CN106154269A - One is applicable to circumferential synthetic aperture radar fast time-domain formation method - Google Patents

Abstract

One of the present invention is applicable to circumferential synthetic aperture radar fast time-domain formation method, and whole flow process includes that three process step: the first step, sub-aperture divides and generates with initial subimage；Second step, circular recursion sub-aperture merges and subimage generates；3rd step, full aperture merges and final image generates.The inventive method its provide the benefit that: use sub-aperture treatment technology, keeping time-domain imaging method high-precision while, considerably reduce the amount of calculation of time-domain imaging method, thus improve the efficiency of imaging processing, and then achieve the quick high accuracy imaging processing of CSAR, it is thus achieved that high-quality CSAR image.

Description

One is applicable to circumferential synthetic aperture radar fast time-domain formation method

Technical field

The invention belongs to synthetic aperture radar (Synthetic Aperture Radar, SAR) imaging field, relate to one It is applicable to circumferential synthetic aperture radar (Circular SAR, CSAR) fast time-domain formation method.

Background technology

CSAR refers to that radar platform (or claiming radar station) does 360 ° of circumference or wide angle circular motion around observation scene, and And wave beam points to target scene all the time and is observed the radar system of imaging；This radar system has acquisition target scattering information Abundant, high-resolution imaging and the advantages such as three-dimensional imaging can be realized, cause extensive concern in recent years；But, special motion Track processes to the data of CSAR and brings new problem and challenge, and as echo data amount is big, echo distance orientation coupling is strong Deng, these all substantially increase the difficulty of CSAR high accuracy imaging processing.

Existing CSAR formation method mainly has time domain BPA (Backprojection Approach, rear orientation projection side Method)；Time domain BPA is without any approximate processing, it is possible to accurately process distance orientation coupling and its special thunder of CSAR echo Reach movement locus, thus realize the high accuracy imaging processing of CSAR

But, time domain BPA needs great amount of calculation, thus reduces imaging efficiency, and therefore time domain BPA can not become fast The effective CSAR formation method of speed；How to solve to be applicable to a fast time-domain formation method skill urgently to be resolved hurrily just of CSAR Art problem.

Summary of the invention

It is an object of the invention to provide one and be applicable to circumferential synthetic aperture radar fast time-domain formation method, to improve CSAR imaging processing efficiency.

The technical scheme is that first, CSAR echo-signal is carried out Range compress, the full aperture of radar is divided For several sub-aperture and generate initial subimage grid, then by corresponding with sub-aperture Range compress echo-signal rear orientation projection To initial subimage grid, coherent superposition generates initial subimage；Then, the sub-aperture being circulated recurrence merges and new son Image lattice generates, then the subimage of upper level is interpolated into new subimage grid, and coherent superposition generates new subimage；? After, by all sub-aperture image projection to same imaging region, coherent superposition generates CSAR image.

One of the present invention is applicable to circumferential synthetic aperture radar fast time-domain formation method, including following process step:

The first step, sub-aperture divides and generates with initial subimage；

It is f that known CSAR launches signal center frequency_c, carrying a width of B, range resolution ratio is ρ_x, azimuth resolution is ρ_y；False If cartesian coordinate system initial point is image scene center, in image scene, the position of arbitrary target P is r_P=(x_P,y_P,0)；Radar Platform moves in a circle about the z axis with speed V, and slow its coordinate of moment time η is (R_xycos(φ),R_xysin(φ),z_M), R_xyAnd z_M Being respectively radius and the height of radar platform circular path, φ ∈ [0,2 π] is the angle variables of radar platform, and φ (η)=V η/R_xy；The initial position of radar platform is (R_xy,0,z_M)；If the baseband signal of radar emission is p (τ), the then CSAR received Echo-signal is after quadrature demodulation:

S (τ, φ)=σ_P·p[τ-R(φ,r_P)/c₀]·exp[-j2πf_cR(φ,r_P)/c₀]

Wherein, τ is the slow time, σ_PFor the scattering coefficient of target P, c₀For the light velocity；R(φ,r_P) it is that radar platform arrives target P Round trip distance oblique distance, it may be assumed that

$R(\mathrm{\φ},r_P)=2\sqrt{{\left(R_{xy}cos\right(\mathrm{\φ})-x_P)}^2+{\left(R_{xy}sin\right(\mathrm{\φ})-y_P)}^2+z_M^2}$

