CN113075658B - Ionosphere tomography method fusing satellite-borne full-polarization SAR and GPS - Google Patents
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- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
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- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
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Abstract
The invention relates to an ionospheric tomography method, computer equipment and a computer-readable storage medium for fusing satellite-borne full-polarization SAR and GPS, wherein the method comprises the following steps: setting M ground receiving stations at intervals below an ionosphere region, and determining the coordinates of each ground receiving station; acquiring at least one group of rays above a ground receiving station by using a satellite-borne full-polarization SAR and inverting the TEC value corresponding to each ray, and acquiring N groups of rays at different positions by using a GPS and inverting the TEC value corresponding to each ray; dividing the ionization layer region into n grids to obtain the coordinates of each grid, and determining the initial value of the electron density of each grid; calculating the projection length of each ray in each grid; and carrying out tomography iterative inversion based on a multiplicative algebraic reconstruction method, and obtaining the electron density distribution in the ionization layer region after multiple iterations. The invention increases the available ionized layer information and can finally reconstruct the ionized layer electron density information with higher precision.
Description
Technical Field
The invention relates to the technical field of radar detection, in particular to an ionosphere tomography method, computer equipment and a computer readable storage medium fusing satellite-borne full-polarization SAR and GPS.
Background
In the atmospheric layer region 60-1000 km away from the earth's surface, there are a large number of free electrons and ions, forming the earth's ionosphere. Changes in the ionosphere can disrupt the orbit of radio communication systems, ground grids, satellites and space debris, and seismic precursors can also cause abnormal changes in electron density. The study of the ionosphere not only facilitates the understanding of the ionosphere itself, the search for methods to avoid ionosphere effects and to utilize the ionosphere, but also facilitates the development of relevant theories and applications in the field of geology.
Conventional global navigation system (GPS) -based ionospheric tomography (CIT) techniques receive several GPS satellite signals by ground-based reception stations, and derive a total ionospheric electron content (TEC) value on a path, where TEC is defined as an integral of the total electron content of the path per unit area. According to the path TEC, the projection length of the ray in the ionosphere divided into a plurality of grids and the iteration initial value, the electron density value of the space can be finally reconstructed. However, the final precision of the CIT depends on the accuracy of the initial values of the iteration on the one hand and on the sparseness of the rays on the other hand. When the number of available rays is small or the number of ground stations is small, the accuracy is significantly reduced. The GPS satellite orbit is fixed and far away from the ground, the detection stability is poor, and the detection precision is limited.
Disclosure of Invention
The invention aims to provide an ionospheric tomography technology fusing satellite-borne full-polarization SAR and GPS data aiming at least part of defects, so as to improve the accuracy and stability of ionospheric tomography by utilizing satellite-borne full-polarization SAR detection data.
In order to achieve the purpose, the invention provides an ionosphere tomography method fusing satellite-borne fully-polarized SAR and GPS, which comprises the following steps:
s1, arranging M ground receiving stations at intervals below an ionosphere region, and determining coordinates of the ground receiving stations, wherein M is a positive integer greater than or equal to 6;
s2, acquiring at least one group of rays above the ground receiving station by using the satellite-borne full-polarization SAR, inverting TEC values corresponding to the rays, and recording coordinates of the satellite-borne full-polarization SAR in detection; acquiring N groups of rays at different positions by using a GPS (global positioning system), inverting TEC (thermoelectric cooler) values corresponding to the rays, and respectively recording coordinates when the GPS detects N times; each group of rays comprises M rays corresponding to the M ground receiving stations, and N is a positive integer greater than or equal to 20;
s3, dividing the ionization layer area into n grids to obtain the coordinates of each grid, setting the electron density value in each grid as a constant, and determining the electron density initial value of each grid; wherein the number of the grids in the horizontal direction after the division is not more than N;
s4, calculating the projection length of each ray in each grid;
and S5, carrying out tomography iterative inversion based on a multiplicative algebraic reconstruction method by utilizing the initial electron density value of each grid, the projection length of each ray in each grid and the TEC value corresponding to each ray, and obtaining the electron density distribution of the ionization layer region after multiple iterations.
