Method for determining the radioelectric properties of a non-homogeneous medium using a radio frequency detection system

Abstract

Method for determining the radioelectric properties of a medium comprising the steps of: Determining (101) a measure of a frequency transfer function of a transmission channel characterizing said medium, Determining (102) a model of said frequency transfer function as a function of at least one position variable and at least one variable characterizing a radioelectric property of the medium, Determining (104) an overall estimation function of the correlation coefficient between the transfer function measurements and the models, Finding (105) at least one local maximum of the estimation function on the domain defined by at least one position variable and at least one variable characterizing a radioelectric property of the medium, Deducing (106) at least one value of the variable characterizing the radioelectric property of the medium as that which yields said local maximum. Figure 1

Description

Title of the invention: Method for determining the radioelectric properties of a non-homogeneous 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 may also relate to the field of health, for example, the characterization of biological tissues.

[0002] The invention relates more specifically to a method for determining the radioelectric properties of a non-homogeneous medium using a radio frequency system.

[0003] 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.

[0004] 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.

[0005] 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.

[0006] 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.

[0007] 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.

[0008] In the field of ground penetration radars, there are several methods of detecting the position of a target.

[0009] 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".

[0010] All these observation techniques make it possible to obtain a hyperbolic shape 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].

[0011] This method is very common for calibrating GPR data, but it has several major drawbacks. The accuracy of the method 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. Moving the antennas can be avoided if several spatially distributed Tx and Rx antennas are available, 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 in reference [4].

[0012] Another known type of method concerns migration methods, such as those presented, for example, in reference [5]. These methods seek to reduce the imprecision of the hyperbola fitting method due to uncertainties. observation of 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 allows the hyperbolas acquired by the radar to be reduced to a single localization point. However, implementing this technique proves challenging 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].

[0013] The main parameter required to reduce the hyperbola to a single point corresponds to the dielectric properties of the soil as described 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. A drawback of these methods is their relative inaccuracy when the material is composed of several layers with different permittivities.

[0014] 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.

[0015] 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.

[0016] 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.

[0017] 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. The method The proposed solution must, in particular, be of low complexity to be compatible with implementation in an embedded system with limited resources.

[0018] A new characterization method is proposed which operates in the frequency domain and which has reduced complexity compared to prior art methods.

[0019] The invention relates to a method for determining the radioelectric properties of a 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, a measurement of a frequency transfer function of a transmission channel characterizing said medium, - Determine, for each of the said pairs, a model of the said frequency transfer function as a function of at least one position variable and at least one variable characterizing a radioelectric property of the medium, - Determine, for each of the aforementioned pairs, a correlation coefficient between the measurement of the frequency transfer function and the model, - Determine an overall estimation function for the correlation coefficient between the transfer function measurements and the models, for all pairs, - Search for at least one local maximum of the estimation function on the domain defined by at least one position variable and at least one variable characterizing a radioelectric property of the medium, - Deduce at least one value of the variable characterizing the radioelectric property of the medium as that which allows obtaining said local maximum.

[0020] According to a particular aspect of the invention, the step of searching for at least one local maximum of the estimation function is carried out by means of several iterations of the substeps of: - Define a first level of sampling of the search space, - To find a local maximum for this first level of sampling, - Reduce the search space around the local maximum and define a second sampling level within the reduced search space, with the step size of the second sampling level being smaller than the step size of the first sampling level.

[0021] According to a particular aspect of the invention, the step of searching for at least one local maximum of the estimation function comprises the substeps of: - Find a first local maximum of the estimation function, - Determine the backscattering coefficient of the first scatterer associated with the first local maximum, based on said local maximum of the global estimation function. - Determine the contribution of the first scatterer in the measurement of the frequency transfer function as equal to the product of the backscattering coefficient of the first scatterer and the value of the transfer function model taken at the coordinates of the first local maximum, - Subtract the contribution of the first diffuser from the measurement of the frequency transfer function, - Iterate the previous steps to search for another local maximum of the global estimation function determined from the corrected measurement of the frequency transfer function

[0022] 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.

[0023] In one embodiment, the method includes searching for several local maxima of the estimation function, each local maxima providing a position value of a scatterer in the medium and a value of the variable characterizing the radioelectric property at said position.

[0024] According to a particular aspect of the invention, the correlation coefficient is determined by an equalization method of type ZF, MMSE or MRC.

