CN102466799B - Method for simulating interference SAR (Synthetic Aperture Radar) echo data based on POS (Posture) motion data - Google Patents

Abstract

The invention discloses a method for simulating interference SAR (Synthetic Aperture Radar) echo data based on POS (Posture) motion data, relating to an information acquiring and processing technology. POS data contain position information and posture information of an airborne platform of synthetic aperture radar (SAR). By using the method, airborne interference SAR original echo simulation based on actual motion data is realized through establishing a transformational relation between a POS coordinate system and a target scene coordinate system and fusing the motion information of the airborne platform into interference synthetic aperture radar echo calculation. The method comprises the following steps of: firstly, calculating the coordinate of a double-antenna phase center under a scene coordinate system by utilizing coordinate transformation; secondly, generating a correlation complex backscattering coefficient pair on the basis of real SAR image data; and thirdly, introducing DEM (Digital Elevation Model) topographic information, calculating two paths of original echo data according to an echo signal model, imaging and interfering to obtain an SAR image and an interference fringe.

Description

Interference SAR echo data simulation method based on POS motion data

Technical Field

The invention relates to the technical field of information acquisition and processing, in particular to an interference SAR data simulation method based on POS (POSition and Orientation System) motion data.

Background

The interferometric Synthetic Aperture Radar (SAR) data simulation has important significance for researching SAR imaging algorithm verification, SAR image processing, interference processing methods and the like. The existing interference SAR echo data simulation technology can be divided into a time domain method and a frequency domain method, the frequency domain method has the biggest advantage of high calculation speed, and compared with a time domain algorithm, the interference SAR echo data simulation technology has the defects that a motion error model is difficult to introduce, the phase calculation precision is low, and for interference SAR echo simulation, the phase precision determines the precision of interference SAR elevation measurement, so that the method adopting the frequency domain usually does not meet the simulation requirement.

In the interferometric SAR data simulation considering motion errors, a commonly used method at present is to introduce an artificially established idealized motion error model into echo calculation, such as a single-frequency sinusoidal model. However, in practice, the motion trajectory of the platform is affected by various factors, the motion trajectory is complex and variable, the motion error is not simple single-frequency jitter, and usually there are motion trajectory offsets of multiple frequencies. Therefore, the introduction of an idealized motion error model established artificially still cannot realize airborne interference SAR original echo simulation based on actual motion data.

Disclosure of Invention

The invention aims to solve the problems in the prior art, provides an interference SAR data simulation method based on POS motion data, fuses the position and posture information of a carrier platform measured by a motion measurement system into interference SAR echo data simulation, and is an echo simulation method based on actual motion error data.

In order to achieve the purpose, the technical scheme of the invention is as follows:

a simulation method of interference SAR echo data based on POS motion data is characterized in that a conversion relation between a POS coordinate system and a target scene coordinate system is established, and motion errors of an airborne platform are fused into interference Synthetic Aperture Radar (SAR) echo calculation, so that the simulation of airborne interference SAR original echoes based on actual motion data is realized; the method comprises the following steps: firstly, solving the coordinates of a dual-antenna phase center in a scene coordinate system by utilizing coordinate transformation; secondly, generating a correlation complex backscattering coefficient pair based on the real SAR image data; and thirdly, introducing DEM topographic information, calculating two paths of original echo data according to an echo signal model, and obtaining an SAR image and interference fringes through imaging and interference processing.

The first step of the interference SAR echo data simulation method based on POS motion data is that position information and attitude information are introduced into the calculation of an antenna phase center coordinate through three times of coordinate system rotation, and the method comprises the following steps:

a) converting the POS center geocentric rotating coordinate system actually containing the position information into a geodetic horizontal plane coordinate system;

b) then converting the coordinate system of the ground horizontal plane into a scene coordinate system;

c) and calculating coordinates of the phase center of the antenna in a platform coordinate system according to the attitude information of the carrier, converting the coordinates into a scene coordinate system to obtain coordinates of the double antennas in the scene coordinate system, and establishing a space geometric relationship between the radar and the target, thereby realizing the introduction of position information and attitude information motion errors in echo calculation.

