CN102680974B - Signal processing method of satellite-bone sliding spotlight synthetic aperture radar - Google Patents

Abstract

The invention discloses a signal processing method of a satellite-bone sliding spotlight synthetic aperture radar. The method includes: performing molecule aperture processing on original echo data of the sliding spotlight synthetic aperture radar (SAR); performing range compression and range migration correction through a chirp scaling (CS) algorithm; introducing squint angle compensation in the CS algorithm; compensating scene space-variant performance; adjusting range migration amount of all sub-apertures to be identical with Doppler parameters of full apertures in CS scalar variable factors as the standard; performing azimuth compression and quadratic term compensation in the frequency domain, and performing frequency modulation processing in the time domain; splicing data of all the sub-apertures and restoring resolution ratio of the full apertures; and enabling signals to have phase preservation performance through spectrum analyzer (SPECAN) processing. By adopting the signal processing method, imaging quality can be improved under the condition of large scene squinting.

Description

A kind of signal processing method of spaceborne slip spot beam SAR

Technical field

The present invention relates to a kind of method that the synthetic aperture radar signal is handled, particularly the signal processing method under a kind of beam bunching mode large scene stravismus condition of sliding.

Background technology

Synthetic aperture radar (SAR) is a kind of typical radar system of scouting imaging over the ground, is mainly used in military surveillance and disaster monitoring, and it is can realize round-the-clock at present, one of important microwave remote sensing instrument of all weather operations.At present, common synthetic-aperture radar mode of operation mainly contains band pattern, scan pattern, beam bunching mode, slip beam bunching mode and TOPS pattern etc.In these several SAR imaging patterns, band pattern can realize the orientation to wide swath, yet is difficult to realize high resolving power; Though can obtain distance under the scan pattern simultaneously upwards and the orientation make progress the mapping band wide, be cost with sacrifice resolution, its resolution is lower than the band pattern under the square one; Though beam bunching mode can obtain high resolving power, yet the mapping band that its orientation makes progress is very little, has only the size of a wave beam footprint; The slip beam bunching mode can be broken through the restriction of beam bunching mode, can realize that not only high resolving power can realize that also wide orientation is to the mapping band.The Processing Algorithm of slip beam bunching mode mainly contain sub-aperture method and based on the orientation to pretreated method.Its neutron aperture is handled the signal of slip beam bunching mode and is handled block diagram as shown in Figure 1.Handle block diagram as shown in Figure 2 based on the orientation to pretreated slip pack.The signal processing method of existing slip spot beam SAR may be summarized to be: gather echoed signal, adopt sub-aperture or adopt the orientation to reduce PRF to pretreated method, avoid the orientation of imaging to fuzzy, adopt conventional algorithm again, such as the CS algorithm, the RD algorithm, the RMA algorithm carries out imaging.

In satellite or aircraft practical flight process, because control or other principle, the target Doppler shift that may cause antenna phase center to point to is also non-vanishing, and there is angle of squint to a certain degree in antenna phase center.Meeting snr loss when the existence of angle of squint will cause radar imagery, the azimuth ambiguity degree descends, image shift.In addition, the scope of satellite-borne synthetic aperture radar wave beam irradiation is big, and especially in the high-resolution imaging, the space-variant of scene can not be ignored.Existing glide Spotlight SAR Imaging imaging algorithm is not considered the situation under the angle of squint, do not have to consider the situation under the large scene is carried out the compensation of scene space-variant yet, the phase place in each sub-aperture is not carried out uniformity compensation (can influence picture quality when splicing at last in a plurality of sub-apertures), three above aspects all can influence image quality.Therefore, must develop a kind of slip Spotlight SAR Imaging imaging algorithm that can under large scene stravismus condition, improve picture quality.

Summary of the invention

Technical matters to be solved by this invention is: at the deficiencies in the prior art, provide a kind of signal processing method of spaceborne slip spot beam SAR, can improve image quality under large scene stravismus condition.