After Range compress, CSAR echo-signal is:

s_rc(τ, φ)=σ_p·p_rc[B(τ-R(φ,r_P)/c₀)]·exp[-j2πf_cR(φ,r_P)/c₀]

Wherein, p_rc() is Range compress signal envelope；

If the real aperture sampling number of radar platform synthetic aperture is L, it is uniformly divided into K sub-circular arc pore size data (typically take K/L_full≤ 1/8), then every cross-talk pore size data sampling number isTrue according to factorization principle Determine optimal initial aperture length l of circular arc data₀, and sub-aperture factoring I；Then there is N=l₀×I^P, wherein P is decomposition level Number；

To the first order the n-th sub-aperture, n=1,2 ..., I^P, firstly generate the initial subimage grid of the first order n-thWherein grid initial point is the first order the n-th sub-aperture center, pole spanFor grid initial point to any scene point The round trip oblique distance of (x, y, 0), polar angleFor pole spanAnd the angle between the normal of sub-aperture center, it may be assumed that

$\left\{\begin{array}{c}{\mathrm{\ρ}}_n^1=\sqrt{{\[R_{xy}cos\left({\mathrm{\φ}}_n^1\right)-x\]}^2+{\[R_{xy}sin\left({\mathrm{\φ}}_n^1\right)-y\]}^2}\\ {\mathrm{\θ}}_n^1=arctan\left(\frac{y-R_{xy}sin\left({\mathrm{\φ}}_n^1\right)}{x-R_{xy}\cos \left({\mathrm{\φ}}_n^1\right)}\right),{\mathrm{\θ}}_n^1\∈\[0,\mathrm{\π}\]\end{array}\right.$

Wherein,For the angle variables that the first order the n-th sub-aperture center is corresponding；And the initial subimage of the first order n-th The pole span sampling interval of gridWith the polar angle sampling intervalIt is respectively as follows:

$\left\{\begin{array}{c}\mathrm{\Δ}{\mathrm{\ρ}}_n^1\≤c_0/2B\\ \mathrm{\Δ}{\mathrm{\θ}}_n^1\≤c_0/f_c{d}_{Mn}^1\end{array}\right.$

Wherein,Length for the first order the n-th sub-aperture；

Then, by corresponding for the first order the n-th sub-aperture Range compress echo-signal rear orientation projection at the beginning of the first order n-th Beginning subimage gridThen coherent superposition generates the initial subimage of the first order n-th, it may be assumed that

$I_n^1({\mathrm{\ρ}}_n^1,{\mathrm{\θ}}_n^1)=\underset{{\mathrm{\φ}}_n^1-{\mathrm{\φ}}_{In}^1/2}{\overset{{\mathrm{\φ}}_n^1+{\mathrm{\φ}}_{In}^1/2}{\∫}}{s}_{rc}\left(R\right(\mathrm{\φ},{\mathrm{\ρ}}_n^1,{\mathrm{\θ}}_n^1)/c_0,\mathrm{\φ})\·\exp \[j2{\mathrm{\πf}}_{c}R(\mathrm{\φ},{\mathrm{\ρ}}_n^1,{\mathrm{\θ}}_n^1)/c_0\]d\mathrm{\φ}$

Wherein, s_rc() is Range compress echo-signal,For the accumulation angle corresponding to the first order the n-th sub-aperture,For radar platform to the initial subimage grid of the first order n-thRound trip distance oblique distance；

Second step, circular recursion sub-aperture merges and subimage generates；

When pth level processes, p=1 ..., P, every-1 grade of sub-aperture of I pth is merged into a pth level sub-aperture；For pth Level q-th sub-aperture, q=1,2 ..., I^P-p, firstly generate pth level q-th subimage gridWherein grid initial point For pth level q-th sub-aperture center, pole spanFor the distance of grid initial point to any scene point (x, y, 0), polar angle For pole spanAnd the angle between the normal of sub-aperture center, it may be assumed that