Preferably, in step S2, when at least one group of rays is acquired above the ground receiving stations by using a satellite-borne fully-polarized SAR, an elevation angle range of the rays formed by the satellite-borne fully-polarized SAR and each of the ground receiving stations is 87 to 90 °.
Preferably, in step S2, when at least one group of rays is obtained above the ground receiving station by using a satellite-borne fully-polarized SAR and the TEC value corresponding to each ray is inverted, the TEC value of each ray is determined by the following formula:
wherein f represents the carrier frequency of the satellite-borne fully-polarized SAR, B represents the geomagnetic field intensity in an ionization layer region, theta represents the included angle between the geomagnetic field in the ionization layer region and the satellite-borne fully-polarized SAR signal, and omega represents the Faraday rotation angle offset caused by the ionization layer region.
Preferably, in step S2, the faraday rotation angle offset Ω caused by the ionosphere region is determined by echo scattering matrix data of the satellite-borne fully-polarized SAR, and the expression is:
wherein arg (. Cndot.) represents the argument of complex element, Z 11 、Z 12 、Z 21 And Z 22 Respectively represents the echo information received by four polarization channels of the satellite-borne fully-polarized SAR,
is Z 21 Conjugation of (A), S hh H-polarized wave, S, representing ground scattering of horizontally polarized waves vv V-polarized wave, S, representing ground scattering of vertically polarized waves hv Represents the V-polarized wave scattered from the ground by the horizontally polarized wave, and i represents an imaginary unit.
Preferably, in step S2, when the GPS is used to obtain N groups of rays at different positions and invert the TEC value corresponding to each ray, the TEC value of each ray is determined by the following formula:
wherein f is 1 、f 2 Representing two different frequencies, L, of the GPS 1 、L 2 Respectively represent f 1 、f 2 Corresponding carrier pseudoranges, or L 1 、L 2 Respectively represents f 1 、f 2 The corresponding carrier phase value.
Preferably, in step S3, when the initial value of the electron density of each grid is determined, each grid value is given as an iteration initial value based on an ionosphere IRI empirical model.
Preferably, in step S5, when performing tomography iterative inversion based on a multiplicative algebraic reconstruction method, the iterative formula is:
wherein, N ej k+1 Represents the electron density, TEC, of the jth grid at the (k + 1) th iteration m Indicating the TEC value corresponding to the m-th ray,<·>represents the inner product, | | · | | | represents the norm,
is A m Transpose of (A) m Is represented by a matrix { A } mj The m-th row element, the matrix { A } mj Element A of row m and column j in the mj Represents the projection length of the mth ray in the jth grid, N e k Represents the electron density distribution, λ, obtained at the k-th iteration of all n grids k Is an iterative relaxation factor with the value range of 0 to lambda k ≤1。
Preferably, in step S5, after at least 5 iterations, the electron density distribution in the ionization region is obtained.
The invention also provides computer equipment which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the ionospheric tomography method for fusing the satellite-borne full-polarization SAR and the GPS when executing the computer program.
The invention also provides a computer-readable storage medium, on which a computer program is stored, which when executed by a processor, implements the steps of any of the above-mentioned ionospheric tomography method with satellite-borne fully-polarized SAR and GPS fusion.
The technical scheme of the invention has the following advantages: the invention relates to an ionospheric tomography method, computer equipment and a computer readable storage medium for fusing satellite-borne full-polarization SAR and GPS. The invention integrates two ionized layer information sources, increases available ionized layer TEC information, can finally reconstruct ionized layer electron density distribution information with higher precision and more stability, does not need a large amount of GPS data or SAR data, and is simpler and more feasible.