The interference SAR echo data simulation method based on POS motion data comprises a second step of generating a correlation complex backscattering coefficient pair by utilizing real SAR image amplitude data, and comprises the following steps:

a) generating random phases which obey uniform distribution in the range of [ -pi ] by taking the SAR image amplitude as the backscattering coefficient amplitude of the main antenna;

b) on the basis of linear combination of a real part and an imaginary part of a backscattering coefficient of the main antenna, adding an independent normally distributed random number for controlling the correlation between the backscattering coefficients of the main antenna and the auxiliary antenna to generate an auxiliary antenna backscattering coefficient pair: real and imaginary parts.

The simulation method of the interference SAR echo data based on the POS motion data generates the real part and the imaginary part of the backscattering coefficient of the auxiliary antenna, and comprises the following steps:

taking the backscattering coefficient gamma of the main antenna₁Real part x of₁And imaginary part y₁Then x₁ y₁Obedience mean 0 and variance σ²Are normally distributed and independent of each other; the real and imaginary parts of the secondary antenna backscatter coefficients are then:

x₂＝a_xx₁+b_xy₁+c_xz

y₂＝a_yx₁+b_yy₁

a_x＝(2ρ-1)cos(ψ_ρ)

b_x＝(2ρ-1)sin(ψ_ρ)

wherein, a_y＝-sin(ψ_ρ)

b_y＝cos(ψ_ρ)

$c_x=2\sqrt{\mathrm{\ρ}(1-\mathrm{\ρ})}$

Where p, ψ_ρRespectively the amplitude and phase of the correlation coefficient of the backscattering coefficient, z is the variance σ of 0 obeying the mean value²Is normally distributed with random number, and is related to x₁ y₁Are independent of each other.

The simulation method of the interference SAR echo data based on the POS motion data comprises the step of generating a real part x of a backscattering coefficient of an auxiliary antenna₂And imaginary part y₂The following three conditions are satisfied:

1)x₂、y₂obeying a mean value of 0 and a variance of σ²A normally distributed random variable of (a);

2)x₂、y₂the correlation coefficient between is 0;

3) back scattering coefficient x of main antenna₁+jy₁And the auxiliary antenna backscattering coefficient x₂+jy₂The correlation coefficient between is

J and e in the expression are an imaginary number unit and a natural constant respectively.

The third step of the simulation method for the interference SAR echo data based on the POS motion data is to generate an original echo signal by adopting a time domain echo signal model according to the space geometric model and the backscattering model of the radar and the target established in the first step and the second step; the time domain echo algorithm is based on the continuous pulse transmitted by the radar and generates an echo signal of each pulse along with the movement of the radar platform.

The third step of the interference SAR echo data simulation method based on POS motion data comprises the following steps:

a) for azimuth time t_sCalculating the slant distance R of the target scattering unit (i, j) in the beam irradiation region_ijAnd determining R_ijThe distance door m is located;

b) azimuth echo signal g to range gate m_aPlus the doppler phase contribution from point (i, j):

g_a＝g_a+σ_i，jw_aexp(-j4πR_ijλ), where λ is the wavelength, w_aIs the antenna pattern gain, σ_i，jIs the backscattering coefficient;

c) repeating the steps a and b, traversing all scattering points irradiated by the radar at the azimuth moment to obtain an azimuth moment t_sAzimuth echo signal g of all points_a；

d) G is prepared from_aConvolving with the distance emission signal to obtain an echo signal of a pulse, and traversing each azimuth moment to obtain the echo signal of the whole simulation scene.

e) Respectively calculating echo data of the double antennas according to the steps a) to d), then carrying out SAR imaging through a CS (Chirpscaling) algorithm, and obtaining interference fringes through motion error compensation.

The method realizes the original echo simulation of the airborne interferometric Synthetic Aperture Radar (SAR) based on actual motion data.

Drawings

FIG. 1 is a schematic diagram of a geometry simulation scheme based on POS data;

FIG. 2 is a flow chart of a time domain echo generation algorithm;

fig. 3 is a graph of primary and secondary antenna correlation backscattering coefficients, wherein:

FIG. 3a is a graph of the magnitude of the backscatter coefficient of a main antenna;

FIG. 3b is the magnitude of the secondary antenna backscatter coefficients produced according to the correlation generation principle;

FIG. 4 is a diagram of a target terrain (DEM) corresponding to a simulation scenario;

FIG. 5 is two-channel raw echo data, in which:

FIG. 5a is the simulated raw echo data of the main antenna;

FIG. 5b is secondary antenna echo data;

fig. 6 is a SAR image after processing echo data, wherein:

FIG. 6a is a graph of the amplitude of the SAR image of the main antenna after CS imaging processing;

FIG. 6b is a graph of the amplitude of the secondary antenna image obtained after processing;

fig. 7 shows an interference phase diagram obtained by simulation, wherein:

FIG. 7a is an ideal fringe pattern;

FIG. 7b shows interference fringes obtained by imaging simulation data without motion compensation;

FIG. 7c is an interference fringe pattern obtained after motion compensation;

FIG. 8 is a flow chart of simulation of interferometric SAR echo data based on POS motion data.