$\left\{\begin{array}{c}{\mathrm{\ρ}}_q^p=\sqrt{{\[R_{xy}\cos \left({\mathrm{\φ}}_q^p\right)-x\]}^2+{\[R_{xy}\sin \left({\mathrm{\φ}}_q^p\right)-y\]}^2}\\ {\mathrm{\θ}}_q^p=\arccos \left(\frac{y-R_{xy}\sin \left({\mathrm{\φ}}_q^p\right)}{x-R_{xy}\cos \left({\mathrm{\φ}}_q^p\right)}\right),{\mathrm{\θ}}_q^p\∈\[0,\mathrm{\π}\]\end{array}\right.$

Wherein,For the angle variables that pth level q-th sub-aperture center is corresponding；And pth level q-th subimage grid The pole span sampling intervalWith the polar angle sampling intervalIt is respectively as follows:

$\left\{\begin{array}{c}{\mathrm{\Δ\ρ}}_q^p\≤c_0/2B\\ {\mathrm{\Δ\θ}}_q^p\≤c_0/f_c{d}_{Mq}^p\end{array}\right.$

Wherein,Length for pth level q-th sub-aperture；

Then ,-1 grade of subimage of I pth is interpolated into pth level q-th subimage gridLast coherent superposition Generation pth level q-th subimage:

$I_q^p({\mathrm{\ρ}}_q^p,{\mathrm{\θ}}_q^p)={\mathrm{\Σ}}_{t=1+(q-1)I}^{qI}{I}_t^{(q-1)}({\mathrm{\ρ}}_t^{q-1},{\mathrm{\θ}}_t^{q-1})$

Wherein,For pth level q-th subimage,For-1 grade of the t subimage of pth, t=1,2 ..., l₀I^P-(p-1),For in-1 grade of t of pth sub-image lattice with pth level q-th subimage gridCorresponding position Put；So circular recursion processes, until obtaining P level subimage result；K sub-circular arc pore size data carries out above-mentioned place respectively Reason, it is thus achieved that K P level subimage；

3rd step, full aperture merges and final image generates；

If distance samples interval delta x and azimuth sample interval delta y that are ultimately imaged result images grid are respectively as follows:

$\left\{\begin{array}{c}\mathrm{\Δ}x\≤{\mathrm{\ρ}}_x\\ \mathrm{\Δ}y\≤{\mathrm{\ρ}}_y\end{array}\right.$

Then, (x, y), last coherent superposition generates CSAR K P level subimage of second step gained to be interpolated into image lattice Image:

$I(x,y,0)={\mathrm{\Σ}}_{m=1}^K{I}_m^P({\mathrm{\ρ}}^P,{\mathrm{\θ}}^P)$

Wherein, I (x, y, 0) is full resolution CSAR image；For m-th sub-aperture image result, m=1,2 ..., N, (ρ^P,θ^P) it is in corresponding sub-aperture image lattice and to be ultimately imaged the position that grid (x, y, 0) is corresponding.

One of the present invention is applicable to circumferential synthetic aperture radar fast time-domain formation method, and it provides the benefit that:

Use sub-aperture treatment technology, keeping time-domain imaging method high-precision while, considerably reduce time domain The amount of calculation of image space method, thus improve the efficiency of imaging processing, and then achieve the quick high accuracy imaging processing of CSAR, obtain Obtain high-quality CSAR image.

Accompanying drawing explanation

Fig. 1 is the fast time-domain formation method schematic flow sheet of circumference SAR of the present invention.

Fig. 2 is the point target imaging results that the imaging of time domain BPA obtains.

Fig. 3 is the point target imaging results that the present invention obtains.

Fig. 4 is the radar platform movement locus in measured data admission.

Fig. 5 a～Fig. 5 e is the measured data imaging results that the imaging of time domain BPA obtains.

Fig. 6 a～Fig. 6 e is the measured data imaging results that the present invention obtains.

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is further explained.

Fig. 1 is the schematic flow sheet of circumference SAR fast time-domain formation method of the present invention；As it is shown in figure 1, whole flow process includes Three process step: the first step, sub-aperture divides and generates with initial subimage；Second step, circular recursion sub-aperture merges and son Image generates；3rd step, full aperture merges and final image generates.

Circumference SAR fast time-domain formation method of the present invention is verified by emulation experiment and measured data, theoretical point Analyse with the results show effectiveness of the invention.

In emulation experiment, the system emulation parameter in the present invention is as shown in table 1 below；

Table 1

Image scene is arranged and target arrangement is as follows: image scene size is 200m × 200m (distance × orientation), Being provided with 9 point targets in image scene altogether, wherein 1 point target is positioned at scene center, and other 8 point targets are distributed in one 8 directions of individual annulus, distance scene center is 180m.