The present invention includes following technical scheme:

A kind of signal processing method of spaceborne slip spot beam SAR is characterized in that, comprises the steps:

(1) the slip spot beam SAR raw data of gathering being carried out sub-aperture divides;

(2) to each the sub-aperture number after dividing according to carrying out following processing respectively:

Carry out the orientation to the FFT conversion; The data of orientation after the Fourier transform be multiply by become the mark factor; Carry out distance to the FFT conversion, carry out distance compression and range migration correction then; Carry out distance to contrary FFT conversion; Do the orientation to compression and compensate for residual phase place after the contrary FFT conversion; The quadratic term compensation is carried out in the orientation after compression; Carry out the orientation then to contrary FFT conversion; The frequency modulation removal processing is carried out in the orientation after contrary FFT conversion;

(3) the sub-aperture data after handling are synthesized synthetic full aperture data;

(4) the full aperture data are carried out the orientation to the FFT conversion;

(5) carry out residual frequency modulation compensation;

(6) carry out the orientation to contrary FFT conversion;

(7) carry out the Specan compensation, make signal have the phase place retentivity.

The formula that becomes the mark factor in the described step (2) is as follows: $H1=\exp (\mathrm{j\π}*k(f_a;R)*c\left(f_a\right)*{(t-\frac{2R(f_a,R_0)}{c})}^2),$ Wherein, $c\left(f_a\right)=\frac{\mathrm{\Δ\α}\left(f_a\right)}{\mathrm{\α}\left(f_{\mathrm{dc}}\right)},$ Δα(f _a)＝α(f _a)-α(f _dc)， $\mathrm{\α}\left(f_a\right)=\sin \left({\mathrm{\θ}}_{\mathrm{ref}}\right)/{\sqrt{1-{\left(\frac{f_a\mathrm{\λ}}{2V}\right)}^2}}^{-1},$ $\mathrm{\α}\left(f_{\mathrm{dc}}\right)=\sin \left({\mathrm{\θ}}_c\right)/{\sqrt{1-{\left(\frac{f_{\mathrm{dc}}\mathrm{\λ}}{2V}\right)}^2}}^{-1}$

Wherein, f _DcBe the doppler centroid of full aperture, t is the satellite flight time, f _aFor the orientation to frequency, c is the light velocity; R ₀Be the scene center oblique distance, k (f _aR) be the equivalent FM rate; R (f _a, R ₀) be the instantaneous distance that scene center arrives satellite; V is the speed of satellite flight, θ _RefBe the angle of squint at scene center place, θ _cBe the angle of squint of full aperture center, λ is wavelength.

$k(f_a;R)=\frac{k_r}{k_{r}R\sin \left({\mathrm{\θ}}_{\mathrm{ref}}\right)\frac{2\mathrm{\λ}}{c^2}\·\frac{{\left(\frac{{\mathrm{\λf}}_a}{2V}\right)}^2}{{[1-{\left(\frac{{\mathrm{\λf}}_a}{2V}\right)}^2]}^{3/2}}}$

k _rBe linear signal frequency modulation rate, wherein R=R ₀+ c/2/f _s[nrn/2:nrn/2-1], R ₀Be scene center oblique distance, wherein f _sBe signal sampling rate, nrn is that distance is to sampling number.

In the described step (2), the orientation to the orientation of compression and compensate for residual phase place to compression function is:

$H3=\exp \left(j\frac{4\mathrm{\π}}{\mathrm{\λ}}\left(R(f_a;r)\right)\right[\sin {\mathrm{\θ}}_{\mathrm{ref}}\sqrt{1-{\left(\frac{{\mathrm{\λf}}_a}{2V}\right)}^2}-1\left]\right)\exp \left(\mathrm{j\Θ}(f_a;r)\right)\exp \left(j\frac{{2\mathrm{\πf}}_a}{V}\cos {\mathrm{\θ}}_{\mathrm{ref}}\right),$ Wherein $\mathrm{\Θ}(f_a;r)=\frac{4\mathrm{\π}}{c^2}k(f_a;R)(c\left(f_a\right)+1)c\left(f_a\right){(R/\sin \left({\mathrm{\θ}}_{\mathrm{ref}}\right)-R_0)}^2,$ R (f _aR) be the oblique distance of satellite to terrain object point.

The present invention compared with prior art has following advantage:

Method of the present invention is carried out imaging at the slip pack mode of operation under the large scene stravismus.The present invention had both considered the compensation of angle of squint, had considered phase equalization compensation between sub-aperture, had considered the space-variant of range migration under the large scene situation again.

