variable characterizing the position of the plane and at least one variable characterizing a radioelectric property of the medium, - Deduce (106) at least one position value of a plane and a value associated with this plane of the variable characterizing the radioelectric property of the medium.

2. Method for determining radioelectric properties of layers of a stratified medium according to claim 1 wherein the plane is parallel to the surface of the medium, the detection system is arranged parallel to the surface of the medium and at least one variable characterizing the position of the plane includes the depth of the plane.

3. A method for determining the radioelectric properties of layers of a stratified medium according to claim 1, wherein the plane is not parallel to the surface of the medium, and the detection system is arranged parallel to the surface of the medium or inclined with respect to it. to the surface of the medium and at least one variable characterizing the position of the plane includes the depth of the plane relative to a point of the detection system and the angle of inclination of the plane relative to the surface of the medium or relative to the detection system.

4. Method for determining radioelectric properties of layers of a stratified medium according to any one of the preceding claims wherein the steps of determining (101) at least one measurement of the frequency transfer function and of determining (102) a model of said transfer function are carried out for each pair associating a transmitting antenna and a receiving antenna of the detection system, the method further comprising the determination (103) of a correlation coefficient between said measurement and said model for each of said pairs, the estimation function being calculated (104) from all the correlation coefficients.

5. Method for determining radioelectric properties of layers of a stratified medium according to claim 4 wherein the amplitude and phase of the model of the frequency transfer function depend on the distance between a transmitting antenna and a point in the plane and on the distance between the point in the plane and a receiving antenna.

6. Method for determining radioelectric properties of layers of a stratified medium according to any one of claims 4 to 5 wherein the correlation coefficient estimation function is determined (104) as an average of the correlation coefficients for all pairs and for one or more discrete frequency values.

7. Method for determining radioelectric properties of a medium according to claim 6 wherein each correlation coefficient is weighted by a predefined weighting coefficient.

8. Method for determining radioelectric properties of layers of a stratified medium according to claim 7 wherein each weighting coefficient is inversely proportional to the number of pairs that have the same geometric arrangement between the transmitting antenna, the point in the plane and the receiving antenna as that of the pair associated with the correlation coefficient.

9. Method for determining the radioelectric properties of layers of a stratified medium according to any one of the claims previous in which at least one variable characterizing a radioelectric property of the medium is taken from: the real part or the imaginary part of the dielectric permittivity or of the permeability.

10. Method for determining radioelectric properties of layers of a stratified medium according to any one of the preceding claims wherein the correlation coefficient is determined by an equalization method of type ZF, MMSE or MRC.

11. Method for determining radioelectric properties of layers of a stratified medium according to any one of claims 2 to 9 comprising a step of replacing, in the estimation function, the depth variable by an electric depth variable _ [~7 , where e'r is the real part of the ^el ~ r dielectric permittivity.

12. Method for determining radioelectric properties of layers of a stratified medium according to any one of the preceding claims, further comprising the application of a Dix-type algorithm to determine the respective permittivities of the layers of the medium from the estimated permittivities.

13. Method for determining radioelectric properties of layers of a stratified medium according to any one of the preceding claims wherein the stratified medium is the ground and the detection system is a ground-penetrating radar.

14. Device (1000) for determining radioelectric properties of layers of a stratified medium comprising a radio frequency detection (RAD) system including at least one transmitting antenna and one receiving antenna and a processing unit (TU), the device being configured to implement the method according to any one of the preceding claims.

15. A computer program comprising code instructions that cause the device according to claim 14 to perform the steps of the method according to any one of claims 1 to

16. 13. Computer-readable medium on which the computer program according to claim 15 is recorded.

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