CN105044716B - It is a kind of to compensate parametrization self-focusing method of the background ionosphere to GEOSAR Imagings - Google Patents
It is a kind of to compensate parametrization self-focusing method of the background ionosphere to GEOSAR Imagings Download PDFInfo
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- 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
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- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- 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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- G01S13/9019—Auto-focussing of the SAR signals
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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- G01S13/9017—SAR image acquisition techniques with time domain processing of the SAR signals in azimuth
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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Abstract
It is a kind of to compensate parametrization self-focusing method of the background ionosphere to GEOSAR Imagings, GEOSAR raw radar datas are compressed into row distance to pulse first with matched filtering；One piece of rectangular area is selected in GEOSAR imaging regions and carries out mesh generation；Then adjust the distance and carry out envelope alignment and phase compensation to the compressed GEOSAR data of pulse, and background ionosphere is calculated with coefficient of the orientation slow time with respect to high-order change function using image Minimum Entropy criteria；Finally judge whether to terminate iteration, if terminate iteration, the envelope of the high-order change all imaging region echoes of function pair then obtained using iteration and phase compensation, and then realize that the GEOSAR in the region is imaged, can be approximately polynomial feature present invention utilizes variation tendency of the background ionosphere within the GEOSAR synthetic aperture times, realize by way of iteration that the echo envelope caused by ionosphere high-order changes is walked about correction and phase error compensation based on Minimum Entropy criteria, so as to effectively increase GEOSAR image quality.
Description
Technical field
Method of the background ionosphere to GEOSAR Imagings is compensated the present invention relates to a kind of, particularly a kind of compensation background
Ionosphere belongs to geostationary orbit SAR system and develops field to the parametrization self-focusing method of GEOSAR Imagings.
Background technology
Geostationary orbit SAR has wide coverage, revisits outstanding advantages of speed is fast, is supervised in Earthquake Disaster Alleviation, environment
Many fields such as survey have great application prospect.But since satellite orbit is high, the speed of service is slow, during its synthetic aperture
Between reach the magnitude (and comparing in contrast, the low rail SAR synthetic aperture times are second level) of hundreds of seconds or even kilosecond, so long
In the synthetic aperture time, there are many non-ideal factors can cause the decoherence between target echo, thus reduce GEOSAR into
Image quality amount, and the change in time and space of background ionosphere is to influence one of mostly important factor of GEO SAR image quality.
Domestic and international many research units at present, such as Cranfield universities of Britain, the National University of Defense technology, China's Space technology
Research institute, Beijing Institute of Technology etc. have carried out the correlative study for ionosphere compensation.From the ionosphere compensation proposed at present
From the point of view of method, it is broadly divided into two classes：1st, the compensation method of absolute ionized layer TEC value is estimated using SAR echo datas；2nd, compensate
The orientation self-focusing method of the opposite change in ionosphere；When wherein first kind method mainly utilizes the echo caused by the dispersion of ionosphere
Prolong and estimate ionized layer TEC data with blooming effect, then receive pulse to each orientation respectively and carry out phase compensation, main bag
Distance is included to adaptive matched filter method, distance to more vision methods etc..It is main to utilize electricity for adaptive matched filter method
Distance defocuses situation caused by absciss layer, carries out tune frequency search, realizes Range Focusing.This method is mainly adjusted the distance to be carried out to data
Processing, defocuses for pattern-band distance and compares serious conditions and have good validity, but for L band above distance to several
Do not defocus (such as by taking L-band as an example, under 60M bandwidth situations, maximum phase difference is less than 0.01 arc caused by 1TECU
Degree), therefore, it is difficult to accurately estimate TEC values, compensated so as to fulfill to the precise phase of orientation echo.Pass through apart from more vision methods
SAR echo signal distance is split to frequency spectrum, is then imaged respectively, by two width visible images carry out registration with
Estimation time delay, further obtains the estimation of TEC values, and this method substantially belongs to double frequency measurement TEC methods, its precision depends on two
Relative frequency difference between a frequency, relative frequency difference is bigger, then precision is higher.For SAR echo signal, due to
Relative bandwidth is limited, therefore estimated accuracy is very low, for low signal-to-noise ratio situation, influences even more serious.Above method does not have at the same time
There is an influence for considering ionosphere space-variant, and (pitching and orientation can reach hundreds of since GEOSAR beam coverages are very wide
Kilometers), the influence of ionosphere space-variant can not be ignored, therefore the compensation method of first kind ionosphere is difficult to be applicable in.Pass through
In ground configuration SAR signal receivers, subband segmentation then is carried out to SAR echoes, finally can be with using the method for phase interference
High-precision TEC estimations are obtained, but this method is needed in the substantial amounts of receiver of ground configuration, it is therefore desirable to higher cost.