Description of drawings

Fig. 1 is that existing sub-aperture slip pack is handled block diagram;

Fig. 2 existingly handles block diagram based on the orientation to pretreated slip pack;

Fig. 3 is process flow figure of the present invention;

Fig. 4 is 1 imaging of sub-aperture;

Fig. 5 is sub-aperture 1 point target frequency spectrum;

Fig. 6 is 2 imagings of sub-aperture;

Fig. 7 is sub-aperture 2 point target frequency spectrums;

Fig. 8 is the imaging of slip Spotlight SAR Imaging full aperture;

Fig. 9 is full aperture imaging point target spectrum.

Embodiment

Below just by reference to the accompanying drawings the present invention is done further introduction.As shown in Figure 3, disposal route of the present invention comprises the steps:

(1) sub-aperture is divided

At first should carry out sub-aperture to original slip Spotlight SAR Imaging data and divide, the length in sub-aperture should be greater than the instant bandwidth of slip Spotlight SAR Imaging impact point.Can be according to formula

Determine the number that sub-aperture is divided, PRF is pulse repetition rate, B _aBe signal transient bandwidth, k _RotBe the chirp rate of satellite to rotary middle point.By dividing sub-aperture, removed slip spot beam SAR orientation effectively to fuzzy, and reduced the repetition frequency of system, can significantly reduce the data volume that the synthetic-aperture radar number passes so that system's choosing under the selection on the pulse repetition rate and band pattern is consistent.In addition on the one hand, the division by sub-aperture has reduced the range migration amount, reduce distance to the orientation to the coupling amount, the solution coupling that is conducive in the imaging algorithm is handled.

(2) the sub-aperture data after dividing are carried out the orientation respectively to the FFT conversion

Be expressed as follows after Fourier transform through the orientation:

$S(t,f_a;r)=\mathrm{rect}\left(\frac{X-v_{a}t}{L}\right)\mathrm{rect}((t-2R(f_a;r)/c)/T)\exp (-j4\mathrm{\π}\frac{R(f_a;r)\sin \mathrm{\θ}}{\mathrm{\λ}}\sqrt{1-{\left(\frac{{\mathrm{\λf}}_a}{2V}\right)}^2}-j\frac{{2\mathrm{\πf}}_a}{V}\cos \mathrm{\θ})\exp (-\mathrm{j\πk}(f_a;R){(t-2R(f_a;r)/c)}^2)$

In the formula,

For the orientation to window function, X be terrain object point orientation to reference position, the length of L wave beam footprint, v _aFor the wave beam footprint at ground speed, t is the satellite flight time, rect ((t-2R (f _aR)/c)/T) be distance to window function, T be apart to the echo time delay cycle, R (f _aR) be satellite to the oblique distance of terrain object point, r be platform to the minimum distance on ground, θ is the angle of squint, λ is wavelength, V is satellite velocities, k (f _aR) be the equivalent FM rate, f _aFor the orientation to frequency, c is the light velocity.

(3) data of orientation after the Fourier transform be multiply by become the mark factor

$H1=\exp (\mathrm{j\π}*k(f_a;R)*c\left(f_a\right)*{(t-\frac{2R(f_a,R_0)}{c})}^2)$

The CS factor of this moment is: $c\left(f_a\right)=\frac{\mathrm{\Δ\α}\left(f_a\right)}{\mathrm{\α}\left(f_{\mathrm{dc}}\right)},$

Δα(f _a)＝α(f _a)-α(f _dc)

$\mathrm{\α}\left(f_a\right)=\sin \left({\mathrm{\θ}}_{\mathrm{ref}}\right)/{\sqrt{1-{\left(\frac{f_a\mathrm{\λ}}{2V}\right)}^2}}^{-1}$

$\mathrm{\α}\left(f_{\mathrm{dc}}\right)=\sin \left({\mathrm{\θ}}_c\right)/{\sqrt{1-{\left(\frac{f_{\mathrm{dc}}\mathrm{\λ}}{2V}\right)}^2}}^{-1}$

R (f _a, R ₀) be the instantaneous distance that scene center arrives satellite, f _DcBe the doppler centroid of full aperture before the synthetic aperture division, θ _cBe the angle of squint of full aperture center, θ _RefAngle of squint for the scene center place.Here it should be noted that: for the consistance of last sub-aperture stitching, need carry out normalized choosing in order to the CS factor that changes frequency modulation rate yardstick, namely make the CS factor value in each sub-aperture be unanimity by normalized.

