CN103675813B - A Circular SAR Trajectory Reconstruction Method Based on Phase Gradient Extraction of Marker Points - Google Patents

Abstract

The present invention provides a circular track SAR trajectory reconstruction method based on marker point phase gradient extraction, which includes: selecting a plurality of marker points in the scene, and obtaining the geoid coordinate system coordinates of the circular SAR carrier aircraft and each marker point; According to the geoid coordinate system coordinates of the circular SAR carrier aircraft and each marker point, the phase gradient of each marker point is extracted from the target echo signal received by the circular track SAR, and the phase gradient of each marker point is calculated according to the phase gradient to the real track The real slant distance variation of the slant distance; using the geoid coordinate system coordinates of the circular SAR aircraft and the marker points, and the slant distance variation of each marker point, the circular SAR trajectory is reconstructed. The above method solves the problem that the existing circular SAR relies on high-precision navigation measurement, and can not only be used for high-precision trajectory reconstruction of circular synthetic aperture radar, but also suitable for high-precision trajectory reconstruction of arbitrary trajectory SAR.

Description

A Circular SAR Trajectory Reconstruction Method Based on Phase Gradient Extraction of Marker Points

technical field

The invention relates to the field of radar signal processing, in particular to a circular SAR trajectory reconstruction method based on marker point phase gradient extraction, which is used for high-precision focused imaging of high-resolution airborne circular SAR.

Background technique

As an active remote sensing device, Synthetic Aperture Radar (SAR) has the advantages of all-time, all-weather, long-distance, high-resolution, and wide swath. In the distance direction, it obtains high resolution by transmitting large-bandwidth signals. In the azimuth direction, it uses the movement of the platform to construct an equivalent long antenna aperture to achieve high resolution in this direction. After nearly 60 years of development, SAR has become a mature space remote sensing technology and one of the important means of earth observation.

Circular SAR (Circular SAR, CSAR) is a SAR working mode proposed in the 1990s. It uses the SAR platform to move in a circular trajectory in the air, and controls the beam so that the center of the beam always points to the center of the same scene to achieve the target area. Carry out 360° all-round observation. Compared with the traditional linear SAR, the circular track SAR has a larger coherent accumulation angle for the target observation, and can achieve higher resolution; and different from the traditional linear SAR oblique plane imaging geometry, the circular track SAR has the ability to perform three-dimensional In addition, the omnidirectional observation of circular SAR can effectively reduce the inherent shadow phenomenon of conventional SAR, and is of great significance for obtaining the backscattering information of the target changing with the azimuth angle. Therefore, based on these unique advantages, circular track SAR has attracted widespread attention once it was proposed.

Since 2004, research institutes such as Aerospace France, the Swedish National Defense Research Institute, Deutscher Aerospace, and the Institute of Electronics of the Chinese Academy of Sciences have successively carried out circular SAR flight tests using airborne test platforms. In July 2011, the German Aerospace Agency (DLR) demonstrated for the first time at the IGARSS conference the 360° all-round high-resolution circular SAR image (L-band full polarization) acquired by the E-SAR airborne system. In August 2011, the National Key Laboratory of Microwave Imaging Technology of the Institute of Electronics, Chinese Academy of Sciences used the self-developed airborne SAR system to carry out the first circular SAR flight test in China, and successfully obtained the P-band fully polarized 360° omnidirectional high-resolution circular Trace SAR image. The test results preliminarily demonstrate the application potential of circular SAR in the fields of high-precision surveying and mapping, disaster assessment and fine resource management.

