CN103235304B - SAR (synthetic aperture radar) geometric correction method for modifying error equivalent RD (range-Doppler) model - Google Patents

Abstract

The invention provides an SAR (synthetic aperture radar) geometric correction method for modifying an error equivalent RD (range-Doppler) model. The SAR geometric correction method includes firstly, creating range-Doppler equations on the basis of modifying for the error equivalent RD model; secondly, performing primary Tailor series expansion for the equations obtained in the first step to obtain an error equation; thirdly, solving the error equation obtained in the second step by a least square process; and fourthly, geometrically positioning each pixel by the modified range-Doppler equations after the error equation is solved so as to geometrically correct SAR. The SAR geometric correction method has the advantages that required control points are few, the requirement on the uniform distribution character of the control points is low, and an excellent result can be obtained by a conventional numerical solution process without iteration.

Description

A kind of SAR geometric correction method based on the correction of error equivalence RD model

Technical field

The present invention is a kind of SAR geometric correction method based on the correction of error equivalence RD model, relates to synthetic aperture radar (SAR) signal process field, is specifically related to diameter radar image geometry correction process field.

Background technology

The geometric correction of imagery is the important step of satellite-borne SAR data processing, only has by geometry correction, by each pixel of SAR image, gives geographical location information, and SAR image could really become the carrier of geospatial information, supports follow-up application.The precision of the SAR geometric correction of imagery has vital impact to the performance of SAR image applications benefit.SAR geometry correction can be divided into conventionally without control proofreaies and correct (claiming again system-level geometry correction) and has control to proofread and correct two kinds.Wherein system-level geometry correction refers to based on track or flight path measurement result, SAR systematic parameter and imaging processing parameter SAR image is carried out to geometry correction, yet be limited to orbit measurement precision, SAR system time precision etc., SAR image position accuracy after system-level geometry correction cannot meet the demand of application sometimes, especially in the current system development level of China be not also very high in the situation that, this phenomenon is more outstanding.For this reason, conventionally need to utilize ground control point, be also the point of geographic position Accurate Calibration, has control to proofread and correct, and improves SAR image geometry positioning precision.

The method that has control to proofread and correct has the method based on multinomial model, the method based on in-line model [Konecny G, Schuhr W.Reliability of radar image data.Proceedings of16 _thiSPRS Congress, Kyoto, 1998,1～10.], and the distance-Doppler based on SAR image-forming principle (RD) model method etc.Why wherein the method coincidence imaging based on RD model is several has best precision in principle, so becomes the prefered method in current SAR processing.In prior art, the control bearing calibration that has based on RD model generally completes geometric accurate correction [You Hongjian by the model trajectory of refining, pay a kind of jade, < < diameter radar image is precisely processed > >, Beijing: Science Press, 2011, ISBN987-7-03-031168-9], the reason equivalence that is about to positioning error is summed up as by orbital position, speed and has error and cause, conventionally uses the initial position ([X of SAR antenna ₀, Y ₀, Z ₀] ^t), speed ([V _x, V _y, V _z] ^t) and acceleration ([a _x, a _y, a _z] ^t) satellite orbit or airborne flight path are carried out to modeling, and set up Range-Doppler equations based on reference mark, equation is as follows

Range equation: $R_{\mathrm{near}}+N_i\mathrm{\&delta;r}=\sqrt{{(X_{\mathrm{si}}-x_i)}^2+{(Y_{\mathrm{si}}-y_i)}^2+{(Z_{\mathrm{si}}-z_i)}^2}$

Doppler equation: $f_d=-\frac{2}{\mathrm{\&lambda;}}\frac{V_{\mathrm{sxi}}(X_{\mathrm{si}}-x_i)+V_{\mathrm{syi}}(Y_{\mathrm{si}}-y_i)+V_{\mathrm{szi}}(Z_{\mathrm{si}}-z_i)}{R_{\mathrm{near}}+N_i\mathrm{\&delta;r}}$

R wherein _nearpresentation video distance is to oblique distance corresponding to initial pixel, i.e. low coverage; δ r is that the distance of image is to pixel separation; λ is wavelength; I=1 ..., K is for controlling period, and K is reference mark sum; N _ibe _ithe distance at individual reference mark is to pixel number; [x _i, y _i, z _i] ^tit is the three-dimensional location coordinates at i reference mark; f _dthe doppler centroid adopting for imaging processing; All the other parameters are as follows,