In the equivalent FM rate, consider the space-variant of large scene, $k(f_a;R)=\frac{k_r}{k_{r}R\sin \left({\mathrm{\θ}}_{\mathrm{ref}}\right)\frac{2\mathrm{\λ}}{c^2}\·\frac{{\left(\frac{{\mathrm{\λf}}_a}{2V}\right)}^2}{{[1-{\left(\frac{{\mathrm{\λf}}_a}{2V}\right)}^2]}^{3/2}}}$

k _rBe linear signal frequency modulation rate, wherein R=R ₀+ c/2/f _s[nrn/2:nrn/2-1], R ₀Be scene center oblique distance, wherein f _sBe signal sampling rate, nrn is that distance is to sampling number.

(4) next carry out distance to the FFT conversion

(5) carry out distance compression and range migration correction then

After the work of drilling, need carry out distance compression and range migration correction, phase function is

$H2=\exp \left(\mathrm{j\π}\frac{1}{k(f_a;R)(1+c\left(f_a\right))}{f}_r^2\right)\exp \left(j\frac{4\mathrm{\πR}(f_a;R_0)}{c}{f}_r\right)$

f _rFor the distance to frequency.

(6) carry out distance to contrary FFT conversion,

(7) do after the conversion orientation to compression and compensate for residual phase multiplication with following orientation to compression function:

$H3=\exp \left(j\frac{4\mathrm{\π}}{\mathrm{\λ}}\left(R(f_a;r)\right)\right[\sin {\mathrm{\θ}}_{\mathrm{ref}}\sqrt{1-{\left(\frac{{\mathrm{\λf}}_a}{2V}\right)}^2}-1\left]\right)\exp \left(\mathrm{j\Θ}(f_a;r)\right)\exp \left(j\frac{{2\mathrm{\πf}}_a}{V}\cos {\mathrm{\θ}}_{\mathrm{ref}}\right)$

Wherein, $\mathrm{\Θ}(f_a;r)=\frac{4\mathrm{\π}}{c^2}k(f_a;R)(c\left(f_a\right)+1)c\left(f_a\right){(R/\sin \left({\mathrm{\θ}}_{\mathrm{ref}}\right)-R_0)}^2$

(8) carry out the quadratic term compensation after the orientation compression

Take advantage of second compensation item function H4:

$H_4=\exp \left(j\frac{{\mathrm{\πf}}_a^2}{\mathrm{kscl}\left(r\right)}\right)$

Wherein $\mathrm{kscl}\left(r\right)=-\frac{{2V}^2}{{\mathrm{\&lambda;r}}_{\mathrm{scl}}\left(r\right)},$ Wherein $r_{\mathrm{scl}}\left(r\right)=\frac{r_{\mathrm{scl}0}}{r_{\mathrm{rot}0}}{r}_{\mathrm{rot}}\left(r\right),$ $r_{\mathrm{rot}}\left(r\right)=\frac{r_{\mathrm{rot}0}-r}{1-{\mathrm{<figure-callout\; id="0"\; label="r\; scl"\; filenames="HSA00000724329500033.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{scl}}/{\mathrm{<figure-callout\; id="0"\; label="r\; rot"\; filenames="HSA00000724329500033.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{rot}}},$ r _Scl(r) be scene oblique distance function, r _Rot(r) be rotation oblique distance function, r _Rot0Be the distance of platform to the point of rotation, r _Scl0Choose at interval relevantly with image orientation, general value is the distance that platform arrives terrain object point.

(9) orientation is to contrary FFT conversion

(10) carrying out frequency modulation removal after the conversion handles

The orientation behind contrary FFT, for further reduce the orientation to the processing bandwidth, adopt frequency modulation removal to handle H ₅=exp (j π k _Rot(r) (t _a-t _Mid)), wherein

t _aFor the orientation to the time, t _MidBe the scene center moment.

(11) data in each sub-aperture are handled the back to carry out sub-aperture according to time sequencing synthetic in (2)-(10) set by step, the data of a synthetic full aperture.