Compared with conventional linear SAR, circular SAR has higher requirements for navigation measurement system. In order to achieve high-quality focusing, the phase error of imaging needs to be controlled at π/4, that is, the trajectory measurement error needs to be controlled at λ/16. The synthetic aperture time of conventional straight-track SAR is relatively short, usually only a few seconds, and the navigation system can guarantee relatively high relative measurement accuracy in a short time. However, the synthetic aperture time of circular track SAR is as long as several minutes. On the one hand, it is difficult for the navigation system to Such a long period of time maintains good stability, on the other hand, the cumulative error will reduce the relative measurement accuracy of the entire trajectory. In addition, the navigation system measures the motion parameters of the platform that is always in a turning state than the motion of a platform that is stably moving in a straight line. Parameter measurements have larger errors. Even if the airborne linear SAR has a high wave band, it generally only needs to perform motion compensation based on POS data to meet the focus imaging requirements, or use self-focusing technology on this basis to obtain higher focusing quality. However, when the airborne circular track When the SAR band is relatively high (C-band and above), the existing trajectory measurement accuracy can no longer meet the requirements of its focused imaging. At present, the tests that have successfully obtained all-round high-resolution airborne circular SAR images use low wave bands (P and L). De Yuhang uses the circular SAR self-focusing technology to improve the focusing performance of the image, but the self-focusing technology can only Corrects for small residual phase errors and does not take into account the spatial variability of phase errors. At present, there is no method that can solve the problem of the dependence of the existing circular track SAR on the high-precision navigation measurement system.

Contents of the invention

The purpose of the present invention is to provide a circular SAR trajectory reconstruction method based on the phase gradient extraction of marker points, which can solve the problem that the existing circular SAR relies on high-precision navigation measurement, and can provide technical support for realizing high-band circular SAR imaging .

In order to achieve the above object, the technical solution adopted in the present invention is:

A circular track SAR trajectory reconstruction method based on marker point phase gradient extraction, comprising:

Step S1, select a plurality of marker points in the scene, and obtain the geoid coordinate system coordinates of the circular SAR carrier aircraft and each marker point;

Step S2, according to the geoid coordinate system coordinates of the circular SAR carrier aircraft and each marker point, extract the phase gradient of each marker point from the target echo signal received by the circular track SAR, and calculate each marker point according to the phase gradient Slope distance variation to the real trajectory;

Step S3: Reconstruct the circular SAR track by using the geoid coordinate system coordinates of the circular SAR carrier aircraft and the marker points, and the slant distance variation of each marker point.

The beneficial effects of the present invention are: using POS data and marker points with known positions, extracting the phase gradient of the marker points from the echo data, establishing position and distance equations about marker points and trajectories, and reconstructing a circle with higher precision flight trajectory, thereby improving the focus quality during imaging, and solving the problem that the existing circular SAR relies on high-precision navigation measurement. The method of the present invention can not only be used for high-precision trajectory reconstruction of circular synthetic aperture radar, but also suitable for any trajectory High-precision trajectory reconstruction for SAR.

Description of drawings

Fig. 1 is the general flow chart of the circular track SAR trajectory reconstruction method based on marker point phase gradient extraction in the present invention;

Fig. 2 is the coordinate conversion schematic diagram of POS data and mark point data among the present invention;

Fig. 3 is a flow chart of extracting phase gradients of each marker point from echo data in the present invention;

Fig. 4 is the flow chart of the method for reconstructing high-precision trajectory in the present invention;

Fig. 5 is real trajectory, measurement trajectory and reconstructed trajectory simulation figure among the present invention;

Fig. 6 is the simulation figure of the point target that uses measurement track to carry out imaging in the present invention;

Fig. 7 is a simulation diagram of a point target for imaging using reconstructed trajectories in the present invention.

detailed description

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

Fig. 1 shows the overall flow chart of the method for reconstructing the circular SAR trajectory based on the phase gradient extraction of marker points in the present invention. As shown in Figure 1, the specific implementation steps of this method are as follows:

Step S1: Select multiple marker points in the scene to ensure that at least three marker points are irradiated at the same time under each azimuth perspective. These marker points can be artificially placed scalers or prominent points in the scene Target. Use external GPS/DGPS to measure the coordinates E _{g, k} of each marker point in the geocentric rotation coordinate system, where k represents the serial number of the marker point, k=1, 2, ..., M, and M is the total number of marker points. The coordinates of the SAR carrier trajectory measured by the navigation subsystem (POS) on the circular SAR in the geocentric rotation coordinate system are E _{g, pos} , using coordinate transformation, the POS measurement data and marker points are placed in the geocentric rotation coordinate system The coordinates E _{g, pos} and E _{g, k} under the coordinate system are converted to the coordinates E _pos and E _{p, k} under the geoid coordinate system.