[0025] According to a particular aspect of the invention, the overall estimation function of the correlation coefficient is determined as an average of the correlation coefficients for all pairs and for one or more discrete frequency values.

[0026] According to a particular aspect of the invention, each correlation coefficient is weighted by a predefined weighting coefficient.

[0027] According to a particular aspect of the invention, at least one position variable is a depth value and the method includes a step of replacing, in the overall estimation function, the depth variable with an electrical depth variable _ / 77 , where e'r is the real part of the permittivity dielectric.

[0028] The invention also relates to a system for determining radioelectric properties of a medium comprising a radio frequency detection device including at least one transmitter and one receiver and a processing unit, the system being configured to implement the method according to the invention.

[0029] According to a particular aspect of the invention, the radio frequency detection system is a ground penetration radar.

[0030] 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 and a computer-readable medium on which the computer program according to the invention is recorded.

[0031] Other features and advantages of the present invention will become more apparent from the following description in relation to the following accompanying drawings.

[0032] [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,

[0033] [Fig.2] schematically illustrates an example of a radio frequency detection system, capable of putting implementing the invention,

[0034] [Fig.3] illustrates a graphical representation of a transfer function model,

[0035] [Fig.4] represents a flowchart detailing the steps of a first variant of implementation of the method according to the invention,

[0036] [Fig.5] illustrates an application of the variant of [Fig.4],

[0037] [Fig.6] represents a flowchart detailing the steps of a second variant of implementation of the method according to the invention,

[0038] [Fig.7a] represents an illustration of permittivity estimation by focusing in the domain (e'r,z),

[0039] [Fig.7b] represents an illustration of permittivity estimation by focusing in the domain (e'r,zei),

[0040] [Fig.8] schematically illustrates an example of a system suitable for implementing the invention.

[0041] Fig. 1 represents a flowchart of a method for determining the radioelectric properties of a medium according to an embodiment of the invention.

[0042] 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.

[0043] Similarly, the invention is not limited to the use of a ground-penetrating radar device but extends to any radio frequency detection device.

[0044] The method begins in step 101 with a set of frequency transfer function measurements using a radio frequency detection device.

[0045] The radio frequency detection system comprises a transmitter capable of transmitting a radio frequency signal via at least one Tx transmitting antenna and a receiver capable of receiving this radio frequency signal via at least one Rx receiving antenna. Several versions of the transmitted signal are observed and depend on the positions of the Tx and Rx antennas.

[0046] 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)".

[0047] Figure 2 schematically illustrates an example of such a radio frequency detection system in the form of an RPS ground penetration radar having five transmitting antennas and four receiving antennas.

[0048] Alternatively, the different measurements can also be obtained by carrying out successive transmissions, and by moving the Tx or Rx antennas between each transmission.

[0049] 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.

[0050] 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.

[0051] 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.

[0052] 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.

[0053] 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 frequency values ​​f.

[0054] Several methods for obtaining the transfer function Hmn(f) and for choosing a signal to be transmitted exist in the prior art and are known techniques in the field of channel estimation or radio sounding. References [9],

[10] and

[11] give examples of such methods.

[0055] The transfer function Hmn(f) depends on the composition of the medium through which the signal passes, and in particular on the spatial distribution of the radioelectric properties of the medium, and in the case of the presence of targets, on the position and the Radar Equivalent Area (SER) of the targets.

[0056] 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.

[0057] 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.

[0058] For example, the chosen model is adapted to a point diffuser located at a position rp in a homogeneous medium with permittivity of real part e'r and negligible imaginary part. The transfer function between the emitter m and the receiver n is modeled by the following equation (1):

[0059]

[0060] rm and rn are respectively the positions of the transmitting antenna and the receiving antenna,

[0061] Gm and Gn are the respective gains of the transmitting and receiving antennas,

[0062] That's the speed of light in a vacuum.

[0063] 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]).

[0064] Fig. 3 schematically represents a graphical representation of the model of equation (1) for M=N=8 and for two diffusers 301, 302. Reference 303 represents a test point located at coordinates (x, z).

[0065] Without departing from the scope of the invention, other models can be developed as a replacement for that of equation (1) insofar as they take into account at least one radioelectric property of the medium, for example the permittivity e'r.

