Polarization synthetic aperture radar forest and city target scattering confusion removing method considering wavelength dependence
By using polarimetric synthetic aperture radar technology, combined with wavelength dependence analysis and eigenvalue-eigenvector decomposition, the problem of volume scattering feature confusion between forest and urban targets was solved, achieving high-precision target identification and classification.
Patent Information
- Application Number
- CN202511327845.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-17
- Publication Date
- 2025-12-05
AI Technical Summary
Existing polarimetric synthetic aperture radar (PSAR) technology suffers from severe volume scattering feature confusion in forest and urban target identification, and existing methods fail to effectively consider the dependence of radar wavelength, resulting in insufficient identification accuracy and robustness.
By constructing a wavelength-dependent polarimetric synthetic aperture radar method, and utilizing eigenvalue-eigenvector decomposition and geocoding techniques, combined with scattering mechanism power calculation and separation factors, forest and urban targets are identified and separated. In particular, accurate target classification is achieved through L-band and C-band scattering characteristic correction.
It improves the interpretation accuracy of scattering features of forest and urban targets in PolSAR data, balances the effectiveness and simplicity of the algorithm, ensures the accuracy and robustness of the identification results, and solves the problem of poor cross-band applicability caused by wavelength dependence.
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Figure CN121069387A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical fields of polarimetric synthetic aperture radar (PolSAR) image processing and ground object classification, and particularly relates to a polarization synthetic aperture radar forest and urban target scattering confusion removal method considering wavelength dependence. BACKGROUND
[0002] Forest canopy and urban targets with large azimuth angles both have depolarization effects on incident electromagnetic waves, and both show strong volume scattering characteristics in PolSAR data, resulting in serious volume scattering feature confusion between the two types of radar targets (see Figure 1 Both types of radar targets show strong volume scattering characteristics in PauliRGB images and are displayed as green). Polarization decomposition is an effective method for analyzing PolSAR data, mainly divided into two types of algorithms based on models and eigenvalue-eigenvector. The polarization decomposition algorithm based on the model has good physical interpretability, but the number of unknowns is more than the number of knowns, the algorithm has high time and space complexity, and the accuracy and robustness of parameter solving face great challenges. The polarization decomposition algorithm based on eigenvalue-eigenvector has a simple solving process and unique decomposition result, but the physical interpretability of the decomposition result is poor. Both methods have great limitations in interpreting the scattering characteristics of forest and urban targets in PolSAR data. In addition, the electromagnetic scattering characteristics of forest targets have serious wavelength dependence, and the existing polarization decomposition methods have poor applicability in different waveband PolSAR data without considering radar wavelength information. SUMMARY
[0003] The present application proposes a polarization synthetic aperture radar forest and urban target scattering confusion removal method considering wavelength dependence to overcome the shortcomings of the prior art, aiming to ensure the accuracy and stability of radar target electromagnetic scattering feature extraction while considering effectiveness and simplicity; at the same time, fully considering the dependence of forest scattering characteristics on radar wavelength, establishing a wavelength correction method of electromagnetic scattering mechanism, enhancing the cross-waveband capability of PolSAR data interpretation method, and further improving the scattering feature interpretation accuracy of forest and urban targets in PolSAR data.