Fig. 2 shows a schematic diagram of coordinate conversion between POS measurement data and marker point data in the present invention. As shown in Figure 2, after a coordinate system rotation, the coordinates of POS and marker points in the geocentric rotating coordinate system can be converted to the geoid coordinate system.

The definition of the geocentric rotating coordinate system: the origin of the coordinates is located at the center of the earth, the Z axis points to the earth's rotation axis, the X axis points to the zero-degree meridian, and the Y axis and the X and Z axes form a right-handed coordinate system. Definition of the geoid coordinate system: the origin of the coordinate system is the scene center of the observation target, the X-axis points to the geographic south, the Y-axis points to the geographic east, and the Z-axis is vertical to the ground.

The transformation relationship from the geocentric rotating coordinate system to the geodetic coordinate system is:

E _pos = A _pg (E _{g, pos} - A _pg0 )

E _{p, k} = A _pg (E _{g, k} - A _pg0 )

Among them, A _pg0 is the coordinate of the origin of the geoid coordinate system in the geocentric rotating coordinate system. φ ₀ and Λ ₀ are the latitude and longitude of the coordinate origin of the geoid coordinate system.

Step S2: Extract the phase gradient φ _d (k, n) of each marker point from the echo data S according to the geoid coordinate system coordinates E _pos and E _{p, k} of POS and marker points, and calculate according to the phase gradient The actual slant distance variation R _d (k, n) from each marker point to the real trajectory; wherein, n is the sampling number in the azimuth direction, n=1, 2, ..., N, N is the total number of sampling points in the azimuth direction. In SAR, the azimuth refers to the tangential direction of the circular trajectory, which changes with the change of the observation angle.

Fig. 3 shows a flowchart of a method for extracting phase gradients of each marker point from echo data in the present invention. As shown in Figure 3, the extraction process specifically includes:

Step S21: Perform range matching filter processing on the baseband echo signal S(t, n) to obtain the filtered signal S ₁ (t, n). The specific operation is to combine S(t, n) with the reference signal S ₀ ^* ( -t, n) for convolution, the expression of the reference signal S ₀ ^* (-t, n) is:

Signal S ₁ (t, n) obtained after matched filtering:

Among them: fc is the carrier frequency of the radar transmission signal, _t is the range time, _t0 is the round-trip delay time from POS to the reference target, the reference target can be the target located at the center of the scene illuminated by the circular track SAR, and T is the radar transmission The duration of the chirp pulse signal, K is the modulation frequency of the chirp signal transmitted by the radar.

Step S22: Select a marker point k, and calculate the migration distance R _k (n) and R _k (n) of the marker point according to the coordinates E _pos and E _p,k of POS and the marker point in the geoid coordinate system in step S1 is the distance between E _pos (n) and E _p,k , and E _pos (n) is the position of the nth sampling point of the POS coordinate E _pos in the azimuth direction. Where n=1, 2, ..., N, N is the total number of sampling points in the azimuth direction.

Step S23: Perform range interpolation on the filtered signal S ₁ (t, n), extract the migration data S ₂ (k, n) at the migration distance R _k (n), use Substitute t into S ₁ (t, n) to obtain signal S ₂ (k, n), c represents the speed of light, where:

Step S24: Multiply the signal S ₂ (k, n) by the phase function H ₁ (k, n), and perform azimuth discrete Fourier transform to obtain the range-Doppler signal S ₃ ( k, f _η ), f _η is the azimuth frequency, and the phase function H ₁ (k, n) is the phase function of the distance migration of the marker point measurement.