Drawings
FIG. 1 is a schematic diagram of steps of an ionospheric tomography method with fusion of satellite-borne fully-polarized SAR and GPS in an embodiment of the present invention;
FIG. 2 is a schematic diagram of ionosphere regions and rays in an embodiment of the present invention;
fig. 3 (a) to 3 (c) are simulation image results; wherein, fig. 3 (a) is ionospheric tomography under the real distribution condition, and fig. 3 (b) is ionospheric tomography of the method provided by the present invention; fig. 3 (c) is a conventional GPS-based ionospheric tomography.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
As shown in fig. 1, an ionosphere tomography method fusing a satellite-borne fully-polarized SAR and a GPS provided in an embodiment of the present invention includes the following steps:
s1, M ground receiving stations are arranged below an ionized layer area to be measured at intervals, and coordinates of all the ground receiving stations are determined, wherein M is a positive integer larger than or equal to 6.
In this step, the coordinates of each ground receiving station can be recorded by longitude and latitude. The ground receiving stations are preferably uniformly spaced, and the spacing distance can be selected from 8-12 km, preferably 10km.
S2, acquiring at least one group of rays above a ground receiving station by using the satellite-borne full-polarization SAR, inverting TEC values corresponding to the rays, and recording coordinates of the satellite-borne full-polarization SAR in detection; acquiring N groups of rays at different positions by using a GPS (global positioning system), inverting TEC (thermoelectric cooler) values corresponding to the rays, and respectively recording coordinates when the GPS detects N times; each group of rays comprises M rays corresponding to the M ground receiving stations, and N is a positive integer greater than or equal to 20.
As shown in fig. 2, when a satellite-borne fully-polarized SAR (SAR for short) is detected, at least one group of rays (preferably one group) can be obtained from the SAR to each ground receiving station, that is, at least M rays; similarly, during each GPS detection, a group of rays can be obtained from the GPS to each ground receiving station, N times of detection of different positions are carried out, N multiplied by M rays are summed, and at least (N + 1) multiplied by M different rays which penetrate through the ionization layer area to be detected can be finally obtained, wherein each ray has a corresponding TEC value.
And S3, dividing the ionization layer region into n grids to obtain the coordinates of each grid, setting the electron density value in each grid as a constant, and determining the electron density initial value of each grid. The number of the divided horizontal grids is preferably not more than N, that is, the value of N should be as large as possible or equal to the number of the divided horizontal grids in the ionization region.
For ease of calculation, the ionization region can be uniformly divided into n grids in a matrix form, as shown in fig. 2. The value range of n can be selected according to the size of the ionosphere area to be measured and the precision required, and is not further limited herein. If more meshes need to be segmented, the value of N should be increased accordingly.
And S4, calculating the projection length of each ray in each grid.
As shown in FIG. 2, after the GPS and SAR ray paths and the ground receiving station coordinates are determined, the projection length A of each ray in each grid can be calculated mj I.e. the projection length of the mth ray (path) on the jth grid.
And S5, carrying out tomography iterative inversion based on a multiplicative algebraic reconstruction Method (MART) by utilizing the initial electron density value of each grid, the projection length of each ray in each grid and the TEC value corresponding to each ray, and obtaining the electron density distribution in an ionization layer region after multiple iterations, namely reconstructing the spatial electron density value.
According to the invention, the satellite-borne full-polarization SAR data and the GPS data are fused, and the ionosphere information inverted by the satellite-borne full-polarization SAR is fused into the traditional tomography technology, so that the number of effective rays for tomography, especially high-elevation rays, can be increased, TEC information is effectively supplemented, the reconstruction precision is improved, a large amount of GPS data or SAR data is not required, and the method is simple and easy to implement.
Preferably, in step S2, when at least one group of rays is acquired above the ground receiving station by using the satellite-borne fully-polarized SAR, an elevation angle range of the rays formed by the satellite-borne fully-polarized SAR and each ground receiving station is 87 to 90 °, more preferably 87.95 to 89.95 °, that is, an off-angle of the rays formed by the SAR and the ground receiving station with respect to a vertical direction is not more than 3 °. The final precision of ionospheric tomography is greatly influenced by high elevation rays, and the precision and the stability can be effectively improved by fusing satellite-borne fully-polarized SAR signal data right above a group of ground receiving stations.