Detailed Description

The invention discloses an interference SAR data simulation method based on POS motion data, which fuses the position and attitude information of an airborne platform measured by a motion measurement system into interference SAR echo data simulation and is an echo simulation method based on actual motion error data. The method comprises the following concrete steps: 1) and calculating the position of the phase center of the double antennas under the condition of considering the motion offset and the attitude disturbance.

As shown in fig. 1, position information and attitude information can be introduced into the calculation of the antenna phase center coordinates through three coordinate system rotations.

First, several important coordinate system definitions will be explained. The earth center rotation coordinate system is defined as follows: the origin of coordinates is located at the center of the earth, the Z axis points to the earth rotation axis, the X axis points to the zero meridian, and the Y axis and the X and Z axes form a right-hand system; definition of geodetic horizontal plane coordinate system: the origin of the coordinate system observes the center of a scene of a target early, the X axis points to the geographical south direction, and the XY plane is the horizontal plane of the ground, so that the Y axis points to the east-righting direction, and the Z axis is vertical to the ground and faces upwards; scene coordinate system definition: the origin of the coordinate system observes the center of a scene of a target early, the X axis points to the ideal flight direction of the carrier platform, the XY plane is the ground horizontal plane, and the Z axis is vertical to the ground and faces upwards.

The conversion relation between the earth center rotating coordinate system and the earth horizontal plane coordinate system can be expressed as follows:

E_p＝A_pg(E_g-A_pg0)

$A_{\mathrm{pg}}=\left(\begin{array}{ccc}\cos (\mathrm{\π}/2-{\mathrm{\Φ}}_0)& 0& -\sin (\mathrm{\π}/2-{\mathrm{\Φ}}_0)\\ 0& 1& 0\\ \sin (\mathrm{\π}/2-{\mathrm{\Φ}}_0)& 0& \cos (\mathrm{\π}/2-{\mathrm{\Φ}}_0)\end{array}\right)\left(\begin{array}{ccc}\cos {\mathrm{\Λ}}_0& {\sin \mathrm{\Λ}}_0& 0\\ {-\sin \mathrm{\Λ}}_0& {\cos \mathrm{\Λ}}_0& 0\\ 0& 0& 1\end{array}\right)$

wherein E_g E_pRespectively a rotation coordinate system of the earth's center and a horizontal coordinate system of the earth, A_pg0The coordinate of the origin of the horizontal plane coordinate system of the earth is under the rotation coordinate system of the earth center. Phi₀And Λ₀The geodetic latitude and the geodetic longitude, respectively, of the origin of the coordinates of the geodetic horizontal coordinate system. The geodetic horizontal coordinate system and the scene coordinate system transformation relationship may be expressed as:

E_c＝A_cp.E_p

wherein $A_{\mathrm{cp}}=\left(\begin{array}{ccc}{\cos \mathrm{\θ}}_{\mathrm{pc}}& {\sin \mathrm{\θ}}_{\mathrm{pc}}& 0\\ {-\sin \mathrm{\θ}}_{\mathrm{pc}}& {\cos \mathrm{\θ}}_{\mathrm{pc}}& 0\\ 0& 0& 1\end{array}\right)$

Wherein E_cIs the coordinate in the scene coordinate system, theta_pcIs the included angle between the direction of the flying platform of the carrier and the south direction. Through the coordinate transformation, the coordinate E of the POS center scene coordinate system can be calculated_c0：

E_c0＝A_cpA_pg(E_g-A_pg0)

The attitude information causes the antenna support arm to flutter, thereby affecting the position of the dual antenna phase center. The coordinates of the dual antenna in the coordinate system of the POS platform can be expressed as:

E_pos1＝A_re.[0 -Bcosα/2 -Bsinα/2]^T

E_pos2＝A_re.[0 Bcosα/2 Bsinα/2]^T

wherein: $A_{\mathrm{re}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& {\cos \mathrm{\θ}}_r& {-\sin \mathrm{\θ}}_r\\ 0& {\sin \mathrm{\θ}}_r& {\cos \mathrm{\θ}}_r\end{array}\right]\left[\begin{array}{ccc}{\cos \mathrm{\θ}}_p& 0& {\sin \mathrm{\θ}}_p\\ 0& 1& 0\\ {-\sin \mathrm{\θ}}_p& 0& {\cos \mathrm{\θ}}_p\end{array}\right]\left[\begin{array}{ccc}{\cos \mathrm{\θ}}_y& {-\sin \mathrm{\θ}}_y& 0\\ {\sin \mathrm{\θ}}_y& {\cos \mathrm{\θ}}_y& 0\\ 0& 0& 1\end{array}\right]$

θ_r θ_p θ_yrespectively, three-axis attitude angle: roll angle, pitch angle and yaw angle, B is the base length, alpha is the base inclination angle, and POS is located at the center of the base. And then converting the coordinates of the platform coordinate system into a scene coordinate system:

E_c1＝E_pos1+E_c0

E_c2＝E_pos2+E_c0

and obtaining coordinates of a dual-antenna scene coordinate system, thereby establishing a spatial position relation between the radar and the target.

2) And generating a correlation complex backscattering coefficient pair by using the amplitude data of the real SAR image.

The backscattering coefficients include amplitude, which follows a sharp distribution, and phase, which follows a uniform distribution. However, two independent sets of uniformly distributed random phases cannot be generated directly and simply, and the two-channel backscatter coefficient phases are correlated. A method for generating a correlation backscattering coefficient is provided by combining actual SAR image amplitude data, and the method comprises the following steps:

a) and (3) generating random phases which obey uniform distribution among [ -pi ] by taking the SAR image amplitude as the backscattering coefficient amplitude of the main antenna.

b) A coherent secondary antenna backscatter coefficient generation scheme is provided. The basic idea is that an independent normally distributed random number is added on the basis of linear combination of a real part and an imaginary part of a backscattering coefficient of a main antenna to control the correlation between backscattering coefficients of the main antenna and an auxiliary antenna, and the generation steps are as follows:

taking the backscattering coefficient gamma of the main antenna₁Real part x of₁And imaginary part y₁Then x₁ y₁Obedience mean 0 and variance σ²Are normally distributed and independent of each other. Then we can construct the real and imaginary parts of the secondary antenna backscatter coefficients:

x₂＝a_xx₁+b_xy₁+c_xz

y₂＝a_yx₁+b_yy₁

a_x＝(2ρ-1)cos(ψ_ρ)

b_x＝(2ρ-1)sin(ψ_ρ)

wherein, a_y＝-sin(ψ_ρ)

b_y＝cos(ψ_ρ)

$c_x=2\sqrt{\mathrm{\ρ}(1-\mathrm{\ρ})}$

Where p, ψ_ρRespectively the amplitude and phase of the correlation coefficient of the backscattering coefficient, z is the variance σ of 0 obeying the mean value²Is normally distributed with random number, and is related to x₁ y₁Are independent of each other. The real part x of the backscattering coefficient of the auxiliary antenna generated by the above formula can be verified₂And imaginary part y₂The following three conditions are satisfied:

(1)x₂、y₂obeying a mean value of 0 and a variance of σ²Is normally distributed random variable.

(2)x₂、y₂The correlation coefficient between them is 0.

(3) Back scattering coefficient x of main antenna₁+jy₁And the auxiliary antenna backscattering coefficient x₂+jy₂The correlation coefficient between is

J and e in the expression are an imaginary number unit and a natural constant respectively.

3) And (4) introducing DEM information, and generating two paths of original echo signals according to an echo signal model.