$\left\{\begin{array}{c}{X}_{\mathrm{si}}=X_0+V_x(t_i-t_0)+\frac{1}{2}{a}_x{(t_i-t_0)}^2\\ Y_{\mathrm{si}}=Y_0+V_y(t_i-t_0)+\frac{1}{2}{a}_y{(t_i-t_0)}^2\\ Z_{\mathrm{si}}=Z_0+V_z(t_i-t_0)+\frac{1}{2}{a}_z{(t_i-t_0)}^2\\ V_{\mathrm{sxi}}=V_x=a_x(t_i-t_0)\\ V_{\mathrm{syi}}=V_y+a_y(t_i-t_0)\\ V_{\mathrm{szi}}=V_z+a_z(t_i-t_0)\end{array}\right.$

[X ₀, Y ₀, Z ₀] ^tfor reference moment t ₀time SAR aerial position, t _ifor orientation time corresponding to reference mark i.

Based on above-mentioned equation, the measured value of existing track or flight path of take is initial value, by Equation Iterative, solves to obtain [X ₀, Y ₀, Z ₀, V _x, V _y, V _z, a _x, a _y, a _zthe modified value of these 12 parameters, then utilizes revised track to reorientate SAR image, to improve the positioning precision of SAR image.Although technique scheme meets SAR imaging mechanism from location model, and is all in fact also a kind of equivalence in fact owing to orbital position velocity error by positioning error.In reality, due to the existence of system time error, propagation in atmosphere delay error etc., the low coverage R in Range-Doppler equations _near, orientation time t _ideng also having error.

Therefore say, the track correction model of prior art scheme is also a kind of equivalent model for SAR system positioning error source.There is following several shortcoming in this error equivalent model:

1) required reference mark is more and require to distribute more even.Because 2 equations can be set up in a reference mark, solving 12 parameters needs 6 reference mark theoretically.Yet, in reality, above-mentioned equation often takes on morbit forms, especially in satellite-borne SAR, because satellite is distant from imaging region, reach the even thousands of kilometers of hundreds of, on ground, scope is relatively limited for a scape image, conventionally tens kilometers of left and right, therefore there is very strong linear dependence in the error equation at each reference mark, and equation presents obvious morbid state.So above-mentioned equation solution is very high to the requirement at reference mark, require on the one hand that reference mark is more and reference mark self error is less; On the other hand, require reference mark to be distributed in scene more uniformly.Engineering practice shows, conventionally needs ten above equally distributed reference mark to reach comparatively desirable positioning result.

2) solution efficiency of ill-condition equation is lower, and the situation that may exist iteration not restrain.As previously mentioned, under SAR leaves the theatre the situation of scape (as satellite-borne SAR) far away, the equation of prior art scheme often presents very serious morbid state, in order to solve the Solve problems of ill-condition equation, people have proposed to estimate [Wang Xinzhou such as ridge estimation, Principal Component Estimation, spectrum correction, Liu Ding tenth of the twelve Earthly Branches. the iterative solution method of normal equation in least-squares estimation. Hubei ethnic university (natural science edition), 2002, the method of estimation such as 20 (3): 1～4], wherein, spectrum correction method of estimation is better to process a kind of alternative manner that satellite-borne SAR ill-condition equation solves.Yet on the one hand, iteration can cause the decrease in efficiency solving, on the other hand, even still may there is the situation that iteration does not restrain in the reasonable method for solving such as spectrum correction.

In a word, the robustness of prior art scheme, robustness need to improve, and to controlling, count and equally distributed dependence also needs further reduction.

Summary of the invention

For the shortcoming of prior art scheme, the invention provides a kind of SAR geometric correction method based on the correction of error equivalence RD model, only need reference mark seldom, and to reference mark to be uniformly distributed characteristic requirements not high; And adopt conventional method of value solving can obtain good result, without iteration.