For the GEOSAR imagings being operated in more than L-band, the order of magnitude of ionized layer TEC to Imaging not
Greatly, its opposite change is to influence the principal element of GEO SAR imagings.The scholars such as Sthphen E.Hobbs are pointed out using orientation certainly
Focus method compensation Ionospheric variability is feasible to the GEOSAR influences being imaged.For compensating the orientation of the opposite change in ionosphere
Self-focusing method can not only compensate the influence of ionosphere time variation, but also can overcome ionosphere space-variant by way of piecemeal compensation
The influence of property.
Orientation self-focusing method currently used for the opposite change in compensation ionosphere mainly includes：Phase gradient autofocus method
(PGA methods), maximum-contrast method, minimum moisture in the soil method etc..It is high for PGA methods computational efficiency, in Airborne SAR Motion Information
In there is good application effect, but PGA methods need to find the very strong isolated scattering point of energy in SAR image, this
The application of PGA methods is constrained to a certain extent.Maximum-contrast method and minimum moisture in the soil method are applied more in ISAR imagings
Extensively, by realizing that ISAR is focused on to the iterative search of phase, above method has good adaptivity.But for GEO
For SAR, transmitting and reception pulse number are up to up to ten thousand or even hundreds of thousands in the synthetic aperture time, in so big space
It is almost not achievable to search for the opposite change in ionosphere, therefore is not directly applicable GEOSAR imagings.
In short, the compensation problem for ionosphere is one of the most key technology that GEO SAR are realized, so far both at home and abroad still
Generally acknowledged effective compensation method is not proposed, therefore the problem is still the hot and difficult issue problem of GEO SAR researchs.
The content of the invention
The technology of the present invention solves the problems, such as：Overcome the deficiencies in the prior art, it is proposed that one kind compensation background ionosphere pair
The parametrization self-focusing method of GEOSAR Imagings, is become using change of the background ionosphere within the GEOSAR synthetic aperture times
Gesture can be approximately polynomial feature, estimate that ionosphere with respect to running parameter, is imaged in BP and calculates by the Minimum Entropy criteria of image
On the basis of method, realize that the echo envelope caused by ionosphere high-order changes is walked about correction and phase error by way of iteration
Compensation, so as to effectively improve GEOSAR image quality.
The present invention technical solution be：It is a kind of to compensate parametrization autohemagglutination of the background ionosphere to GEOSAR Imagings
Burnt method, step are as follows：
(1) GEOSAR raw radar datas are compressed into row distance to pulse using matched filtering；
(2) according to BP algorithm process flow, one piece of rectangular area is selected in GEOSAR imaging regions, and to the square of selection
Shape region carries out mesh generation, and each mesh point be a ground scatter point, makes and M × N number ofly is included in the rectangular area of selection
Area scattering point；
(3) according to the rectangle imaging region and the ephemeris parameter of GEOSAR satellites selected in step (2), in step (1)
Distance carries out envelope alignment to the compressed GEOSAR data of pulse and phase compensation, envelope alignment are dissipated with ground after phase compensation
The orientation echo of exit point (p, q)For：
Wherein p=1,2 ..., M, q=1,2 ..., N, f0For GEOSAR original echo carrier frequencies, c is the light velocity, σpqFor
Target backscattering coefficient, GpqFor Range compress gain, equal to exomonental time width and the product of spectrum width, TEC
For the integration of electron density on Electromagnetic Wave Propagation path, tmFor the orientation slow time, and m=1,2 ..., K, K are the radar course of work
It is middle to launch the pulse number received,For apart from fast time, RpqRepresent ground scatter point (p, q) distance GEOSAR antenna phases
The nearest oblique distance at center, ionosphere is with the slow time t in orientationmChange function with respect to high-orderSpecifically by formula：
Provide, wherein a1,a2,...,an-1It is ionosphere with the slow time t in orientationmWith respect to the coefficient of high-order change function； k
For algorithm iteration number；
(4) ionosphere is calculated with the slow time t in orientation using image Minimum Entropy criteriamWith respect to the coefficient of high-order change function
(5) if k=0 orThen utilize in step (4)
Ionosphere is calculated with the slow time t in orientationmCoefficient with respect to high-order change function calculates ionized layer TEC relative changing valueWalk about for compensating the envelope as caused by ionosphere, and make k=k+1, return
Step (4), otherwise enters step (6)；The ξ is default constant；
(6) obtained using iterationRealize the envelope to all imaging region echoes and phase compensation, and then
Realize the GEOSAR imagings in the region.