(12) full aperture data after handling being made the orientation handles to FFT

(13) carry out residual frequency modulation compensation then

Full aperture data after synthetic be multiply by H ₆:

$H_6=\exp \left(j\frac{\mathrm{\&pi;}}{k_{\mathrm{eff}}}{f}_a^2\right),$ K wherein _Eff(r)=k _Scl(r)-k _Rot(r)

(14) carry out the orientation to contrary FFT conversion

(15) carry out spectrum analysis (Specan) compensation at last

In order to make last imaging results have the phase place retentivity, need multiply by following phase function:

$H_7=\exp \left(j{\mathrm{\&pi;k}}_t\left(r\right){(1-\frac{r_{\mathrm{rscl}0}}{r_{\mathrm{rot}0}})}^2{(t-t_{\mathrm{mid}})}^2\right)$

Wherein, $k_t\left(r\right)=-\frac{{2V}^2}{\mathrm{\&lambda;}(r_{\mathrm{rot}}\left(r\right)-r_{\mathrm{scl}}\left(r\right))}.$

Above-mentioned steps has been considered the processing under the angle of squint, has introduced the compensation of angle of squint in the CS algorithm.As the factor $\mathrm{\&alpha;}\left(f_a\right)=\sin \left({\mathrm{\&theta;}}_{\mathrm{ref}}\right)/{\sqrt{1-{\left(\frac{f_a\mathrm{\&lambda;}}{2V}\right)}^2}}^{-1},$ The orientation is to compression function $H3=\exp \left(j\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}\left(R(f_a;r)\right)\right[\sin {\mathrm{\&theta;}}_{\mathrm{ref}}\sqrt{1-{\left(\frac{{\mathrm{\&lambda;f}}_a}{2V}\right)}^2}-1\left]\right)\exp \left(\mathrm{j\&Theta;}(f_a;r)\right)\exp \left(j\frac{{2\mathrm{\&pi;f}}_a}{V}\cos {\mathrm{\&theta;}}_{\mathrm{ref}}\right),$ Wherein $\mathrm{\&Theta;}(f_a;r)=\frac{4\mathrm{\&pi;}}{c^2}k(f_a;R)(c\left(f_a\right)+1)c\left(f_a\right){(R/\sin \left({\mathrm{\&theta;}}_{\mathrm{ref}}\right)-R_0)}^2$ Deng the compensation of all having introduced the angle of squint.

Below large scene Squint SAR slip pack algorithm is carried out point target emulation, the simulation parameter of choosing is as follows:

Centre frequency: 9.6GHz

The pulse repetition:; 3800Hz

Signal bandwidth: 600MHz

Azimuthal resolution: 1 meter

Rotation center oblique distance: 1234 kms

Scene center oblique distance: 617 kms

Respective antenna angle of squint, scene center place: 3 °

Antenna aperture: 4 meters

Scene size: 15 kilometers (distance to) * 20 kilometers (orientation to)

Point target is placed on scene center

From Fig. 5 and Fig. 7 as can be seen, sub-aperture data have all realized good focusing after handling through this method, and peak value is other than for about-13dB, and the integration secondary lobe is than for about-9.5dB.Because the final step of imaging algorithm has been used the frequency modulation removal processing, at this moment, the orientation to pixel separation be

$\mathrm{\&delta;}=\frac{\mathrm{\&lambda;}\&CenterDot;r\&CenterDot;\mathrm{PRF}}{2\&CenterDot;V\&CenterDot;N}$

Wherein, N is to count to processing in the orientation, differentiates in this way to calculate to be divided into that the orientation is 0.3662 to pixel separation after two sub-apertures, and pixel is spaced apart 0.1881 behind the synthetic full aperture.In Fig. 4 and Fig. 6, the interval at 3dB width place is approximately about 6 and 5, and then sub-aperture imaging resolution is approximately 2 meters, and Fig. 8 brings up to 1 meter through full aperture processing back resolution.As seen, large scene stravismus full aperture processing down not only makes resolution improve, and has obtained the good focusing effect.

The unspecified part of the present invention belongs to general knowledge as well known to those skilled in the art.