Technical scheme of the present invention is as follows:

Be somebody's turn to do the SAR geometric correction method based on the correction of error equivalence RD model, comprise the following steps:

The first step: set up the Range-Doppler equations based on the correction of error equivalence RD model, as follows:

Range equation: $F_{1i}(\mathrm{\&Delta;R},p)=R_{\mathrm{near}}+\mathrm{\&Delta;R}+p{N}_i+N_i\mathrm{\&delta;r}-\sqrt{{(X_{\mathrm{si}}-x_i)}^2+{(Y_{\mathrm{si}}-y_i)}^2+{(Z_{\mathrm{si}}-z_i)}^2}=0;$

Doppler equation: $F_{2i}(\mathrm{\&Delta;R},p,\mathrm{\&Delta;}{f}_d,q)=f_d+\mathrm{\&Delta;}{f}_d+q{M}_i+\frac{2}{\mathrm{\&lambda;}}+\frac{V_{\mathrm{sxi}}(X_{\mathrm{si}}-x_i)+V_{\mathrm{syi}}(Y_{\mathrm{si}}-y_i)+V_{\mathrm{szi}}(Z_{\mathrm{si}}-z_i)}{R_{\mathrm{near}}+\mathrm{\&Delta;R}+p{N}_i+N_i\mathrm{\&delta;}r}=0;$ R wherein _nearpresentation video distance is to oblique distance corresponding to initial pixel, i.e. low coverage; δ r is that the distance of image is to pixel separation; λ is wavelength; I=1 ..., K is for controlling period, and K is reference mark sum; N _ibe that the distance at i reference mark is to pixel number; M _ithat the orientation at i reference mark is to pixel number; [x _i, y _i, z _i] ^tit is the three-dimensional location coordinates at i reference mark; f _dthe doppler centroid adopting for imaging processing; [X _si, Y _si, Z _si] ^tthe Doppler frequency causing for SAR satellite and i reference mark relative displacement is f _dtime, the position vector of satellite; [V _sxi, V _syi, V _szi] ^tthe Doppler frequency causing for SAR satellite and i reference mark relative displacement is f _dtime, the relative velocity vector of satellite and target; Δ R, p, Δ f _d, q is four error equivalent model parameters undetermined; Claim Δ R+pN herein _ifor range correction, Δ R and p are distance model corrected parameter; Claim Δ f _d+ qM _ifor Doppler's correction, Δ f _dwith q be Doppler's model corrected parameter;

Second step: the equation obtaining in the first step is carried out to Taylor series one-level and launch to obtain error equation;

The 3rd step: adopt the method for least square to solve the error equation that second step obtains;

The 4th step: try to achieve after the solution of error equation, adopt revised Range-Doppler equations to carry out geometry location to each pixel, realized the geometry correction of SAR.

Wherein the range correction described in (1) step adopts wherein, L _pfor the exponent number of range correction with pixel distance change in location, L _gfor the exponent number of range correction with the variation of pixel position of orientation, for N _il power, for M _il power, p _land g _lfor undetermined parameter, this formula show range correction be distance to the polynomial function of orientation to position; Or/and doppler centroid correction adopts for the exponent number of Doppler's correction with pixel distance change in location, L _hfor the exponent number of Doppler's correction with the variation of pixel position of orientation, for N _il power, for M _il power, q _land h _lfor undetermined parameter, this formula show centre frequency correction model for distance to the polynomial function of orientation to position.

Wherein the range correction described in (1) step adopts centre frequency correction adopts x wherein _ifor with apart from pixel number N _ilinear variable, y _ifor with orientation to pixel number M _ilinear variable.

Beneficial effect of the present invention:

1, the present invention only needs reference mark seldom (while adopting two parameters, only needing in theory 1 reference mark), and to reference mark to be uniformly distributed characteristic requirements not high; Adopt conventional method of value solving can obtain good result simultaneously, without iteration, improved operation efficiency.

2, the present invention has set up the RD equation of error equivalence correction model, introduces the model corrected parameter of range correction and the two class equivalences of doppler centroid correction, to improve geometric positioning accuracy.

Accompanying drawing explanation

A kind of SAR geometric correction method techniqueflow chart based on the correction of error equivalence RD model of Fig. 1.

Embodiment

Below in conjunction with accompanying drawing, the invention will be described further.

As shown in Figure 1, the SAR geometric correction method based on the correction of error equivalence RD model of the present invention, comprises the following steps:

The first step: set up the Range-Doppler equations based on the correction of error equivalence RD model, as follows:

Range equation: $F_{1i}(\mathrm{\&Delta;R},p)=R_{\mathrm{near}}+\mathrm{\&Delta;R}+p{N}_i+N_i\mathrm{\&delta;r}-\sqrt{{(X_{\mathrm{si}}-x_i)}^2+{(Y_{\mathrm{si}}-y_i)}^2+{(Z_{\mathrm{si}}-z_i)}^2}=0;$