Preferably, in step S2, when at least one group of rays is obtained above the ground receiving station by using the satellite-borne fully-polarized SAR and the TEC value corresponding to each ray is inverted, the TEC value of each ray is determined by the following formula:
wherein f represents the carrier frequency of the satellite-borne fully-polarized SAR, B represents the geomagnetic field intensity in an ionization layer region, theta represents the included angle between the geomagnetic field in the ionization layer region and the satellite-borne fully-polarized SAR signal, and omega represents the Faraday rotation angle offset caused by the ionization layer region. TEC (thermoelectric cooler) SAR Representing the TEC value of a ray acquired based on SAR.
Further, in step S2, the faraday rotation angle shift Ω caused by the ionization region is determined by the echo scattering matrix data of the satellite-borne fully polarized SAR, and the expression is:
wherein arg (·) represents the argument of complex element, Z 11 、Z 12 、Z 21 And Z 22 Respectively representing echo information received by four polarization channels of the satellite-borne full-polarization SAR to form echo scattering matrix data of the satellite-borne full-polarization SAR,
is Z 21 Conjugation of (1); s hh 、S vv And S hv The scattered waves representing ground scattering represent H-polarized waves horizontally polarized (H-polarized) waves ground scattering, V-polarized waves vertically polarized (V-polarized) waves ground scattering, and V-polarized waves horizontally polarized (H-polarized) waves ground scattering, respectively, and i represents an imaginary number unit.
Preferably, in step S2, when acquiring N groups of rays at different positions by using the GPS and inverting the TEC value corresponding to each ray, the TEC value of each ray is determined by the following formula:
wherein f is 1 、f 2 Representing two different frequencies, L, of the GPS 1 、L 2 Respectively represents f 1 、f 2 Corresponding carrier pseudoranges, or L 1 、L 2 Respectively represents f 1 、f 2 The corresponding carrier phase value. TEC (thermoelectric cooler) GPS A TEC value representing a ray acquired based on GPS.
Preferably, in step S3, when determining the initial value of the electron density of each grid, each grid value is given as an iteration initial value based on the ionosphere IRI empirical model.
In step S4, as shown in fig. 2, the projection lengths of different ray paths corresponding to the GPS in each grid of the ionosphere region are calculated according to the coordinates of the ground receiving station and the coordinates of the GPS during detection, and the projection lengths of different ray paths corresponding to the SAR in each grid of the ionosphere region are calculated according to the coordinates of the satellite-borne fully-polarized SAR during detection.
Preferably, in step S5, when performing tomographic iterative inversion based on a multiplicative algebraic reconstruction method, the iterative formula is:
wherein N is ej k+1 Represents the electron density of the jth grid in the (k + 1) th iteration, j = ∈ {1, 2.. N }, TEC m Showing the TEC value corresponding to the m ray, wherein the m ray is a ray acquired based on SAR or GPS,<·>represents the inner product, | | · | | | represents the norm,
is A m Transpose of (A) m Is represented by a matrix { A } mj The vector formed by the m-th row elements, the matrix { A } mj Element A of the mth row and jth column mj Represents the projection length of the mth ray in the jth grid, N e k Representing the electron density distribution obtained for all N grids at the k-th iteration, i.e. N e k Is { N ej k J =1, 2.. N } of a vector, λ k Is an iterative relaxation factor with the value range of 0 to lambda k ≤1。
Preferably, in step S5, the electron density distribution in the ionization region is obtained after at least 5 iterations.
As shown in FIG. 2, in a specific embodiment, 6 ground receiving stations distributed at intervals are adopted to receive GPS signals and reflect SAR signals, white small squares in FIG. 2 represent GPS satellite positions (1 to N) for acquiring N groups of rays, gray small squares represent SAR satellite positions for acquiring a group of rays, and the grid area isThe ionization layer area is horizontally detected within 200km, and the vertical range is 100km to 500km. After the SAR satellite signal passes through the ionosphere, the SAR acquires echo scattering matrix information, passing through the off-diagonal elements (i.e., Z) in the scattering matrix 12 、Z 21 ) And the Faraday rotation angle offset omega caused by the ionosphere region can be inverted, and then the TEC value of each ray path corresponding to the SAR can be deduced. The ionization region is divided into n grids, coordinate values of each grid are obtained, and the electron density value in each grid is assumed to be constant. Each grid size can be set to 10km x 10km, i.e. there are 800 grids. In addition, since the CIT technology needs to provide the iterative initial value N of the spatial electron density distribution ini And obtaining an initial electron density value of each grid as an iteration initial value through an ionosphere IRI empirical model. Lambda is used for space electron density reconstruction based on iteration k The relaxation factor can take a value of 0.5. The space electron density value N can be reconstructed by 5 general iterations fin And obtaining the electron density distribution in the ionization layer region.