Claims (3)

1. the signal processing method of a spaceborne slip spot beam SAR is characterized in that, comprises the steps:

(1) the slip spot beam SAR raw data of gathering being carried out sub-aperture divides;

(2) to each the sub-aperture number after dividing according to carrying out following processing respectively:

Carry out the orientation to the FFT conversion; The data of orientation after the Fourier transform be multiply by become the mark factor; Carry out distance to the FFT conversion, carry out distance compression and range migration correction then; Carry out distance to contrary FFT conversion; Do the orientation to compression and compensate for residual phase place after the contrary FFT conversion; The quadratic term compensation is carried out in the orientation after compression; Carry out the orientation then to contrary FFT conversion; The frequency modulation removal processing is carried out in the orientation after contrary FFT conversion;

(3) the sub-aperture data after handling are synthesized synthetic full aperture data;

(4) the full aperture data are carried out the orientation to the FFT conversion;

(5) carry out residual frequency modulation compensation;

(6) carry out the orientation to contrary FFT conversion;

(7) carry out the Specan compensation, make signal have the phase place retentivity.

The formula that becomes the mark factor in the described step (2) is as follows:

$H1=\exp (\mathrm{j\&pi;}*k(f_a;R)*c\left(f_a\right)*{(t-\frac{2R(f_a,R_0)}{c})}^2),$

Wherein, $c\left(f_a\right)=\frac{\mathrm{\&Delta;\&alpha;}\left(f_a\right)}{\mathrm{\&alpha;}\left(f_{\mathrm{dc}}\right)},$ Δα(f _a)＝α(f _a)-α(f _dc)， $\mathrm{\&alpha;}\left(f_a\right)=\sin \left({\mathrm{\&theta;}}_{\mathrm{ref}}\right)/\sqrt{1-{\left(\frac{f_a\mathrm{\&lambda;}}{2V}\right)}^2}-1,$ $\mathrm{\&alpha;}\left(f_{\mathrm{dc}}\right)=\sin \left({\mathrm{\&theta;}}_c\right)/\sqrt{1-{\left(\frac{f_{\mathrm{dc}}\mathrm{\&lambda;}}{2V}\right)}^2}-1,$

Wherein, f _DcBe the doppler centroid of full aperture, t is the satellite flight time, f _aFor the orientation to frequency, c is the light velocity; R ₀Be the scene center oblique distance, k (f _aR) be the equivalent FM rate; R (f _a, R ₀) be the instantaneous distance that scene center arrives satellite; V is the speed of satellite flight, θ _RefBe the angle of squint at scene center place, θ _cBe the angle of squint of full aperture center, λ is wavelength.

2. the method for claim 1 is characterized in that:

$k(f_a;R)=\frac{k_r}{k_{r}R\sin \left({\mathrm{\&theta;}}_{\mathrm{ref}}\right)\frac{2\mathrm{\&lambda;}}{c^2}\&CenterDot;\frac{{\left(\frac{\mathrm{\&lambda;}{f}_a}{2V}\right)}^2}{{[1-{\left(\frac{\mathrm{\&lambda;}{f}_a}{2V}\right)}^2]}^{3/2}}}$

k _rBe linear signal frequency modulation rate, wherein R=R ₀+ c/2/f _s[nrn/2:nrn/2-1], R ₀Be scene center oblique distance, wherein f _sBe signal sampling rate, nrn is that distance is to sampling number.

3. method as claimed in claim 2 is characterized in that: in the described step (2), the orientation to the orientation of compression and compensate for residual phase place to compression function is:

$H3=\exp \left(j\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}\left(R(f_a;r)\right)\right[\sin {\mathrm{\&theta;}}_{\mathrm{ref}}\sqrt{1-{\left(\frac{\mathrm{\&lambda;}{f}_a}{2V}\right)}^2}-1\left]\right)\exp \left(\mathrm{j\&Theta;}(f_a;r)\right)\exp \left(j\frac{2\mathrm{\&pi;}{f}_a}{V}\cos {\mathrm{\&theta;}}_{\mathrm{ref}}\right),$ Wherein $\mathrm{\&Theta;}(f_a;r)=\frac{4\mathrm{\&pi;}}{c^2}k(f_a;R)(c\left(f_a\right)+1)c\left(f_a\right){(R/\sin \left({\mathrm{\&theta;}}_{\mathrm{ref}}\right)-R_0)}^2,$ R (f _aR) be the oblique distance of satellite to terrain object point, r is that platform is to the minimum distance on ground.

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