[0004] The technical scheme adopted by the present application is as follows:
[0005] In a first aspect, the present application provides a polarization synthetic aperture radar forest and urban target scattering confusion removal method considering wavelength dependence, which comprises the following steps:
[0006] Step 1, input the single look complex polarimetric synthetic aperture radar (PolSAR) data of the target area, which is usually represented as a 2x2 scattering matrix [S2]; thus, based on the reciprocity principle, the 3x3 polarimetric covariance matrix ([C3]) can be obtained by vectorization and vector conjugate multiplication of [S2];
[0007] Filter the input PolSAR data to eliminate coherent speckle noise; then, the 3x3 polarimetric covariance matrix ([C3]) can be obtained by vectorization and vector conjugate multiplication;
[0008] Based on the digital elevation model (DEM) of the target area, the polarimetric covariance matrix ([C3]) is geocoded, converting the radar coordinates of the PolSAR image into real geographic coordinates, enabling accurate overlay application with maps, so that the target geographic location information can be carried when outputting the target analysis information;
[0009] Step 2, extract the eigenvalues and eigenvectors from the PolSAR data based on eigenvalue-eigenvector polarization decomposition, obtaining three components: [C3]1, [C3]2 and [C3]3;
[0010] Then, map the three components [C3]1, [C3]2 and [C3]3 to the corresponding radar target electromagnetic scattering mechanisms to obtain the scattering expressions of singular scattering Sgl, double scattering Dbl and volume scattering Vol: [C3] Sgl , [C3] Dbl and [C3] Vol ;
[0011] Based on the scattering expressions [C3] Sgl , [C3] Dbl and [C3] Vol , obtain the power of each scattering mechanism: P Sgl = trace([C3] Sgl ), P Dbl = trace([C3] Dbl ), P Vol = trace([C3] Vol );
[0012] Step 3, if the scattering power P Vol of volume scattering accounts for more than a specified proportion of the total power, the target is considered a strong volume scattering radar target, including forest targets and urban targets with large azimuth angles; the total power is the sum of the scattering powers of singular scattering, double scattering and volume scattering;
[0013] Step 4, based on the scattering characteristic separation factor, distinguish between urban targets and forest targets for strong volume scattering radar targets, and output the target recognition results with target geographic location information;
[0014] Separate the scattering feature separation factor of strong volume scattering radar targets in L-band and C-band PolSAR data respectively
[0015]
[0016] Wherein, f(λ) and h(λ) represent the function of radar wavelength λ respectively, which are used to correct the surface scattering energy and volume scattering energy of forest targets respectively;
[0017] For L-band PolSAR data, f(λ) and g(λ) are both 1;
[0018] For C-band PolSAR data, λ C , λ L represent the wavelength of C-band and L-band respectively;
[0019] And transform the scattering feature separation factor to [0,1], get the separation metric value corresponding to L-band and C-band;
[0020] When the separation metric value is greater than the preset separation threshold, the strong volume scattering radar target is determined as an urban target; otherwise, it is determined as a forest target.
[0021] Further, the polarization covariance matrix [C3] is:
[0022]
[0023] Wherein, e1, e2, e3 are three eigenvalues obtained by polarization decomposition of PolSAR data, μ1, μ2, μ3 are three eigenvectors obtained by polarization decomposition of PolSAR data. [C3]1, [C3]2 and [C3]3 are the results of corresponding eigenvalues and eigenvectors, the conjugate transpose product of eigenvectors respectively.
[0024] Further, [C3]1, [C3]2 and [C3]3 correspond to the components of odd scattering ([C3] Sgl ), even scattering ([C3] Dbl ) and volume scattering ([C3] Vol ) mechanisms of radar targets respectively.
[0025] First, in the three decomposition components ([C3]1, [C3]2 and [C3]3), the decomposition component corresponding to the maximum value of the matrix element in the second row and the second column is volume scattering; for the remaining two decomposition components, the first row and the third column matrix element is taken, and the real part of the element is positive, then the decomposition component corresponds to odd scattering; otherwise, the decomposition component corresponds to even scattering.
[0026] Further, the scattering power of odd scattering, even scattering and volume scattering is respectively:
[0027] P Sgl = trace([C3] Sgl ), P Dbl = trace([C3] Dbl ), P Vol = trace([C3] Vol ).
[0028] Further, the scattering feature separation factor is transformed to [0, 1] by using the Sigmoid function.
[0029] Secondly, the present application provides an electronic device, comprising a memory and a processor and computer instructions stored in the memory and running on the processor, when the computer instructions are run by the processor, the method of the first aspect is completed.
[0030] Thirdly, the present application provides a computer readable storage medium for storing computer instructions, when the computer instructions are executed by the processor, the method of the first aspect is completed.
[0031] Fourthly, the present application provides a computer program product, comprising computer program / instructions, characterized in that, when the computer program / instructions are executed by the processor, the method of the first aspect is completed.