As shown in fig. 3 (a) to 3 (c), fig. 3 (a) shows the real electron density distribution, fig. 3 (b) shows the method provided by the present invention to fuse the SAR and GPS inversion results, and the root mean square value of the difference between the SAR and the real value is 2.3527e 9 /m 3 Closer to that shown in FIG. 3 (a), FIG. 3 (c) shows that the conventional method only uses the result of the GPS inversion, and lacks a high elevation ray whose root mean square value is 5.9287e from the true value 9 /m 3 The difference from the graph (a) is large. It can be seen that when imaging is performed only by using the GPS method, if high elevation angle rays are missing and no other source is used for compensation, the error of the reconstruction result is large. The ionosphere tomography method fusing the satellite-borne full-polarization SAR and the GPS can effectively improve the reconstruction accuracy only by adding a group of rays corresponding to the SAR, and does not need to supplement data from other sources.
In particular, in some preferred embodiments of the present invention, there is also provided a computer device, including a memory and a processor, where the memory stores a computer program, and the processor implements the steps of the ionospheric tomography method of fusing satellite-borne fully-polarized SAR and GPS in any of the above embodiments when executing the computer program.
In other preferred embodiments of the present invention, there is further provided a computer-readable storage medium, on which a computer program is stored, and the computer program is executed by a processor to implement the steps of the ionospheric tomography method with satellite-borne fully-polarized SAR and GPS fusion as described in any of the above embodiments.
It will be understood by those skilled in the art that all or part of the processes of the method of the above embodiments may be implemented by a computer program, which may be stored in a non-volatile computer readable storage medium, and when executed, may include the processes of the embodiments of the ionospheric tomography method of fused satellite-borne fully-polarized SAR and GPS, and will not be described again here.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
1. An ionospheric tomography method fusing satellite-borne full-polarization SAR and GPS is characterized by comprising the following steps:
s1, arranging M ground receiving stations at intervals below an ionosphere region, and determining coordinates of the ground receiving stations, wherein M is a positive integer greater than or equal to 6;
s2, acquiring at least one group of rays above the ground receiving station by using the satellite-borne full-polarization SAR, inverting TEC values corresponding to the rays, and recording coordinates of the satellite-borne full-polarization SAR in detection; acquiring N groups of rays at different positions by using a GPS (global positioning system), inverting TEC (thermoelectric cooler) values corresponding to the rays, and respectively recording coordinates when the GPS detects N times; each group of rays comprises M rays corresponding to the M ground receiving stations, and N is a positive integer greater than or equal to 20; in the step S2, at least one group of TEC values corresponding to M rays are obtained by the satellite-borne full-polarization SAR, the TEC values corresponding to N multiplied by M rays are obtained by the GPS, and at least (N + 1) multiplied by M different TEC values corresponding to rays penetrating through the ionization layer area to be detected are finally obtained;
s3, dividing the ionization layer region into n grids to obtain the coordinates of each grid, setting the electron density value in each grid as a constant, and determining the initial electron density value of each grid; wherein the number of the grids in the horizontal direction after the division is not more than N;
s4, calculating the projection length of each ray in each grid;
and S5, carrying out tomography iterative inversion based on a multiplicative algebraic reconstruction method by using the initial electron density value of each grid, the projection length of each ray in each grid and the TEC value corresponding to each ray, and obtaining the electron density distribution of an ionization layer region after multiple iterations.