The expression of the phase function H ₁ (k, n) is:

Step S25: Perform azimuth low-pass filtering on the range-Doppler signal S ₃ (k, f _η ) to suppress the interference of clutter, specifically, combine S ₃ (k, f _η ) with the azimuth frequency domain filter function H ₂ ( k, f _η ) are multiplied together to obtain the signal S ₄ (k, f _η ) after filtering out clutter interference, where the filter function is:

Wherein, f _{d, k} are 1/10 to 1/20 of the pulse repetition frequency PRF (Pulse Repetition Frequency).

Step S26: Perform azimuth inverse discrete Fourier transform on the signal S ₄ (k, f _η ), transform it into the azimuth time domain, and obtain the signal S ₅ (k, n).

Calculate the phase gradient of the signal S ₅ (k, n) along the azimuth direction to obtain the real phase gradient of the marker point k and filter out the measured distance migration residual phase gradient φ _d1 (k, n), n=1, 2, ..., N. The calculation of φ _d1 (k, n) is as follows:

φ _d1 (k, n)=arg(S ₅ (k, n)*S ₅ ^* (k, n-1)) n=2, . . . N

φ _d1 (k,n)=0 n=1

The symbol S ^* stands for the conjugate of the complex signal S.

Step S27: Calculate the azimuth phase gradient of the complex conjugate phase function H ₁ ^{* (} k, n ₎ , and obtain the distance migration phase gradient signal φ _d2 (k, n); and add φ _d1 (k, n) and φ _d2 (k, n) to obtain the phase gradient function φ _d (k, n) of the actual distance migration of the kth marker point. The purpose of the addition is to compensate the phase gradient φ _d2 (k, n) lost due to the multiplication of the phase function H ₁ (k, n) in step S24.

The calculation of φ _d2 (k, n) is as follows:

φ _d2 (k, n)=arg(H ₁ ^* (k, n+1)*H ₁ (k, n)) n=2, . . . , N

φ _d2 (k,n)=0 n=1

Add φ _d1 (k, n) and φ _d2 (k, n) to get φ _d (k, n):

φ _d (k, n) = φ _d1 (k, n) + φ _d2 (k, n)

Step S28: Utilize the phase gradient function φ _d (k, n) of the k mark point obtained in step S27 to calculate the real slope distance variation R _d (k, n) of the k mark point to the real track, where :

Step S29: Repeat steps S22-S28 to traverse all marker points k.

Step S3: Using the coordinates of POS in step S1 and the coordinates of the marker points E _pos and E _p,k , and the slope distance variation R _d (k,n) of each marker point in step S2, reconstruct a high-precision trajectory.

Fig. 4 shows the flowchart of the method for reconstructing high-precision trajectory in the present invention. As shown in Figure 4, the process specifically includes:

Step S31: choose a sampling point i from N azimuth sampling points n, n=1, 2..., N, 1≤i≤N, take the POS coordinate E _pos (i) of the sampling point as the initial position, Select any three marker points that can be observed at this azimuth moment, their serial numbers are marked as 1, 2, 3, and their coordinates in the geoid coordinate system are (E _{p, 1x} , E _{p, 1y} , E _{p , 1z} ), (E _{p, 2x} , E _{p, 2y} , E _{p, 2z} ), (E _{p, 3x} , E _{p, 3y} , E _{p, 3z} ), calculate the distance R _i from the initial position to the observable marker point _,1 , R _i,2 , R _i,3 .

Step S32: Utilize the three marker point coordinates selected in step S31 and the slope distance variation R _d (1, n), R _d (2, n), R d (2, n) of these three marker points obtained in step S2 to the real track R _d (3, n), establish a system of equations about the position and distance of the marker point and the reconstruction trajectory, solve the equation system, and obtain the coordinates of the reconstruction trajectory at i-1/i+1 (P _{i-1, x} , P _{i -1, y} , P _{i-1, z} ) and (P _{i+1, x} , P _{i+1, y} , P _{i+1, z} ).

The specific operation is to solve the reconstruction trajectory coordinates (P _{i-1, x} , P _{i-1, y} , P _{i-1, z} ), (P _{i+1, x} , P _{i+ 1, y} , P _{i+1, z} ) ternary quadratic equation system.