Ionosphere is calculated with the slow time t in orientation using image Minimum Entropy criteria in the step (4)mChange letter with respect to high-order
Several coefficientsSpecifically by formula：
Provide, wherein SpqFor the pixel of ground scatter point (p, q) in GEOSAR images, argminf (x) representative function f (x)
Corresponding independent variable x when being minimized.
The pixel S of ground scatter point (p, q) in the GEOSAR imagespqSpecifically by formula：
Provide.
Utilized in the step (5) in step (4) and ionosphere is calculated with the slow time t in orientationmChange letter with respect to high-order
Several coefficients calculates ionized layer TEC relative changing valueFor compensating by ionizing
Envelope caused by layer is walked about, the orientation echo S after compensationpq(tm) by formula：
Provide.
The present invention has the beneficial effect that compared with prior art：
(1) present invention constructs the ionosphere based on optiaml ciriterion at any time based on background ionosphere parameterized model
Between the parameter estimation model that changes, the model realization is simple, it is only necessary to estimates that a small amount of unknown parameter (generally only needs to estimate 4-6
A unknown parameter) it can be achieved to estimate the accurate of background ionosphere high-order change；
(2) present invention is on the basis of BP imaging algorithms, using the mode to iterate, while realizes to by ionosphere high-order
The correction of echo envelope migration and phase error compensation caused by change, so as to which SAR image quality is greatly improved；
(3) relative to Phase gradient autofocus method (PGA), the special aobvious point letter in any ground is not required in the method in the present invention
Breath, the influence that can effectively overcome background ionosphere to be imaged GEO SAR, realizes the self-focusing of distributed scene, has good
Robustness and practicality；
(4) method in the present invention need not increase special Ionospheric measurement equipment, the completely angle from signal processing
Realize estimation and compensation to the change of background ionosphere high-order, there is the advantages of cost of implementation is low, and compensation effect is good.
Brief description of the drawings
The process chart of method in Fig. 1 present invention；
The ionized layer TEC value that Fig. 2 is obtained using the method for the present invention estimation；
Fig. 3 is the SAR imaging results that Autofocus processing is carried out using the method for the present invention；
Fig. 4 does not carry out the SAR imaging results of ionosphere effect compensation.
Embodiment
The present invention proposes that flow chart to the parametrization self-focusing method of GEOSAR Imagings, is realized in a kind of compensation ionosphere
As shown in Figure 1, introduce embodiment with reference to instantiation：
The first step：First with matched filtering to the obtained GEOSAR raw radar datas of emulation into row distance to pulse pressure
Contracting (is specifically shown in：Protect polished, Xing Mengdao, Wang Tong radar imaging technology [M] Beijing：Electronic Industry Press, 2004, the page number：Page 19
To page 24).
Second step：According to BP algorithm process flow, fritter region to be imaged is selected to carry out in GEOSAR imaging regions
Mesh generation, each mesh point are a ground scatter point, altogether comprising M × N number of ground scatter point (M in example in the region
=300, N=300).