[0032] The technical scheme provided by the present application at least brings the following beneficial effects:
[0033] (1) balance the effectiveness and simplicity of the algorithm: combine the model-based data decomposition method and the eigenvalue-eigenvector-based PolSAR decomposition method, and consider the timeliness and physical interpretability of the scattering feature extraction at the same time;
[0034] (2) comprehensive consideration of the mutual relationship of the three scattering mechanisms for radar target recognition, to ensure the accuracy and robustness of the results;
[0035] (3) physical driving correction: quantifying the regulation of wavelength on penetration depth, fundamentally solving the model cross-band failure problem. BRIEF DESCRIPTION OF DRAWINGS
[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings needed in the embodiments description. Obviously, the drawings in the following description only represent some of the embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative effort based on these drawings.
[0037] Figure 1 Cross-polarization (S HV ) intensity maps generated for PolSAR data in San Francisco, USA, where (1a) is L-band PALSAR-2 data, and (1b) is C-band Radarsat-2 data. Higher gray values indicate stronger cross-polarization scattering (i.e. volume scattering) echoes.
[0038] Figure 2 A flowchart of the method for removing forest and urban scattering confusion of the polarization synthetic aperture radar considering wavelength dependence provided by the embodiments of the present application;
[0039] Figure 3 R Vol value maps calculated for PolSAR data in San Francisco, USA, where (3a) is L-band PALSAR-2 data, and (3b) is C-band Radarsat-2 data. Higher gray values indicate larger R Vol values, and larger differences in gray values indicate stronger separability between radar targets;
[0040] Figure 4 Histograms of R Vol values for forest and urban areas with large azimuth angles for PolSAR data in San Francisco, USA, where (4a) is L-band PALSAR-2 data, and (4b) is C-band Radarsat-2 data. The solid line represents the sampling results of RVolvalues of forest targets, and the dashed line represents the sampling results of RVolvalues of urban areas with large azimuth angles. The less overlap between the two lines, the higher the separability between the two types of radar targets. DETAILED DESCRIPTION
[0041] In order to make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the following will describe the technical solutions in the embodiments of the present application in detail and completely with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, and not all the embodiments. Generally, the components of the embodiments of the present application described and shown in the drawings can be arranged and designed using different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application.
[0042] The embodiment of the present application provides a polarization synthetic aperture radar forest and urban target scattering confusion removal method considering wavelength dependence, as shown in the figure, which comprises the following steps: Figure 2
[0043] Step S1, PolSAR data preprocessing;
[0044] Firstly, the obtained single-view complex (SLC) PolSAR data is subjected to multi-view processing to obtain a polarization covariance matrix [C3]; then, the data is subjected to filtering processing by using a refined Lee filtering algorithm, so that the influence of coherent class noise on data analysis is eliminated; finally, the polarization covariance [C3] is subjected to geographic coding with reference to DEM (Digital Elevation Model) data of a research area (target area);
[0045] Step S2, scattering mechanism power calculation;
[0046] The polarization decomposition algorithm based on eigenvalue-eigenvector is used to extract three scattering mechanism powers of radar targets in the PolSAR data, namely, odd scattering power P Sgl , even scattering power P Dbl and volume scattering power P Vol .
[0047] Step S3, strong volume scattering radar target extraction;
[0048] According to the decomposition structure, the volume scattering mechanism power P Vol is considered as a strong volume scattering radar target if the proportion of the volume scattering mechanism power P Vol in the total power (P Sgl +P Dbl +P Vol ) is greater than a specified value (0.5 in the embodiment), and the strong volume scattering radar target mainly includes forest targets and urban targets with large azimuth angles;
[0049] Step S4, volume scattering mechanism separation;
[0050] Firstly, the volume scattering separation factor R Vol under different wavelengths is calculated according to the electromagnetic scattering models of the forest and the urban target with the large azimuth angle. Then, the typical radar targets are sampled, and the separation threshold is obtained by drawing a histogram. Finally, the scattering mechanism separation of the forest and the urban target with the large azimuth angle in the PolSAR data is realized according to the separation threshold.