Among them, the forward calculation of the reconstructed trajectory coordinates (P _{i-1, x} , P _{i-1, y} , P _{i-1, z} ) at i-1 uses the following equations:

Calculate the reconstructed trajectory coordinates at i+1 backwards (P _{i+1, x} , P _{i+1, y} , P _{i+1, z} ) using the following equations:

Directly solving the equation system, the expression is more complicated, so the coordinate system rotation is used to write the solution in the form of matrix multiplication to simplify the expression.

The solution to this system of equations is:

The calculation of M ₁ and M ₂ is as follows:

A=(Ep _,2y -Ep _,1y )(Ep _,3z -Ep _,1z )-(Ep _,3y -Ep _,1y )(Ep _,2z -Ep _,1z )

B=(Ep _,2z -Ep _,1z )(Ep _,3x -Ep _,1x )-(Ep _,3z -Ep _,1z )(Ep _,2x -Ep _,1x )

C=(Ep _,2x -Ep _,1x )(Ep _,3y -Ep _,1y )-(Ep _,3x -Ep _,1x )(Ep _,2y -Ep _,1y )

D=-(E _{p, 1x} *A+E _{p, 1y} *B+E _{p, 1z} *C)

And E _x , E _y , E _z are calculated as follows:

E _x =-[(E' _{p, 3y} -E' _{p, 2y} )*(E' _{p, 2y} -E' _{p, 1y} )*(E' _{p, 1y} -E' _{p, 3y} )+(E' _{p, 2x} ² -E′ _{p, 1x} ² +r ₁ ² -r ₂ ² )*(E′ _{p, 3y} -E′ _{p, 2y} )-(E′ _{p, 3x} ² -E′ _{p, 2x} ² + r ₂ ² -r ₃ ² )*(E′ _p,2y −E′ _p,1y )]/2C′

E _y = [(E' _{p, 3x} -E' _{p, 2x} )*(E' _{p, 2x} -E' _{p, 1x} )*(E' _{p, 1x} -E' _{p, 3x} )+(E' _{p , 2y} ² -E _{p, 1y} ² +r ₁ ² -r ₂ ² )*(E′ _{p, 3x} -E′ _{p, 2x} )-(E′ _{p, 3y} ² -E′ _{p, 2y} ² +r ₂ ² -r ₃ ² )*(E' _{p, 2x} -E' _{p, 1x} )]/2C'

in:

C'=( _E'p,2x -E'p _,1x )( _E'p,3y -E'p _,1y )-( _E'p,3x -E'p _,1x )( _E'p,2y- Ep _,1y )

If the coordinates of the reconstructed trajectory at i-1 are calculated forward, then:

r ₁ =R _i,1 -R _d (1,i)

r ₂ =R _i,2 -R _d (2,i)

r ₃ =R _i,3 -R _d (3,i)

If the coordinates of the reconstructed trajectory at i+1 are calculated backwards, then:

r ₁ =R _i,1 +R _d (1,i)

r ₂ =R _i,2 +R _d (2,i)

r ₃ =R _i,3 +R _d (3,i)

Step S33: Select any three marker points 1, 2, and 3 observable at i-1/i+1, and update the reconstructed trajectory at i-1/i+1 (P _{i-1, x} , P _{i -1, y} , P _{i-1, z} ), (P _{i+1, x} , P _{i+1, y} , P _{i+1, z} ) to mark point 1, 2, 3 distance R _{i-1, 1} , R _i-1 , 2 , R _{i-1, 3} and R _i+1 , 1 , R _{i+1, 2} , R _{i+1, 3} , forward/backward point-by-point reconstruction of the remaining sampling points Track coordinates until the entire track is traversed.

The advantages of the present invention are further illustrated through simulation experiments below.

The simulation parameters are shown in Table 1, and the placement positions of the marker points: (0, 0), (-800, 0), (800, 800).