Fig. 2 is the point target imaging results that the imaging of time domain BPA obtains；Wherein horizontal direction is azimuth direction (unit: rice), Vertical direction is range direction (unit: rice), the imaging processing result that middle figure is whole image scene in Fig. 2, and with two Rectangular broken line frame identifies two point targets being positioned at image scene center and the upper right corner respectively；Left figure in Fig. 2 and right figure difference For scene center point target and the enlarged drawing of non-scene center point target (knowledge of rectangular broken line collimation mark)；As shown in Figure 2, all of point Target all achieves good focusing, and therefore time domain BPA is capable of the accurately image process of circumference SAR；But, time domain BPA Amount of calculation is relatively big, thus reduces imaging efficiency.

Fig. 3 is the point target imaging results that the present invention obtains；Wherein horizontal direction is azimuth direction (unit: rice), vertically Direction is range direction (unit: rice), the imaging processing result that middle figure is whole image scene in Fig. 3, and with two rectangles Dotted line frame identifies two point targets being positioned at image scene center and the upper right corner respectively；Left figure and right figure in Fig. 3 are respectively field Scape central point target and the enlarged drawing of non-scene center point target (knowledge of rectangular broken line collimation mark)；From the figure 3, it may be seen that all of point target All achieving good focusing, and its focusing effect is with Fig. 2 closely, therefore the present invention also is able to realize the essence of circumference SAR Really imaging processing；Compared with time domain BPA, the present invention can greatly reduce amount of calculation, and under this simulated conditions, its imaging efficiency carries High about 12.2 times；Therefore the inventive method is the formation method of a kind of high-efficiency high-precision.

For the performance of qualitative assessment circumference of the present invention SAR fast time-domain formation method, calculate respectively in Fig. 2 and Fig. 3 Scene center point target and two-dimensional resolution (X-direction and the Y-axis side of non-scene center point target (knowledge of rectangular broken line collimation mark) To) and two-dimensional peak value secondary lobe ratio (X-direction and Y direction), point target focusing performance parameter comparison is as shown in table 2 below；

Table 2

The X-axis of scene center point target in Fig. 2 and the resolution of Y direction are respectively 0.098m and 0.099m, X-axis and The peak sidelobe ratio of Y direction respectively-9.127dB and-8.249dB, and the X-axis of the scene center point target in Fig. 3 and Y-axis The resolution in direction be respectively 0.106m and 0.105m, X-axis and Y direction peak sidelobe ratio be respectively-8.106dB and- 7.842dB；The non-X-axis of scene center point target and the resolution of Y direction in Fig. 2 are respectively 0.099m and 0.099m, X-axis It is respectively-8.093dB and-8.069dB with the peak sidelobe ratio of Y direction, and the X-axis of the non-scene center point target in Fig. 3 The peak sidelobe ratio being respectively 0.098m and 0.094m, X-axis and Y direction with the resolution of Y direction is respectively-8.379dB With-7.798dB；Contrast These parameters parameter can find: the focusing performance of the point target that the present invention obtains obtains with time domain BPA The focusing performance of point target is sufficiently close to.

In measured data processes, the present invention uses multipolarization CSAR data disclosed in USAF laboratory gotcha；The used signal of these data is X-band (9.6GHz), the linear FM signal of bandwidth 640MHz；Measured data is enrolled In radar platform movement locus as shown in Figure 4；Fig. 5 and Fig. 6 sets forth time domain BPA and the present invention is directed to scene size and be The imaging results of 100m × 100m (X-direction × Y direction)；During wherein Fig. 5 b, Fig. 5 c are respectively Fig. 5 a, rectangle frame a-quadrant is starved Target enlarged drawing and corresponding photo in kind, Fig. 5 d, Fig. 5 e are respectively the target enlarged drawing in rectangle frame B region in Fig. 5 a And its corresponding photo in kind, during wherein Fig. 6 b, Fig. 6 c are respectively Fig. 6 a rectangle frame a-quadrant starve target enlarged drawing and Corresponding photo in kind, Fig. 6 d, Fig. 6 e are respectively target enlarged drawing and its corresponding reality in rectangle frame B region in Fig. 6 a Thing photo, and by the imaging results of comparison diagram 5 and Fig. 6: the measured data result that the present invention obtains and time domain BPA The measured data result obtained is quite similar.