And generating an original echo signal by adopting a time domain echo signal model according to the space geometric model and the backscattering model of the radar and the target which are established in the front. The basic idea of the time domain echo algorithm is to generate an echo signal of each pulse along with the motion of a radar platform on the basis of transmitting continuous pulses by a radar. The steps of the algorithm are as follows (see fig. 2):

a) for azimuth time t_sCalculating the slant distance R of the target scattering unit (i, j) in the beam irradiation region_ijAnd determining R_ijAt a distance gate m.

b) Azimuth echo signal g to range gate m_aPlus the doppler phase contribution from point (i, j):

g_a＝g_a+σ_i，jw_aexp(-j4πR_ijλ), where λ is the wavelength, w_aIs the antenna pattern gain, σ_i，jIs the backscattering coefficient.

c) And repeating the steps a and b, and traversing all scattering points irradiated by the radar at the azimuth moment. Obtaining the azimuth time t_sAzimuth echo signal g of all points_a。

d) G is prepared from_aConvolving with the distance emission signal to obtain an echo signal of a pulse, and traversing each azimuth moment to obtain the echo signal of the whole simulation scene.

e) Respectively calculating echo data of the double antennas according to the steps a) to d), then carrying out SAR imaging through a CS (Chirpscaling) algorithm, and obtaining interference fringes through motion error compensation.

In fig. 1, the position information (latitude, longitude, and altitude) included in the POS data is transformed into the scene coordinate system through the geocentric rotating coordinate system and the geodetic horizontal plane coordinate system to obtain the coordinate of the POS center in the scene coordinate system. Because the POS is positioned at the center of the base line supporting arm, the attitude information in the POS data can be fused, and the coordinates of the main and auxiliary antenna phase centers at the two ends of the base line under a scene coordinate system are solved.

FIG. 2 is a time domain echo algorithm flow, and the basic idea is to generate an echo signal of each pulse along with the motion of a radar platform on the basis that a radar transmits continuous pulses.

Fig. 3a is a graph of the magnitude of the backscattering coefficient of the main antenna, and fig. 3b is the magnitude of the backscattering coefficient of the auxiliary antenna generated according to the principle of correlation generation, and the backscattering coefficient of the main antenna and the auxiliary antenna corresponds to a correlation coefficient of 0.98.

FIG. 4 is elevation data of a simulated scene, where the terrain near the left side of the scene is relatively flat and the terrain on the right side is wavy.

Fig. 5a is the primary echo data of the primary antenna obtained by simulation, and fig. 5b is the echo data of the secondary antenna.

Fig. 6a is a graph of the amplitude of the SAR image of the main antenna after CS imaging processing, and fig. 6b is a graph of the amplitude of the SAR image of the auxiliary antenna obtained after processing, and the echo data is better focused.

Fig. 7a is an ideal fringe image, fig. 7b is an interference fringe image obtained by imaging simulation data without motion compensation, and fig. 7c is an interference fringe image obtained by motion compensation, which is consistent with an ideal fringe.

Fig. 8 is a flow of a simulation method for interfering SAR echo data based on POS motion data, which includes the steps of:

the interference SAR echo simulation scheme is divided into three parts, wherein the first part is to solve the coordinates of a dual-antenna phase center in a scene coordinate system by utilizing coordinate transformation; the second part is based on real SAR image data to generate correlation complex backscattering coefficient pairs; and the third part is to introduce DEM topographic information and calculate two paths of original echo data according to an echo signal model so as to obtain an SAR image and interference fringes through simulation.

Claims (7)

1. A simulation method of interference SAR echo data based on POS motion data is characterized in that: the method comprises the steps of fusing a motion error of an airborne platform into interferometric synthetic aperture radar echo calculation by establishing a conversion relation between a POS coordinate system and a target scene coordinate system so as to realize airborne interferometric SAR original echo simulation based on actual motion data; the method comprises the following steps: firstly, solving the coordinates of a dual-antenna phase center in a scene coordinate system by utilizing coordinate transformation; secondly, generating a correlation complex backscattering coefficient pair based on the real SAR image data; and thirdly, introducing DEM topographic information, calculating two paths of original echo data according to an echo signal model, and obtaining an SAR image and interference fringes through imaging and interference processing.

2. The method for simulating the interferometric SAR echo data based on the POS motion data according to claim 1, wherein the first step is to introduce the position information and the attitude information into the calculation of the phase center coordinates of the antenna through three times of coordinate system rotation, and comprises the following steps:

1) converting the POS center geocentric rotating coordinate system actually containing the position information into a geodetic horizontal plane coordinate system;

2) then converting the coordinate system of the ground horizontal plane into a scene coordinate system;

3) and calculating coordinates of the phase center of the antenna in a platform coordinate system according to the attitude information of the carrier, converting the coordinates into a scene coordinate system to obtain coordinates of the double antennas in the scene coordinate system, and establishing a space geometric relationship between the radar and the target, thereby realizing the introduction of position information and attitude information motion errors in echo calculation.