3rd step：According to selected ground imaging region and the ephemeris parameter of satellite, adjust the distance compressed to pulse
GEOSAR data carry out envelope alignment and (are specifically shown in phase compensation：Lee's wealth product, Zhang Hongtai, a kind of small quick suitable GEOSAR of of Tan into
As improved rapid bp algorithm [J] modern defense technologies, the phase of volume 2010,38 5, the page number：77-81.), then at this time coordinate for (p,
Q) ground scatter point orientation echoIt is represented by：
Wherein p=1,2 ..., M, q=1,2 ..., N, f0For GEOSAR original echos carrier frequency (f in example0For
1.25GHz), c is the light velocity, σpqFor target backscattering coefficient, GpqFor Range compress gain, equal to the SAR exomonental times
(pulse temporal width of satellite-borne SAR transmitting at present is typically about tens of delicate to hundreds of delicate, frequency to the product of width and spectrum width
Spectral width is more than ten megahertzs to multiple gigahertz, and SAR transmittings pulse temporal width is 41 delicate, spectrum widths 30 in example
Megahertz), TEC be Electromagnetic Wave Propagation path on electron density integration, tmFor the orientation slow time, and m=1,2 ..., K (example
1000) middle K is.Ionosphere is represented by with the time with respect to high-order changeK is
Algorithm iteration number, wherein k=0 (n=4 in example, and choose initial point
4th step：" image minimum entropy " criterion is utilized to calculate ionosphere with the slow time t in orientationmChange function with respect to high-order
Coefficient
(arg min are to optimize to corresponding independent variable x when wherein arg min f (x) representative function f (x) are minimized
General mathematic sign in theory), SpqRepresent that coordinate is the pixel of (p, q) ground scatter point in SAR image, is met：
5th step：If judge k=0 or(wherein
ξ is the constant of a setting, and general value should be less than 10-5, value is 10 in example-8), then calculate the opposite change of ionized layer TEC
ValueAnd the envelope as caused by ionosphere is compensated with this and is walked about：
Wherein p=1,2 ..., M, q=1,2 ..., N, make k=k+1, and make k=k+1, return to the 4th step, otherwise into the
Six steps.
6th step：Obtained using iterationRealize and the envelope and phase of all imaging region echoes are mended
Repay, and realize that the GEOSAR in the region is imaged.
The ionized layer TEC value estimated using the embodiment in the present invention is as shown in Fig. 2, TEC estimates as seen from Figure 2
Precision is better than 0.1 × 1016.And imaging results using institute's extracting method of the present invention as shown in figure 3, do not ionized after the compensation of ionosphere
The results are shown in Figure 4 for layer compensation deals.Comparison diagram 3, Fig. 4 can be seen that institute's extracting method of the present invention greatly improves into image quality
Amount.
Unspecified part of the present invention is those skilled in the art's common knowledge.
Claims (4)
1. a kind of compensate parametrization self-focusing method of the background ionosphere to GEOSAR Imagings, it is characterised in that step is such as
Under：
(1) GEOSAR raw radar datas are compressed into row distance to pulse using matched filtering；
(2) according to BP algorithm process flow, one piece of rectangular area is selected in GEOSAR imaging regions, and to the rectangle region of selection
Domain carries out mesh generation, and each mesh point is a ground scatter point, makes in the rectangular area of selection and being dissipated comprising M × N number of ground
Exit point；
(3) according to the rectangle imaging region and the ephemeris parameter of GEOSAR satellites selected in step (2), to distance in step (1)
Envelope alignment and phase compensation, envelope alignment and ground scatter point after phase compensation are carried out to the compressed GEOSAR data of pulse
The orientation echo S of (p, q)pq(tm) be：
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Wherein p=1,2 ..., M, q=1,2 ..., N, f0For GEOSAR original echo carrier frequencies, c is the light velocity, σpqFor target
Backscattering coefficient, GpqFor Range compress gain, equal to exomonental time width and the product of spectrum width, TEC is represented
The integral function of electron density, t on Electromagnetic Wave Propagation pathmFor the orientation slow time, and m=1,2 ..., K, K are worked for radar
Launch the pulse number received, TEC (t in journeym) represent that electron density is with the product of orientation slow time on Electromagnetic Wave Propagation path
Point,For apart from fast time, RpqRepresent the nearest oblique distance of ground scatter point (p, q) distance GEOSAR antenna phase centers, ionization
Layer is with the slow time t in orientationmChange function with respect to high-orderSpecifically by formula：
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Provide, wherein a1,a2,...,an-1It is ionosphere with the slow time t in orientationmWith respect to the coefficient of high-order change function；K is algorithm
Iterations；
(4) ionosphere is calculated with the slow time t in orientation using image Minimum Entropy criteriamWith respect to the coefficient solution of high-order change function
(5) if k=0 orThen utilize and calculated in step (4)
To ionosphere with the slow time t in orientationmWith respect to the coefficient solution of high-order change functionCalculate ionized layer TEC phase
To changing valueWalk about for compensating the envelope as caused by ionosphere, and make k=
K+1, return to step (4), otherwise enters step (6)；The ξ is default constant；
(6) obtained using iterationRealize the envelope to all imaging region echoes and phase compensation, and then realize
GEOSAR imagings in the region.