The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For Yuan, under the premise without departing from the principles of the invention, it is also possible to make some improvements and modifications, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (1)

1. it is applicable to a circumferential synthetic aperture radar fast time-domain formation method, including following process step:

The first step, sub-aperture divides and generates with initial subimage；

It is f that known CSAR launches signal center frequency_c, carrying a width of B, range resolution ratio is ρ_x, azimuth resolution is ρ_y；Assume flute Karr coordinate origin is image scene center, and in image scene, the position of arbitrary target P is r_P=(x_P,y_P,0)；Radar platform Moving in a circle about the z axis with speed V, slow its coordinate of moment time η is (R_xycos(φ),R_xysin(φ),z_M), R_xyAnd z_MRespectively For radius and the height of radar platform circular path, φ ∈ [0,2 π] is the angle variables of radar platform, and φ (η)=V η/R_xy； The initial position of radar platform is (R_xy,0,z_M)；If the baseband signal of radar emission is p (τ), then the CSAR echo letter received Number after quadrature demodulation it is:

S (τ, φ)=σ_P·p[τ-R(φ,r_P)/c₀]·exp[-j2πf_cR(φ,r_P)/c₀]

Wherein, τ is the slow time, σ_PFor the scattering coefficient of target P, c₀For the light velocity；R(φ,r_P) it is that radar platform arrives the double of target P Journey distance oblique distance, it may be assumed that

$R(\mathrm{\φ},r_P)=2\sqrt{{\left(R_{xy}cos\right(\mathrm{\φ})-x_P)}^2+{\left(R_{xy}sin\right(\mathrm{\φ})-y_P)}^2+z_M^2}$

After Range compress, CSAR echo-signal is:

s_rc(τ, φ)=σ_p·p_rc[B(τ-R(φ,r_P)/c₀)]·exp[-j2πf_cR(φ,r_P)/c₀]

Wherein, p_rc() is Range compress signal envelope；

If the real aperture sampling number of radar platform synthetic aperture is L, it is uniformly divided into K sub-circular arc pore size data, typically Take K/L_full≤ 1/8, then every cross-talk pore size data sampling number isCircular arc is determined according to factorization principle Optimal initial aperture length l of data₀, and sub-aperture factoring I；Then there is N=l₀×I^P, wherein P is decomposed class；

To the first order the n-th sub-aperture, n=1,2 ..., I^P, firstly generate the initial subimage grid of the first order n-th Wherein grid initial point is the first order the n-th sub-aperture center, pole spanFor grid initial point to any scene point (x, y, 0) Round trip oblique distance, polar angleFor pole spanAnd the angle between the normal of sub-aperture center, it may be assumed that

$\left\{\begin{array}{c}{\mathrm{\ρ}}_n^1=\sqrt{{\[R_{xy}cos\left({\mathrm{\φ}}_n^1\right)-x\]}^2+{\[R_{xy}sin\left({\mathrm{\φ}}_n^1\right)-y\]}^2}\\ {\mathrm{\θ}}_n^1=arctan\left(\frac{y-R_{xy}sin\left({\mathrm{\φ}}_n^1\right)}{x-R_{xy}\cos \left({\mathrm{\φ}}_n^1\right)}\right),{\mathrm{\θ}}_n^1\∈\[0,\mathrm{\π}\]\end{array}\right.$

Wherein,For the angle variables that the first order the n-th sub-aperture center is corresponding；And the initial subimage grid of the first order n-th The pole span sampling intervalWith the polar angle sampling intervalIt is respectively as follows:

$\left\{\begin{array}{c}\mathrm{\Δ}{\mathrm{\ρ}}_n^1\≤c_0/2B\\ \mathrm{\Δ}{\mathrm{\θ}}_n^1\≤c_0/f_c{d}_{Mn}^1\end{array}\right.$

Wherein,Length for the first order the n-th sub-aperture；

Then, by corresponding for the first order the n-th sub-aperture Range compress echo-signal rear orientation projection to the initial son of the first order n-th Image latticeThen coherent superposition generates the initial subimage of the first order n-th, it may be assumed that