[0051] In one embodiment, in step S1, the polarization covariance matrix [C3] is obtained by decomposing the PolSAR data based on the eigenvalue-eigenvector, and the process specifically comprises:
[0052] For single station PolSAR system, its 3x3 polarimetric covariance matrix ([C3]) or polarimetric coherence matrix ([T3]) can be represented by three eigenvalues (e1, e2, e3) and eigenvectors (μ1, μ2, μ3) as follows:
[0053]
[0054] where * denotes conjugate transpose. With the amplitude and phase information of each component, a one-to-one correspondence between components and scattering mechanisms can be established. Equation (1) can be rewritten as:
[0055] [C3] = [C3] Sgl + [C3] Dbl + [C3] Vol (2)
[0056] where Sgl, Dbl and Vol represent odd-bounce scattering, even-bounce scattering and volume scattering respectively. Correspondingly, the power of three scattering mechanisms can be obtained by:
[0057] P Sgl = trace([C3] Sgl ), P Dbl = trace([C3] Dbl ), P Vol = trace([C3] Vol ) (3)
[0058] In the embodiment of the present application, the electromagnetic scattering mechanism modeling based on geometric structure can be represented as:
[0059] For urban targets with large azimuth angle, its backscattering echo mainly comes from two types of geometric structures: planar structure (horizontal ground or roof plane) and inclined dihedral structure (wall surface of adjacent buildings).
[0060] where the echo of planar structure can usually be modeled by Bragg scattering model, and the model is as follows:
[0061]
[0062] The electromagnetic scattering model of the echo mainly produced by inclined dihedral structure is as follows:
[0063]
[0064] From equations (4) and (5), the backscattering model of urban targets with large azimuth angle is obtained as follows:
[0065]
[0066] For forest targets, the backscattering is affected by the radar wavelength. Since L-band electromagnetic waves have stronger penetration ability than C-band electromagnetic waves, L-band PolSAR data can obtain more complete vertical structure information of forest. Therefore, first, the forest target is modeled according to the electromagnetic scattering characteristics of L-band. The backscattering information of forest in PolSAR data mainly comes from three parts, the ground, the crown and the interaction between the trunk and the ground. By modeling the electromagnetic scattering of the three typical components, the PolSAR scattering model of the forest target can be obtained.
[0067] For the ground, the Bragg scattering model can also be used for simulation, and for the random scattering body structure (forest canopy), the backscattering can be simulated by using randomly oriented slender dipoles. The corresponding electromagnetic scattering model is as follows:
[0068]
[0069] From equations (4) and (7), the backscattering model of the forest target is obtained as:
[0070]
[0071] In the electromagnetic scattering characteristic correction process considering the radar wavelength, there are:
[0072] The penetration of radar waves into the forest canopy increases with the increase of the wavelength, resulting in a serious wavelength dependence of the energy size of the backscattering mechanism of different geometric structures. The scattering characteristics of urban targets are almost not affected by the radar wavelength. Therefore, the backscattering model of the forest canopy in the C-band PolSAR data needs to be modified to equation (8):
[0073]
[0074] Where f(λ) and h(λ) represent functions of the radar wavelength (λ), respectively correcting the surface scattering energy and the volume scattering energy of the forest target.
[0075] From L-band to C-band PolSAR data, due to the weakening of the canopy penetration, the odd scattering of the canopy surface will be enhanced, and the volume scattering mechanism inside the canopy will be weakened. At this time,
[0076] In an embodiment, when the volume scattering mechanism separation process is implemented in step S4, a separation factor of the scattering characteristics of forest and urban targets with large azimuth angles needs to be constructed first.
[0077] For urban targets with large azimuth angles, the main backscattering mechanisms are odd-order scattering from planar structures and volume scattering from the interaction with inclined walls, while even-order scattering mechanisms are almost non-existent. That is, for urban targets P with large azimuth angles... Dbl =0.
[0078] For forest targets, planar structures produce odd-order scattering echoes, while random scatterers produce volume scattering echoes. Simultaneously, due to the persistent penetration of radar waves through the forest canopy, forest PolSAR echoes also contain energy from even-order scattering mechanisms. Therefore, in the decomposition results of forest PolSAR data, P... Dbl >0. Therefore, the difference in even-order scattering characteristics provides theoretical support for separating the scattering mechanisms of forests and urban targets with large azimuth angles. According to equations (6), (8), and (9), the separation factors of scattering characteristics of forests and urban targets with large azimuth angles in L-band and C-band PolSAR data are respectively,
[0079]
[0080] For urban targets with a large azimuth angle, R Vol >0; For forest targets, R Vol ≤0.