2. a kind of compensation background ionosphere according to claim 1 is to the parametrization self-focusing side of GEOSAR Imagings
Method, it is characterised in that：Ionosphere is calculated with the slow time t in orientation using image Minimum Entropy criteria in the step (4)mWith respect to high-order
Change the coefficient solution of functionSpecifically by formula：
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</mrow>
<mi>M</mi>
</munderover>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mrow>
<mo>|</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>|</mo>
</mrow>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
Provide, wherein SpqFor the pixel of ground scatter point (p, q) in GEOSAR images, arg min f (x) representative function f (x) take
Corresponding independent variable x during minimum value.
3. a kind of compensation background ionosphere according to claim 2 is to the parametrization self-focusing side of GEOSAR Imagings
Method, it is characterised in that：The pixel S of ground scatter point (p, q) in the GEOSAR imagespqSpecifically by formula：
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<msub>
<mi>G</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mi>sin</mi>
<mi> </mi>
<mi>c</mi>
<mrow>
<mo>(</mo>
<mover>
<mi>t</mi>
<mo>^</mo>
</mover>
<mo>-</mo>
<mn>2</mn>
<mfrac>
<mrow>
<mn>40.3</mn>
<mi>T</mi>
<mi>E</mi>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>m</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msubsup>
<mi>f</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mi>c</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mrow>
<mn>2</mn>
<msub>
<mi>R</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
</mrow>
<mi>c</mi>
</mfrac>
<mo>)</mo>
</mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
<mn>80.6</mn>
<mrow>
<mo>(</mo>
<mi>T</mi>
<mi>E</mi>
<mi>C</mi>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>m</mi>
</msub>
<mo>)</mo>
<mo>-</mo>
<msup>
<mover>
<mrow>
<mi>T</mi>
<mi>E</mi>
<mi>C</mi>
</mrow>
<mo>^</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msup>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>m</mi>
</msub>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>f</mi>
<mn>0</mn>
</msub>
<mi>c</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
Provide.
4. a kind of compensation background ionosphere according to claim 1 is to the ginseng of GEOSAR Imagings
Numberization self-focusing method, it is characterised in that：Utilized in the step (5) in step (4) and ionosphere is calculated with side
Position slow time tmWith respect to the coefficient solution of high-order change functionCalculate ionized layer TEC relative changing valueWalk about for compensating the envelope as caused by ionosphere, the orientation after compensation is returned
Ripple Spq(tm) by formula：
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>m</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<msub>
<mi>G</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mi>sin</mi>
<mi>c</mi>
<mrow>
<mo>(</mo>
<mover>
<mi>t</mi>
<mo>^</mo>
</mover>
<mo>-</mo>
<mn>2</mn>
<mfrac>
<mrow>
<mn>40.3</mn>
<mrow>
<mo>(</mo>
<mi>T</mi>
<mi>E</mi>
<mi>C</mi>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>m</mi>
</msub>
<mo>)</mo>
<mo>-</mo>
<msup>
<mover>
<mrow>
<mi>T</mi>
<mi>E</mi>
<mi>C</mi>
</mrow>
<mo>^</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msup>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>m</mi>
</msub>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msubsup>
<mi>f</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mi>c</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mrow>
<mn>2</mn>
<msub>
<mi>R</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
</mrow>
<mi>c</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mn>2</mn>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
<mn>40.3</mn>
<mi>T</mi>
<mi>E</mi>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>m</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>f</mi>
<mn>0</mn>
</msub>
<mi>c</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
Provide.
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| CN103675775A (en) * | 2013-12-12 | 2014-03-26 | 北京理工大学 | Method for analyzing influences of background ionosphere on GEO SAR imaging |
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| CN103675775A (en) * | 2013-12-12 | 2014-03-26 | 北京理工大学 | Method for analyzing influences of background ionosphere on GEO SAR imaging |
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