2. The ionospheric tomography method fused with satellite-borne fully-polarized SAR and GPS according to claim 1, characterized in that:
in step S2, when at least one group of rays is obtained above the ground receiving stations by using the satellite-borne fully-polarized SAR, an elevation angle range of the rays formed by the satellite-borne fully-polarized SAR and each of the ground receiving stations is 87 to 90 °.
3. The ionospheric tomography method fused with satellite-borne fully-polarized SAR and GPS according to claim 1, characterized in that:
in the step S2, when at least one group of rays is obtained above the ground receiving station by using a satellite-borne fully-polarized SAR and the TEC value corresponding to each ray is inverted, the TEC value of each ray is determined by the following formula:
wherein f represents the carrier frequency of the satellite-borne fully-polarized SAR, B represents the intensity of the geomagnetic field in the ionization layer region, theta represents the included angle between the geomagnetic field in the ionization layer region and the satellite-borne fully-polarized SAR signal, and omega represents the Faraday rotation angle offset caused by the ionization layer region.
4. The ionospheric tomography method fused with satellite-borne fully-polarized SAR and GPS according to claim 3, characterized in that:
in step S2, the faraday rotation angle offset Ω caused by the ionosphere region is determined by echo scattering matrix data of the satellite-borne fully-polarized SAR, and the expression is:
wherein arg (·) represents the argument of complex element, Z 11 、Z 12 、Z 21 And Z 22 Respectively represents the echo information received by four polarization channels of the satellite-borne fully polarized SAR,
is Z 21 Conjugation of (A), S hh H-polarized wave, S, representing ground scattering of horizontally polarized waves vv V-polarized wave, S, representing ground scattering of vertically polarized waves hv Represents the V-polarized wave scattered from the ground by the horizontally polarized wave, and i represents an imaginary unit.
5. The ionospheric tomography method fused with satellite-borne fully-polarized SAR and GPS according to claim 3, characterized in that:
in step S2, when N groups of rays at different positions are obtained by using the GPS and the TEC value corresponding to each ray is inverted, the TEC value of each ray is determined by the following formula:
wherein f is 1 、f 2 Representing two different frequencies, L, of the GPS 1 、L 2 Respectively represents f 1 、f 2 Corresponding carrier pseudoranges, or L 1 、L 2 Respectively represent f 1 、f 2 The corresponding carrier phase value.
6. The ionospheric tomography method fused with satellite-borne fully-polarized SAR and GPS according to claim 1, characterized in that:
in the step S3, when the initial value of the electron density of each grid is determined, each grid value is given as an iterative initial value based on the ionosphere IRI empirical model.
7. The ionospheric tomography method fused with satellite-borne fully-polarized SAR and GPS according to claim 1, characterized in that:
in step S5, when tomographic iterative inversion is performed based on a multiplicative algebraic reconstruction method, an iterative formula is as follows:
wherein N is ej k+1 Represents the electron density, TEC, of the jth grid at the k +1 th iteration m Indicating the TEC value corresponding to the m-th ray,<·>represents the inner product, | | · | | | represents the norm,
is A m Transpose of (A) m Is represented by a matrix { A } mj The vector formed by the m-th row elements, the matrix { A } mj Element A of the mth row and jth column mj Represents the projection length of the mth ray in the jth grid, N e k Represents the electrons obtained by all n grids in the k iterationDensity distribution, λ k Is an iterative relaxation factor with the value range of 0 to lambda k ≤1。
8. The ionospheric tomography method fused with satellite-borne fully-polarized SAR and GPS according to claim 1, characterized in that:
in step S5, after at least 5 iterations, the electron density distribution in the ionization layer region is obtained.
9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor when executing the computer program realizes the steps of the ionospheric tomography method of fused spaceborne fully-polarized SAR and GPS of any of claims 1 to 8.
10. A computer readable storage medium having stored thereon a computer program, wherein the computer program, when being executed by a processor, is adapted to carry out the steps of the ionospheric tomography method with fusion of satellite-borne fully polarimetric SAR and GPS of any of claims 1 to 8.
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