[0081] Finally, the Sigmoid function can be used to transform the value of the separating factor to [0,1]:
[0082]
[0083] At this point, the separation threshold can be set to 0.5.
[0084] Figure 3 and Figure 4 R calculated from PolSAR data of the San Francisco area, USA Vol Figure, R Vol Histograms of sampling results in forests and urban areas with large azimuth angles are shown. As can be seen from the figures, the method proposed in this embodiment can effectively identify (or separate) forest targets and urban targets with large azimuth angles in PolSAR data. The corresponding results are shown in Table 1.
[0085] Table 1
[0086] Forest targets Urban targets with large azimuth angles Radarsat-2 C-band data 88.6% 58.7% PALSAR-2 L-band data 79.1% 69.0%
[0087] As shown in Table 1, using the intersection value of the two curves as the segmentation threshold, the pixel accuracy for correctly classifying forests and urban areas with large azimuth angles within the sampling area can be obtained (the sampling area is as follows). Figure 1The correct recognition rates of C-band PolSAR data are 88.6% and 58.7%, and the correct recognition rates of L-band PolSAR data are 79.1% and 69.0%.
[0088] In more embodiments, there are also provided:
[0089] An electronic device includes a memory and a processor, and computer instructions stored on the memory and run on the processor, when the computer instructions are run by the processor, the method provided by the embodiments of the present application is completed. For brevity, it will not be described here.
[0090] A computer readable storage medium for storing computer instructions, when the computer instructions are executed by a processor, the method provided by the embodiments of the present application is completed.
[0091] The method provided by the embodiments of the present application can be directly embodied as a hardware processor to complete, or a combination of hardware and software modules in the processor to complete. The software module can be located in a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, and other mature storage media in the art. The storage medium is located in the memory, and the processor reads the information in the memory and combines the hardware to complete the steps of the above method. To avoid repetition, it will not be described in detail here.
[0092] A computer program product includes a computer program, when the computer program is executed by a processor, the method for removing forest and urban target scattering confusion of polarization synthetic aperture radar considering wavelength dependence provided by the embodiments of the present application is realized and completed.
[0093] The present application also provides at least one computer program product tangibly stored on a non-transitory computer readable storage medium. The computer program product includes computer executable instructions, such as instructions included in program modules, which are executed in devices on the target real or virtual processor to perform processes / methods as described above. Generally, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform specific tasks or implement specific abstract data types. In various embodiments, the functions of the program modules can be combined or divided as needed between program modules. Machine executable instructions for program modules can be executed within a local or distributed device. In a distributed device, program modules can be located in local and remote storage media.
[0094] The computer program code for carrying out the methods of embodiments of the present application can be written in one or more programming languages. These computer program codes can be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the program codes, when executed by the computer or other programmable data processing apparatus, produce a device implemented the functions / operations specified in the flowcharts and / or block diagrams. The program codes can be executed entirely on the computer, partially on the computer, as a stand-alone software package, partially on the computer and partially on a remote computer, or entirely on a remote computer or server.
[0095] In the context of the present application, the computer program code or related data can be carried by any appropriate carrier to enable the device, apparatus or processor to perform the various processes and operations described above. Examples of the carrier include a signal, a computer readable medium, etc. Examples of the signal can include an electrical, optical, radio, sound or other forms of propagated signals, such as a carrier wave, an infrared signal, etc.
[0096] Those skilled in the art can realize that the units and algorithm steps of the examples described in conjunction with the present embodiments can be realized in electronic hardware or in a combination of computer software and electronic hardware. Whether the functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.
[0097] The above describes the specific embodiments of the present application in conjunction with the accompanying drawings, but is not a limitation on the scope of protection of the present application. Those skilled in the art should understand that various modifications or variations made by those skilled in the art on the basis of the technical solutions of the present application without creative labor are still within the scope of protection of the present application.