Doppler equation: $F_{2i}(\mathrm{\&Delta;R},p,\mathrm{\&Delta;}{f}_d,q)=f_d+\mathrm{\&Delta;}{f}_d+q{M}_i+\frac{2}{\mathrm{\&lambda;}}+\frac{V_{\mathrm{sxi}}(X_{\mathrm{si}}-x_i)+V_{\mathrm{syi}}(Y_{\mathrm{si}}-y_i)+V_{\mathrm{szi}}(Z_{\mathrm{si}}-z_i)}{R_{\mathrm{near}}+\mathrm{\&Delta;R}+p{N}_i+N_i\mathrm{\&delta;}r}=0;$ R wherein _nearpresentation video distance is to oblique distance corresponding to initial pixel, i.e. low coverage; δ r is that the distance of image is to pixel separation; λ is wavelength; I=1 ..., K is for controlling period, and K is reference mark sum; N _ibe that the distance at i reference mark is to pixel number; M _ithat the orientation at i reference mark is to pixel number; [x _i, y _i, z _i] ^tit is the three-dimensional location coordinates at i reference mark; f _dthe doppler centroid adopting for imaging processing; [X _si, Y _si, Z _si] ^tthe Doppler frequency causing for SAR satellite and i reference mark relative displacement is f _dtime, the position vector of satellite; [V _sxi, V _syi, V _szi] ^tthe Doppler frequency causing for SAR satellite and i reference mark relative displacement is f _dtime, the relative velocity vector of satellite and target; Δ R, p, Δ f _d, q is four error equivalent model parameters undetermined.Claim Δ R+pN herein _ifor range correction, Δ R and p are distance model corrected parameter; Claim Δ f _d+ qM _ifor Doppler's correction, Δ f _dwith q be Doppler's model corrected parameter;

Second step: above-mentioned equation is carried out to the expansion of Taylor series one-level, obtain following error equation:

$\left[\begin{array}{cccc}\frac{\&PartialD;F_{11}}{\&PartialD;\mathrm{\&Delta;R}}& \frac{\&PartialD;F_{11}}{\&PartialD;p}& 0& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ \frac{\&PartialD;F_{1K}}{\&PartialD;\mathrm{\&Delta;R}}& \frac{\&PartialD;F_{1K}}{\&PartialD;p}& 0& 0\\ \frac{\&PartialD;F_{21}}{\&PartialD;\mathrm{\&Delta;R}}& \frac{\&PartialD;F_{21}}{\&PartialD;p}& \frac{\&PartialD;F_{21}}{\&PartialD;\mathrm{\&Delta;}{f}_d}& \frac{\&PartialD;F_{21}}{\&PartialD;q}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ \frac{\&PartialD;F_{2K}}{\&PartialD;\mathrm{\&Delta;R}}& \frac{\&PartialD;F_{2K}}{\&PartialD;p}& \frac{\&PartialD;F_{2K}}{\&PartialD;\mathrm{\&Delta;}{f}_d}& \frac{\&PartialD;F_{2K}}{\&PartialD;q}\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;R}\\ p\\ \mathrm{\&Delta;}{f}_d\\ q\end{array}\right]=\left[\begin{array}{c}-F_{11}\left(\mathrm{0,0}\right)\\ .\\ .\\ .\\ -F_{1K}\left(\mathrm{0,0}\right)\\ -F_{21}\left(\mathrm{0,0,0,0}\right)\\ .\\ .\\ .\\ -F_{2K}\left(\mathrm{0,0,0,0}\right)\end{array}\right]$

Remember that above-mentioned equation is AX=Y, wherein

$\left\{\begin{array}{c}\frac{\&PartialD;F_{1i}}{\&PartialD;\mathrm{\&Delta;R}}=1\\ \frac{\&PartialD;F_{1i}}{\&PartialD;p}=N_i\\ \frac{\&PartialD;F_{2i}}{\&PartialD;\mathrm{\&Delta;R}}=\frac{2}{\mathrm{\&lambda;}}\frac{(-1)[V_{\mathrm{sxi}}(X_{\mathrm{si}}-x_i)+V_{\mathrm{syi}}(Y_{\mathrm{si}}-y_i)+V_{\mathrm{szi}}(Z_{\mathrm{si}}-z_i)]}{{(R_{\mathrm{near}}+\mathrm{\&Delta;R}+p{N}_i+N_i\mathrm{\&delta;r})}^2}{|}_{\mathrm{\&Delta;R}=0,p=0}\\ \frac{\&PartialD;F_{2i}}{\&PartialD;p}=\frac{2}{\mathrm{\&lambda;}}\frac{(-N_i)[V_{\mathrm{sxi}}(X_{\mathrm{si}}-x_i)+V_{\mathrm{syi}}(Y_{\mathrm{si}}-y_i)+V_{\mathrm{szi}}(Z_{\mathrm{si}}-z_i)]}{{(R_{\mathrm{near}}+\mathrm{\&Delta;R}+p{N}_i+N_i\mathrm{\&delta;r})}^2}{|}_{\mathrm{\&Delta;R}=0,p=0}\\ \frac{\&PartialD;F_{2i}}{\&PartialD;\mathrm{\&Delta;}{f}_d}=1\\ \frac{\&PartialD;F_{2i}}{\&PartialD;\mathrm{\&Delta;q}}=M_i\end{array}\right.$