[0066] For example, equation (1) can be replaced by the following equation (Ibis) in which the coefficient ET" is replaced by 'r.

[0067] IM / ) =

[0068] Indeed, equation (1) provides a transfer function model suitable for a point scatterer located at a position rp in a homogeneous medium with permittivity of real part s'r and 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]).

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] 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 e'r of the medium. The model of equation (Ibis) allows for improved focusing, as explained later. 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 (2) which represents a Zero Forcing (ZF) type equalization. . . , , , (2) A,„, = • î mn\J / p^ f / j * represents the complex conjugation operator Alternatively, the correlation coefficient can be obtained via another equalization formula, such as those of the "Minimum Mean Square Error" (MMSE) or "Maximum Ratio Combining" (MRC) type. The correlation coefficient depends on at least the frequency, at least one spatial coordinate, and at least one radio property, and is representative of a correlation between the measured transfer function Hmn(f) and the model Wmn(f, rp, er)- Steps 101, 102, 103 are iterated for each pair associating a transmitting antenna with index m and a receiving antenna with index n. In step 104, we then determine a global estimation function of the correlation coefficient for all observations made by the radio frequency detection system. 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 (3): A ( rp, S r ) = ( f P rp, £ r ) In step 105, we then search for at least one maximum of the global estimation function, or more precisely, its absolute value when this function is complex. The search is carried out in the multidimensional space consisting of spatial variables and variables characterizing the radioelectric properties forming the domain of definition of this function.

[0083] 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 observation configurations, maximizing the magnitude of the consistent sum of equation (3).

[0084] 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".

[0085] In step 106 of the method, at least one radioelectric property value associated with a spatial position is deduced.

[0086] For example, for the example of equations (2) and (3), we obtain a position value and a dielectric permittivity value associated with this position which are defined by equation (4):

[0087] ( e'™lx ) - argmax | A(er)j(4) rpe'r

[0088] Argmax represents the mathematical function argument of the maximum, which provides the values ​​of the variables for which a function reaches its maximum.

[0089] Given the a priori model given by equation (1), the vector indicates the position of the point scatterer providing the largest Radar Equivalent Area in the observed space and indicates 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 position

[0090] 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(r^ e'r) |.

[0091] For example, we seek the R vertices of the continuous function |A(?> er) | exhibiting the highest values. The coordinates of each local maximum provide both the spatial position of a significant scatterer and the value of the radioelectric property most representative of the medium traversed by the electromagnetic wave between the transmitting antennas and the receiving antennas via this scatterer.

[0092] In one embodiment of the invention, the search for the maximum (step 105) can be carried out in a subdomain of the domain of definition of the function | A(rp, Er) |. Thus, for example, the search for the maximum can be limited to a sub A set 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.

[0093] In another embodiment of the invention, the overall estimation function given by equation (3) is modified by assigning a variable weight to each correlation coefficient. Equation (3) then becomes:

[0094] A(rp, s'r) = e'r)

[0095] y(m, n, l) is a weighting coefficient which can take different values ​​for each observation associated with a frequency and a pair of antennas.

[0096] 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:

[0097] y (m, n, l) = 0, if m = 1

[0098] y(m, n,l) = 1, if m* 1

[0099] To implement the method described in Figure 1, a difficulty lies in exploring the domain of definition of the function | A ( ^'^ ) | . Indeed, following The number of spatial variables and radio parameters that form the dimensions of this domain means that finding a maximum can become very complex and require significant execution time, which may be incompatible with real-time implementation in a resource-limited embedded device.

[0100] To overcome this drawback, a first embodiment of the invention is proposed, described in [Fig. 4], which aims to optimize the exploration space of the global estimation function. In other words, it aims to optimize step 105 of searching for local maxima.

[0101] The flowchart in [Fig.4] details the implementation steps of this variant of the realization of step 105.

[0102] In step 401, a first level of sampling, called coarse, is determined, of the exploration space having a predefined sampling step so as to have a limited number of samples in the exploration space, this number being compatible with the available memory space and computing power.

[0103] In step 402, we search for a first maximum for this first sampling level.

[0104] In step 403, the exploration space is reduced around the maximum found in step 402 and the sampling level is increased in this reduced space with a finer sampling step than in step 401. For example, the exploration domain is reduced by a certain percentage while maintaining the same number of samples as in step 401 due to the reduction in the sampling step.