3. The method for simulating interference SAR echo data based on POS motion data as claimed in claim 1, wherein the second step is to generate a correlation complex backscattering coefficient pair by using real SAR image amplitude data, comprising the steps of:

a) generating random phases which obey uniform distribution in the range of [ -pi ] by taking the SAR image amplitude as the backscattering coefficient amplitude of the main antenna;

b) on the basis of linear combination of the real part and the imaginary part of the backscattering coefficient of the main antenna, an independent normally distributed random number is added to control the correlation between the backscattering coefficients of the main antenna and the auxiliary antenna and generate the real part and the imaginary part of the backscattering coefficient of the auxiliary antenna.

4. The method for simulating interferometric SAR echo data based on POS motion data as claimed in claim 3, wherein the real part and imaginary part of the backscattering coefficient of the auxiliary antenna are generated by the following steps:

taking the backscattering coefficient gamma of the main antenna₁Real part x of₁And imaginary part y₁Then x₁ y₁Obedience mean 0 and variance σ²Are normally distributed and independent of each other; the real and imaginary parts of the secondary antenna backscatter coefficients are then:

x₂＝a_xx₁+b_xy₁+c_xz

y₂＝a_yx₁+b_yy₁

wherein, $\begin{array}{c}{a}_x=(2\mathrm{\ρ}-1)\cos \left({\mathrm{\ψ}}_{\mathrm{\ρ}}\right)\\ b_x=(2\mathrm{\ρ}-1)\sin \left({\mathrm{\ψ}}_{\mathrm{\ρ}}\right)\\ a_y=-\sin \left({\mathrm{\ψ}}_{\mathrm{\ρ}}\right)\\ b_y=\cos \left({\mathrm{\ψ}}_{\mathrm{\ρ}}\right)\\ c_x=2\sqrt{\mathrm{\ρ}(1-\mathrm{\ρ})}\end{array}$

where p, ψ_ρRespectively the amplitude and phase of the correlation coefficient of the backscattering coefficient, z is the variance σ of 0 obeying the mean value²Is normally distributed with random number, and is related to x₁ y₁Are independent of each other.

5. The method of claim 4, wherein the generated real part x of the backscattering coefficient of the auxiliary antenna is used for simulating the interference SAR echo data based on the POS motion data₂And imaginary part y₂The following three conditions are satisfied:

1)x₂、y₂obeying a mean value of 0 and a variance of σ²A normally distributed random variable of (a);

2)x₂、y₂the correlation coefficient between is 0;

3) back scattering coefficient x of main antenna₁+jy₁And the auxiliary antenna backscattering coefficient x₂+jy₂The correlation coefficient between is

J and e in the expression are an imaginary number unit and a natural constant respectively.

6. The interference SAR echo data simulation method based on POS motion data as claimed in claim 1, wherein the third step is to generate original echo signals by adopting a time domain echo signal model according to the space geometric model and the backscattering model of the radar and the target established in the first step and the second step; the time domain echo algorithm is based on the continuous pulse transmitted by the radar and generates an echo signal of each pulse along with the movement of the radar platform.

7. The method for simulating interference SAR echo data based on POS movement data according to claim 1 or 6, wherein the third step comprises the following steps:

a) for azimuth time t_SCalculating the slant distance R of the target scattering unit (i, j) in the beam irradiation region_ijAnd determining R_ijThe distance door m is located;

b) azimuth echo signal g to range gate m_aPlus the doppler phase contribution from point (i, j):

g_a＝g_a+σ_i，jw_aexp(-j4πR_ijλ), where λ is the wavelength, w_aIs the antenna pattern gain, σ_i，jIs the backscattering coefficient;

c) repeating the steps a and b, traversing all scattering points irradiated by the radar at the azimuth moment to obtain an azimuth moment t_SAzimuth echo signal g of all points_a；

d) G is prepared from_aConvolving with the distance emission signal to obtain an echo signal of a pulse, and traversing each azimuth moment to obtain the echo signal of the whole simulation scene;

e) respectively calculating echo data of the double antennas according to the steps a) to d), then carrying out SAR imaging through a CS (Chirpscaling) algorithm, and obtaining interference fringes through motion error compensation.

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