$I_n^1({\mathrm{\ρ}}_n^1,{\mathrm{\θ}}_n^1)=\underset{{\mathrm{\φ}}_n^1-{\mathrm{\φ}}_{In}^1/2}{\overset{{\mathrm{\φ}}_n^1+{\mathrm{\φ}}_{In}^1/2}{\∫}}{s}_{rc}\left(R\right(\mathrm{\φ},{\mathrm{\ρ}}_n^1,{\mathrm{\θ}}_n^1)/c_0,\mathrm{\φ})\·\exp \[j2{\mathrm{\πf}}_{c}R(\mathrm{\φ},{\mathrm{\ρ}}_n^1,{\mathrm{\θ}}_n^1)/c_0\]d\mathrm{\φ}$

Wherein, s_rc() is Range compress echo-signal,For the accumulation angle corresponding to the first order the n-th sub-aperture,For radar platform to the initial subimage grid of the first order n-thRound trip distance oblique distance；

Second step, circular recursion sub-aperture merges and subimage generates；

When pth level processes, p=1 ..., P, every-1 grade of sub-aperture of I pth is merged into a pth level sub-aperture；For pth level Q sub-aperture, q=1,2 ..., I^P-p, firstly generate pth level q-th subimage gridWherein grid initial point is pth Level q-th sub-aperture center, pole spanFor the distance of grid initial point to any scene point (x, y, 0), polar angleFor pole spanAnd the angle between the normal of sub-aperture center, it may be assumed that

$\left\{\begin{array}{c}{\mathrm{\ρ}}_q^p=\sqrt{{\[R_{xy}cos\left({\mathrm{\φ}}_q^p\right)-x\]}^2+{\[R_{xy}sin\left({\mathrm{\φ}}_q^p\right)-y\]}^2}\\ {\mathrm{\θ}}_q^p=arccos\left(\frac{y-R_{xy}sin\left({\mathrm{\φ}}_q^p\right)}{x-R_{xy}\cos \left({\mathrm{\φ}}_q^p\right)}\right),{\mathrm{\θ}}_q^p\∈\[0,\mathrm{\π}\]\end{array}\right.$

Wherein,For the angle variables that pth level q-th sub-aperture center is corresponding；And the pole span of pth level q-th subimage grid Sampling intervalWith the polar angle sampling intervalIt is respectively as follows:

$\left\{\begin{array}{c}{\mathrm{\Δ\ρ}}_q^p\≤c_0/2B\\ {\mathrm{\Δ\θ}}_q^p\≤c_0/f_c{d}_{Mq}^p\end{array}\right.$

Wherein,Length for pth level q-th sub-aperture；

Then ,-1 grade of subimage of I pth is interpolated into pth level q-th subimage gridLast coherent superposition generates Pth level q-th subimage:

$I_q^p({\mathrm{\ρ}}_q^p,{\mathrm{\θ}}_q^p)={\mathrm{\Σ}}_{t=1+(q-1)I}^{qI}{I}_t^{(q-1)}({\mathrm{\ρ}}_t^{q-1},{\mathrm{\θ}}_t^{q-1})$

Wherein,For pth level q-th subimage,For-1 grade of the t subimage of pth, t=1,2 ..., l₀I^P-(p-1),For in-1 grade of t of pth sub-image lattice with pth level q-th subimage gridCorresponding position； So circular recursion processes, until obtaining P level subimage result；K sub-circular arc pore size data carries out above-mentioned process respectively, obtains Obtain K P level subimage；

3rd step, full aperture merges and final image generates；

If distance samples interval delta x and azimuth sample interval delta y that are ultimately imaged result images grid are respectively as follows:

$\left\{\begin{array}{c}\mathrm{\Δ}x\≤{\mathrm{\ρ}}_x\\ \mathrm{\Δ}y\≤{\mathrm{\ρ}}_y\end{array}\right.$

Then, (x, y), last coherent superposition generates CSAR figure K P level subimage of second step gained to be interpolated into image lattice Picture:

$I(x,y,0)={\mathrm{\Σ}}_{m=1}^K{I}_m^P({\mathrm{\ρ}}^P,{\mathrm{\θ}}^P)$

Wherein, I (x, y, 0) is full resolution CSAR image；For m-th sub-aperture image result, m=1,2 ..., N, (ρ^P, θ^P) it is in corresponding sub-aperture image lattice and to be ultimately imaged the position that grid (x, y, 0) is corresponding.