[0105] Steps 402 and 403 are iterated several times in order to refine the exact coordinates of the maximum.

[0106] Figure 5 illustrates an example of an embodiment of this variant for the case of a ground-penetrating radar. The spatial domain exploration space is limited to abscissa values ​​x within a given interval and to depth values ​​z within a given interval. The global estimation function is a function of three variables, xp, zp, and e'r.

[0107] Fig. 5 shows the spatial search space with successive search areas 501-504 which are reduced at each iteration to be centered on the maximum 505.

[0108] One disadvantage of this method is that it is not suitable for the search for several local maxima since the iterative reduction of the search areas may exclude other local maxima.

[0109] Another variant of the invention is proposed which allows the method of [Fig.4] to be adapted to the search for several local maxima.

[0110] This alternative variant consists of performing several iterations of the method in [Fig. 4], each iteration being dedicated to finding a local maximum among several maxima. At each iteration, the diffuser associated with the maximum detected in the previous iteration is progressively subtracted from the observed transfer function, so as to allow an iterative focus on secondary maxima of the global estimation function.

[0111] Figure [Fig. 6] represents a flowchart detailing the implementation steps of this variant embodiment.

[0112] In step 601, a first local maximum corresponding to the largest diffuser is sought. For example, step 601 is implemented using the iterative method described in [Fig. 4] by progressively reducing the search space.

[0113] In step 602, the contribution of the 1st scatterer detected in step 601 is calculated in the spectral transfer function, for each pair of antennas.

[0114] Still placing ourselves in the example of [Fig.5] for which we limit ourselves to a spatial search space in x and z, we obtain the parameters {xi,zi and e'ri] of the first point diffuser at step 601.

[0115] We then calculate an estimator of the complex backscattering coefficient of the first point diffuser which is given for example by relation (6):

[0116] __i_y M y ,v A V 6)

[0117] Alternatively, considering that the backscattering coefficient does not depend on the frequency, relation (6) is replaced by relation (6'):

[0118] ^„_±_y M A (fx 7 p V 6,)

[0119] Next, the contribution of the first scatterer to the spectral transfer function is calculated using relation (7) by multiplying the backscattering coefficient and the model taken at the values ​​of the first extremum:

[0120] H^f,) x„ z,, e ;i <7)

[0121] Then, in step 603, the contribution calculated in step 602 is subtracted from the transfer function initially measured in step 101 in order to obtain a residual transfer function in which the contribution of the first diffuser has been removed:

[0122] (8)

[0123] Steps 601, 602, 603 are then iterated as many times as there are local maxima to be detected, subtracting at each iteration the contribution of the detected diffuser to the transfer function.

[0124] A stopping criterion of the method is for example a predefined number of iterations or a criterion for comparing the power ratio between the residual transfer function and the transfer function initially measured at a predefined threshold.

[0125] In an embodiment particularly applicable to ground-penetrating radars, the global estimation function A(Xp, Zp, Σ f) is modified to introduce a change of variable. Indeed, to facilitate the search for maxima in a multidimensional space, it is relevant to modify the depth variable z by replacing it with an electrical depth variable.

[0126] Figures 7a and 7b illustrate, by way of example, the advantage of such a change of variable.

[0127] Figure 7a represents the value of the function A(Xp, Zp, £ r) represented by its maximum value according to the dimension x in the plane (e'r,z).

[0128] The [Fig.7b] represents the same value in the (e'r,zei) plane.

[0129] 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.

[0130] In figures 7a and 7b two maxima are observed for the values ​​(e'r,zei) = (5, 2.10m) and (6,4.50 m).

[0131] In another embodiment of the invention, Dix's algorithm described in reference [8] is used to estimate the average permittivities of several soil layers.

[0132] Using the example of Figures 7a and 7b, the maxima search detected two objects: one at a depth of 0.95 m with an average permittivity of 5 and the other at a depth of 1.80 m with an average permittivity of 6. The average permittivity values ​​correspond to the portion of the ground between the antenna array and the scatterer associated with the detected maximum.

[0133] Thus, the double detection identified in Figures 7a and 7b confirms the existence of at least two layers of material with different permittivities. 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.

[0134] Thus, the permittivity of the Cn layer is determined from the average permittivities between the antenna array and the Cn layer and between the antenna array and the Cn layer [i^Wt] using the following relations:

[0135] / f— r--\2 II

[0136]

[0137] Zo = O

[0138] Fig. 8 schematically represents a system 800 for determining radioelectric properties of a medium according to an embodiment of the invention.