Claims
1. A method for forest and urban target scattering clutter removal in polarization synthetic aperture radar considering wavelength dependence, characterized in that, The method comprises the following steps: Step 1, input single-view complex polarimetric synthetic aperture radar (PolSAR) data of a target area; Filter the input PolSAR data, and then perform vectorization and vector conjugate multiplication to obtain a 3x3 polarimetric covariance matrix [C3]; Geocode the polarimetric covariance matrix [C3] based on a digital elevation model of the target area, and convert radar coordinates of the PolSAR image into real geographic coordinates; Step 2, extract eigenvalues and eigenvectors in the PolSAR data based on eigenvalue-eigenvector polarimetric decomposition, and obtain three decomposition components: [C3]1, [C3]2 and [C3]3; The three decomposed components [C3]1, [C3]2 and [C3]3 are mapped to the corresponding radar target electromagnetic scattering mechanisms to obtain the scattering expressions of odd scattering Sgl, even scattering Dbl and volume scattering Vol: [C3] Sgl , [C3] Dbl and [C3] Vol ; Based on the scattering representation [C3] Sgl [C3] Dbl [C3] Vol The power of each scattering mechanism is obtained: P Sgl = trace([C3] Sgl ), P Dbl = trace([C3] Dbl ), P Vol = trace([C3] Vol ); Step 3, the scattering power P of volume scattering Vol The proportion of the total power greater than the specified value target is considered as a strong volume scattering radar target, including forest targets and urban targets with large azimuth angles; wherein the total power is the sum of the scattering powers of odd scattering, even scattering and volume scattering. Step 4, distinguish urban targets and forest targets of the strong volume scattering radar target based on the scattering feature separation factor, and output a target recognition result with target geographic location information; Separately calculating the scattering characteristic separation factor of strong volume scattering radar targets in L-band and C-band PolSAR data Where f(λ) and h(λ) represent functions of the radar wavelength λ, and are used to correct the surface scattering energy and volume scattering energy of the forest target, respectively; For L-band PolSAR data, f(λ) and g(λ) are both 1; For C-band PolSAR data, λ C 、λ L denote the wavelength of C-band and L-band, respectively; and separating the scattering characteristics transformed to [0, 1] to obtain a separation metric value corresponding to the L- and C- bands; When the separation metric value is greater than a preset separation threshold, the strong volume scattering radar target is determined to be an urban target; otherwise, it is determined to be a forest target.
2. The method of claim 1, wherein, The polarimetric covariance matrix [C3] is: Where e1, e2, and e3 are three eigenvalues obtained by polarimetric decomposition of the PolSAR data, and μ1, μ2, and μ3 are three eigenvectors obtained by polarimetric decomposition of the PolSAR data.
3. The method of claim 1, wherein, In step 2, the scattering expressions of the odd-order scattering Sgl, the even-order scattering Dbl, and the volume scattering Vol are obtained, which specifically include: For the three decomposition components [C3]1, [C3]2, and [C3]3, the decomposition component corresponding to the maximum matrix element in the second row and the second column is the volume scattering; for the remaining two decomposition components, the first row and the third column matrix element of each is taken, and the real part of the element is positive, then the decomposition component corresponds to the odd-order scattering; otherwise, the decomposition component corresponds to the even-order scattering.
4. The method of claim 1, wherein, Sigmoid function to separate the scattering features from the factor transformed to [0, 1].
5. The method of claim 4, wherein, The separation threshold is set to 0.
5.
6. A computer device comprising a memory, a processor, and a computer program stored on the memory, wherein the computer program comprises instructions that, when executed by the processor, cause the processor to perform the method of any one of claims 1-5. The processor executes the computer program to implement the steps of the method of any one of claims 1 to 5.
7. A computer readable storage medium having stored thereon a computer program / instructions, characterized in that, The computer program / instructions are executed by the processor to implement the steps of the method of any one of claims 1 to 5.
8. A computer program product comprising computer programs / instructions, characterized in that, The computer program / instructions are executed by the processor to implement the steps of the method of any one of claims 1 to 5.