, for K point, have 2K equation, solve 4 positional numbers, theoretical minimum only needs 2 reference mark.

The 3rd step: adopt the method for least square to solve above-mentioned equation, have X=(A ^ta) _-1a ^ty, wherein subscript " ^t" expression transposition, " ^-1" represent to invert.A ^ta is full rank, and usual conditions number is less.

The 4th step: try to achieve after above-mentioned parameter, according to equation below, each pixel is carried out to geometry location, it is identical that Position-Solving method and conventional geometric are proofreaied and correct Position-Solving method:

$\left\{\begin{array}{c}{R}_{\mathrm{near}}+\mathrm{\&Delta;R}+p{N}_j+N_j\mathrm{\&delta;r}=\sqrt{{(X_{\mathrm{sj}}-x_t)}^2+{(Y_{\mathrm{sj}}-y_t)}^2+{(Z_{\mathrm{sj}}-z_t)}^2}\\ f_d+\mathrm{\&Delta;}{f}_d+q{M}_j=-\frac{2}{\mathrm{\&lambda;}}\frac{V_{\mathrm{sxj}}(X_{\mathrm{sj}}-x_t)+V_{\mathrm{syj}}(Y_{\mathrm{sj}}-y_t)+V_{\mathrm{szj}}(Z_{\mathrm{sj}}-z_t)}{R_{\mathrm{near}}+\mathrm{\&Delta;R}+p{N}_j=N_j\mathrm{\&delta;r}}\\ \frac{x_t^2+y_t^2}{{(R_e+h_t)}^2}+\frac{z_t^2}{R_{\mathrm{pt}}^2}=1,R_{\mathrm{Pt}}=(1-f)(R_e+h_t)\end{array}\right.$

[N wherein _j, M _j] be distance to, orientation to pixel number, (x _t, y _t, z _t) ^tfor target location to be asked, h _tfor target place elevation; R _efor earth model equatorial radius, f is the earth model ellipticity factor, under WGS84 earth model, and R _efor 6378137m, f is about 0.003352.

It should be noted that, in actual treatment, can adopt as required 2 error parameters (Δ R, Δ f _d), or adopt following more parameter: distance correction model: l wherein _pexponent number for distance correction model.Centre frequency correction model: l wherein _qcentered by the exponent number of frequency correction model.Determining of model order determined according to the positioning error distribution situation without under control condition conventionally, if positioning error is more consistent, i.e. distortion is very little, adopts 2 error parameters to revise; As positioning error present along distance to or/and orientation to variation, according to situation of change, adopt suitable higher-order revision model.

As distance correction model parameter adopts be distance correction model for distance to the polynomial function of orientation to position, or/and doppler centroid correction model parameter adopts be centre frequency correction model for distance to the polynomial function of orientation to position, within also belonging to category of the present invention.

As distance correction model parameter adopts centre frequency correction model adopts x wherein _ifor with apart from pixel number N _ilinear variable (as oblique distance etc.), y _ifor with orientation to pixel number M _ilinear variable (as orientation to distance etc.), within also belonging to category of the present invention.