Table 1. Airborne circular SAR simulation parameters

parameter value carrier frequency 5GHz bandwidth 500MHz PRF 3000Hz track radius 3km flying height 3km scene size 1km×1km

Simulation content and results:

Fig. 5 shows a comparison diagram of real trajectory, measured trajectory and reconstructed trajectory in the present invention. As shown in Figure 5, the real trajectory is a thin solid line, the measured trajectory is a thick solid line, and the reconstructed trajectory is a cross symbol line. It can be seen that the measured trajectory fluctuates up and down with respect to the real trajectory, and the error is large, and the reconstructed trajectory is closer to the real trajectory, which is consistent with the trend of the real trajectory.

FIG. 6 and FIG. 7 are respectively schematic diagrams of imaging results of a target located at (800, 800) using the measurement trajectory and the reconstruction trajectory in the present invention. As shown in Figure 6, the target is completely defocused when imaging using the measurement trace. As shown in FIG. 7 , after imaging using the circular SAR trajectory reconstruction method based on phase gradient extraction of marker points proposed by the present invention, the target obtains good focus quality.

The effectiveness of the above-mentioned method of the present invention has been verified through simulation experiments.

The specific embodiments described above have further described the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above descriptions are only specific embodiments of the present invention, and are not intended to limit the present invention. Within the spirit and principles of the present invention, any modifications, equivalent replacements, improvements, etc., shall be included in the protection scope of the present invention.

Claims (9)

1. a kind of circular track SAR track reconstructing methods extracted based on mark point phase gradient, it includes：

Step S1, choose multiple index points in the scene, and obtain the earth horizontal plane of circular track SAR carrier aircrafts and each index point and sit Mark system coordinate；

Step S2, the earth level coordinates system coordinate according to circular track SAR carrier aircrafts and each index point, are received from circular track SAR Target echo signal in extract the phase gradient of each index point, and each index point is calculated to true according to the phase gradient The oblique distance variable quantity of real track；

Step S3, the earth level coordinates system coordinate using circular track SAR carrier aircrafts and index point, and each index point oblique distance Variable quantity, rebuilds circular track SAR tracks；

Wherein, the phase gradient of each index point is extracted as follows in step S2：

Step 21, distance is done to target echo signal handled to matched filtering, obtain filtered signal；

Step 22, the earth level coordinates system coordinate according to the circular track SAR carrier aircrafts and each index point, calculate each mark The migration distance of point；

Step 23, enter row distance to the filtered signal to interpolation, extract the migration data being located at the migration distance；

Step 24, according to the migration data and phase function at the migration distance obtain distance-Doppler signal；

Step 25, the phase gradient for obtaining according to the distance-Doppler signal each index point.

2. track reconstructing method as claimed in claim 1, it is characterised in that circular track SAR carrier aircrafts described in step S1 and each The earth level coordinates system coordinate of index point is obtained according to the Coordinate Conversion under its earth's core rotating coordinate system；The circular track The earth's core rotational coordinates of SAR carrier aircrafts is obtained by navigation system POS measurements；The earth's core rotational coordinates of each index point passes through GPS/DGPS measurements are obtained.

3. track reconstructing method as claimed in claim 1, it is characterised in that the migration distance is the circular track SAR carrier aircrafts The distance between the earth level coordinates system coordinate of the earth level coordinates system's coordinate and each index point.

4. track reconstructing method as claimed in claim 1, it is characterised in that the data described in step S23 at migration distance It is obtained as below：

$S_2(k,n)=S_1(\frac{2R_k\left(n\right)}{c},n)$

Wherein, S₂(k, n) is the data at the migration distance,For target echo signal, R_k(n) for migration away from From c is the light velocity, and n is orientation sampled point, and k is k-th of index point.

5. track reconstructing method as claimed in claim 1, it is characterised in that be specially in step 24：By the migration distance The data at place are multiplied with first phase function, and carry out orientation discrete transform, to obtain distance-Doppler signal, the first phase Bit function and distance-Doppler signal are expressed as below：

$H_1(k,n)=\exp \left(\frac{j4{\mathrm{\πf}}_c{R}_k\left(n\right)}{c}\right)$

$S_3(k,f_{\mathrm{\η}})=\underset{n}{DFT}\{S_2(k,n)*H_1(k,n)\}$

Wherein, H₁(k, n) is phase function, R_k(n) it is migration distance, j is the imaginary unit of plural number, S₃(k,f_η) be distance-it is many General Le signal, DFT is discrete Fourier transform, S₂(k, n) is the data at the migration distance, f_cFor circular track SAR transmission signals Carrier frequency, f_ηIt is orientation frequency, c is the light velocity, and n is orientation sampled point, and k is k-th of index point.