[0139] The 800 system 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.

[0140] 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").

[0141] The 800 system may include a user interface for displaying results produced by the method. References

[0142] [1] S. Serkan and V. Borecky, “Estimation methods for obtaining GPR signal velocity,” in Proceedings of the Third International Conference on ACSEE, Zurich, Switzerland, 2015, pp. 10-11.

[0143] [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.

[0144] [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.

[0145] [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.

[0146] [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.

[0147] [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.

[0148] [7] E. F. Knott, I. F. Schaeffer, and M. T. Tulley, Radar Cross Section. SciTech Publishing, 2004.

[0149] [8] C. H. Dix, “Seismic velocities from surface measurements,” Geophysic s, vol. 20, no. l,pp. 68-86,1955.

[0150] [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.

[0151]

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

[0152]

[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

1.

2. Demands Method for determining the radioelectric properties of a medium, comprising the steps of: - Determine (101), using a radio frequency detection system comprising at least one transmitter and one receiver, for each pair associating a receiver and a transmitter, a measure of a frequency transfer function of a transmission channel characterizing said medium, - Determine (102), for each of said pairs, a model of said frequency transfer function as a function of at least one position variable and at least one variable characterizing a radioelectric property of the medium, - Determine (103), for each of the said pairs, a correlation coefficient between the measurement of the frequency transfer function and the model, - Determine (104) a global estimation function for the correlation coefficient between the transfer function measurements and the models, for all pairs, - Search (105) for at least one local maximum of the estimation function on the domain defined by at least one position variable and at least one variable characterizing a radioelectric property of the medium, - Deduce (106) at least one value of the variable characterizing the radioelectric property of the medium as that which allows obtaining said local maximum. Method for determining the radioelectric properties of a medium according to claim 1, wherein step (105) of searching for at least one local maximum of the estimation function is carried out by means of several iterations of the substeps of: - Define (401) a first level of sampling of the search space, - Search (402) for a local maximum for this first sampling level, - Reduce (403) the search space around the local maximum and define a second sampling level in the reduced search space, the step size of the second sampling level being finer than the step size of the first sampling level

3. A method for determining the radioelectric properties of a medium according to any one of the preceding claims, wherein the step of searching for at least one local maximum of the estimation function comprises the substeps of: - Searching (601) for a first local maximum of the estimation function, - Determining (602) the backscattering coefficient of the first scatterer associated with the first local maximum from said local maximum of the overall estimation function, - Determining (602) the contribution of the first scatterer to the measurement of the frequency transfer function as equal to the product of the backscattering coefficient of the first scatterer and the value of the model of the transfer function taken at the coordinates of the first local maximum, - Subtracting (603) from the measurement of the frequency transfer function the contribution of the first scatterer,- Iterate the previous steps to search for another local maximum of the global estimation function determined from the corrected measurement of the frequency transfer function,

4. Method for determining radioelectric properties of a medium according to any one of the preceding claims wherein 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 the permeability.

5. Method for determining radioelectric properties of a medium according to any one of the preceding claims comprising the search for several local maxima of the estimation function, each local maxima providing a position value of a scatterer of the medium and a value of the variable characterizing the radioelectric property at said position.

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

7. Method for determining radioelectric properties of a medium according to any one of the preceding claims wherein the overall estimation function of the correlation coefficient is determined as an average of the correlation coefficients for all pairs and for one or more discrete frequency values.

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

9. Method for determining radioelectric properties of a medium according to any one of the preceding claims wherein at least one position variable is a depth value and the method includes a step of replacing, in the global estimation function, the depth variable with an electric depth variable _ / 77 , where e'r is the real part of the Zel - dielectric permittivity.

10. System for determining radioelectric properties of a medium comprising a radio frequency detection device comprising at least one transmitter and one receiver and a processing unit, the system being configured to implement the method according to any one of the preceding claims.

11. System according to claim 10 wherein the radio frequency detection device is a ground penetration radar.

12. Computer program comprising code instructions that lead the system according to any one of claims 10 or 11 to execute the steps of the method according to any one of claims 1 to 9.

13. Computer-readable medium on which the computer program according to claim 12 is recorded.

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