Processing example below by real data is verified advantage of the present invention.We have surveyed 22 points in Beijing area with differential GPS, provide the positioning error after the Beijing area 2 width satellite-borne SAR image geometry corrections that utilize these points to do reference mark (GCP) or checkpoint below.Table 1 is the correction result of prior art scheme, visible, adopts prior art scheme, the conditional number of error equation solution matrix is very large, therefore, and when GCP point skewness, the zone location error that lacks reference mark obviously increases, and finally causes in the overall position of image error very large.Table 2 has provided geometry correction result of the present invention, and first, because this two width image is before geometry correction, the variance of its site error is just smaller, therefore, selects the single order form of range correction and Doppler's correction, only adopts Δ R and Δ f _dthe model modification method of these two undetermined parameters is revised, and from proofreading and correct result, the solution matrix conditional number of error equation approaches 1, and therefore, equation solution is non-morbid state, visible, and the method is sane; And its correction accuracy and prior art scheme reference mark are more and the result while being evenly distributed is suitable, even better, verified the superiority of the inventive method.

Table 1 prior art scheme geometry correction result

Table 2 the inventive method geometry correction result (adopting 2 parameter correction models)

Claims (3)

1. the SAR geometric correction method based on the correction of error equivalence RD model, is characterized in that, comprises the following steps:

The first step: set up the Range-Doppler equations based on the correction of error equivalence RD model, as follows:

Range equation: $F_{1i}(\mathrm{\&Delta;R},p)=R_{\mathrm{near}}+\mathrm{\&Delta;R}+p{N}_i+N_i\mathrm{\&delta;r}-\sqrt{{(X_{\mathrm{si}}-x_i)}^2+{(Y_{\mathrm{si}}-y_i)}^2+{(Z_{\mathrm{si}}-z_i)}^2}=0;$

Doppler equation: $F_{2i}(\mathrm{\&Delta;R},p,\mathrm{\&Delta;}{f}_d,q)=f_d+\mathrm{\&Delta;}{f}_d+q{M}_i+\frac{2}{\mathrm{\&lambda;}}\frac{V_{\mathrm{sxi}}(X_{\mathrm{si}}-x_i)+V_{\mathrm{syi}}(Y_{\mathrm{si}}-y_i)+V_{\mathrm{szi}}(Z_{\mathrm{si}}-z_i)}{R_{\mathrm{near}}+\mathrm{\&Delta;R}+p{N}_i+N_i\mathrm{\&delta;r}}=0;$

R wherein _nearpresentation video distance is to oblique distance corresponding to initial pixel, i.e. low coverage; δ r is that the distance of image is to pixel separation; λ is wavelength; I=1 ..., K is for controlling period, and K is reference mark sum; N _ibe that the distance at i reference mark is to pixel number; M _ithat the orientation at i reference mark is to pixel number; [x _i, y _i, z _i] ^tit is the three-dimensional location coordinates at i reference mark; f _dthe doppler centroid adopting for imaging processing; [X _si, Y _si, Z _si] ^tthe Doppler frequency causing for SAR satellite and i reference mark relative displacement is f _dtime, the position vector of satellite; [V _sxi, V _syi, V _szi] ^tthe Doppler frequency causing for SAR satellite and i reference mark relative displacement is f _dtime, the relative velocity vector of satellite and target; Δ R, p, Δ f _d, q is four error equivalent model parameters undetermined; Claim Δ R+pN herein _ifor range correction, Δ R and p are distance model corrected parameter; Claim Δ f _d+ qM _ifor doppler centroid correction, Δ f _dwith q be Doppler's model corrected parameter;

Second step: the equation obtaining in the first step is carried out to Taylor series one-level and launch to obtain error equation;

The 3rd step: adopt the method for least square to solve the error equation that second step obtains;

The 4th step: try to achieve after the solution of error equation, adopt revised Range-Doppler equations to carry out geometry location to each pixel, realized the geometry correction of SAR.

2. the SAR geometric correction method based on the correction of error equivalence RD model as claimed in claim 1, is characterized in that, wherein the range correction described in the first step adopts wherein, L _pfor the exponent number of range correction with pixel distance change in location, L _gfor the exponent number that range correction changes with pixel position of orientation, p _land g _lfor undetermined parameter, this formula show range correction be distance to the polynomial function of orientation to position; Or/and doppler centroid correction adopts l _qfor the exponent number of doppler centroid correction with pixel distance change in location, L _hfor the exponent number that doppler centroid correction changes with pixel position of orientation, q _land h _lfor undetermined parameter, this formula show Doppler's model for distance to the polynomial function of orientation to position, described in for N _il power, for M _il power.

3. the SAR geometric correction method based on the correction of error equivalence RD model as claimed in claim 1, is characterized in that, wherein the range correction described in the first step adopts doppler centroid correction adopts x wherein _ifor with distance to pixel number N _ilinear variable, y _ifor with orientation to pixel number M _ilinear variable.