6. track reconstructing method as claimed in claim 1, it is characterised in that the phase gradient of the index point of each in step 25 is such as It is lower to obtain：

Step 251, adjust the distance-Doppler signal does orientation LPF, obtains the signal after filtering clutter interference；

Step 252, orientation inverse discrete Fourier transform is carried out to the signal after resulting filtering clutter interference, obtain orientation Time-domain signal；

The phase gradient of step 253, the calculating orientation time-domain signal along orientation, obtains the first phase gradient letter of index point Number；

Step 254, the orientation phase gradient for calculating complex conjugate phase function, obtain the of index point in complex conjugate phase function Two phase gradient signal, first phase gradient signal is added with second phase gradient signal, obtains the phase gradient of index point.

7. track reconstructing method as claimed in claim 6, it is characterised in that the first phase gradient signal and second phase The expression formula of gradient signal is as follows：

φ_d1(k, n)=arg (S₅(k,n)*S₅ ^*(k, n-1)) n=2 ... N

φ_d1The n=1 of (k, n)=0

φ_d2(k, n)=arg (H₁ ^*(k,n+1)*H₁(k, n)) n=2 ..., N

φ_d2The n=1 of (k, n)=0

Wherein, φ_d1(k, n) and φ_d2(k, n) is respectively first phase gradient signal and second phase gradient signal, S₅(k, n) is Orientation time-domain signal, H₁(k, n) and H₁ ^*(k, n) is phase function and complex conjugate phase function；K is k-th of index point, and n is side Position is to sampled point.

8. the track reconstructing method as described in claim any one of 1-7, it is characterised in that the oblique distance variable quantity R_d(k, n) such as It is lower to calculate：

$R_d(k,n)=-\frac{{\mathrm{c\φ}}_d(k,n)}{4{\mathrm{\πf}}_c},n=1,2,...N$

Wherein, φ_d(k, n) is the phase gradient of k-th of index point, f_cFor the carrier frequency of circular track SAR transmission signals, c is the light velocity, and n is Orientation sampled point, N is the number of orientation sampled point.

9. the track reconstructing method as described in claim any one of 1-7, it is characterised in that step S3 is specifically included：

Step 31, optional a number i, n=1,2..., N, 1≤i≤N from N number of orientation sampled point n, by its POS coordinate E_pos (i) as initial position, any three index points that the orientation moment can observe are selected in, it is in the earth level coordinates system Under coordinate be respectively (E_p,1x,E_p,1y,E_p,1z)、(E_p,2x,E_p,2y,E_p,2z)、(E_p,3x,E_p,3y,E_p,3z), calculate the initial bit The distance for putting above three index point is R_i,1、R_i,2、R_i,3；

The oblique distance of step 32, the earth level coordinates according to three index points and three index points to real trace Variable quantity, sets up on index point and rebuilds the position of track and the equation group of distance, solves equation group, obtains i-1/i+1 Place rebuilds trajectory coordinates (P_i-1,x,P_i-1,y,P_i-1,z) and (P_i+1,x,P_i+1,y,P_i+1,z)；

Step S33：Any three index points 1,2,3 that can observe at i-1/i+1 are selected in, updates and rail is rebuild at i-1/i+1 Mark (P_i-1,x,P_i-1,y,P_i-1,z)、(P_i+1,x,P_i+1,y,P_i+1,z) to index point 1,2,3 apart from R_i-1,1, R_i-1,2, R_i-1,3With R_i+1,1, R_i+1,2, R_i+1,3, the trajectory coordinates of remaining sample point are rebuild in forward/backward pointwise, until complete track of traversal.