A high-precision positioning method for airborne SAR images based on multi-viewpoints

Abstract

The present invention discloses a high-precision positioning method for airborne SAR images based on multiple viewing angles in the field of microwave remote sensing technology. The high-precision positioning method for airborne SAR images based on multiple viewing angles starts from the initial positioning longitude and latitude of the four corner points of the SAR image, calculates the basic transformation matrix of SAR images at different angles; establishes an equivalent equation for the real geographical location of the same-name points, and estimates the system positioning error shared between different SAR images; determines the weighting coefficient using the error transfer matrix between different images, and determines a rough estimate of the system positioning error of the reference SAR image using a weighted method; corrects the rough estimate using the minimum norm least squares criterion, and uses the result as the system positioning error; compensates the estimated system positioning error in the SAR image positioning, and completes the high-precision positioning of the SAR image. The high-precision positioning method for airborne SAR images based on multiple viewing angles has a more robust and more accurate estimation result.

Description

Technical Field

[0001] The present invention relates to the field of microwave remote sensing technology, and in particular to an uncontrolled high-precision positioning method of airborne SAR images based on multiple viewing angles. Background Art

[0002] Airborne SAR is an important branch of SAR system, with the advantages of all-day, all-weather, long-distance and high-resolution. With the development of high-resolution UAV SAR imaging technology, higher requirements are also put forward for the positioning accuracy of airborne SAR images. Airborne SAR systems usually complete basic system-level positioning and can generate system-level geometric correction image products with high efficiency, but the model is relatively simple and the accuracy is limited. On the basis of system-level geometric positioning, the technology to further improve the geometric positioning accuracy is usually called SAR image geometric precision correction. SAR image geometric precision correction technology can usually be divided into two categories: without external data support and with external data support. In the case of external data support, external data such as checkpoints and heterogeneous high-precision images can be used to assist positioning, with high accuracy and reliable performance. In the case of no external data support, a more accurate geometric positioning model can be established based on the UAV SAR imaging mechanism, or the system geometric error parameters can be obtained in advance through geometric calibration technology and corrected in the positioning model. In addition, by using multiple flyby observations of the same area from different perspectives, multi-perspective SAR data fusion can also effectively correct the common geometric errors of the SAR system and obtain high-precision target positioning results. However, in many applications, it is difficult to obtain the accurate geographic location of reliable reference points and recorded aircraft movement information, and the accuracy of traditional positioning methods is not high.

[0003] The two-angle airborne SAR image geometric positioning method starts from two airborne SAR images with different flying angles. On the basis of using the RD model to complete the rough positioning of the four corner points of the airborne SAR image, the system-level geometric positioning model of the multi-view SAR image is combined to estimate the two-dimensional geometric positioning errors of each SAR image in the range and azimuth directions to achieve high-precision planar positioning of the airborne SAR image. The specific method is referenced in the literature "An Image Planar Position Method Base on Fusion of Dual-View Airborne SAR Data. Remote Sens. 15, 2023, 15, 2499). The method in this literature starts from the fact that the two-dimensional geometric positioning errors of the same-source airborne SAR images in the range and azimuth directions are basically consistent. Based on the initial positioning results of the four corner points of each SAR image, the geometric positioning error is solved and compensated, and the high-precision SAR image geometric correction is completed. However, when processing three or more multi-angle SAR images, this method fails to provide an effective multi-angle fusion positioning algorithm, and the robustness and accuracy of this method are insufficient. Summary of the invention

[0004] The purpose of the present invention is to provide a high-precision positioning method for airborne SAR images based on multiple viewing angles, which effectively solves the problem that the existing two-angle airborne SAR image geometric positioning method is difficult to process three or more multi-angle SAR images, and has a more robust and accurate estimation result.

[0005] In order to achieve the above object, the technical solution of the present invention is as follows:

[0006] The present invention provides a method for high-precision positioning of airborne SAR images without control based on multiple viewing angles, comprising the following steps:

[0007] S1. Starting from the initial positioning longitude and latitude of the four corner points of the SAR image, the basic transformation matrix of the SAR image at different angles is calculated;

[0008] S2. Select significant natural landmarks in the SAR images as homonymous points, establish equivalent equations for the true geographical locations of the homonymous points, and estimate the common systematic positioning errors in the range and azimuth directions between different SAR images;

[0009] S3. Determine the weighting coefficients using the error transfer matrix between different images, and determine a rough estimate of the positioning error of the reference SAR image system using a weighted method;

[0010] S4. Correct the rough estimate using the minimum norm least squares criterion and use the result as the system positioning error;

[0011] S5. Compensate the system positioning error in the SAR image positioning to complete the SAR image high-precision positioning.

[0012] Further, the S2 comprises the following steps:

[0013] S21. Select the same road intersections, building corners or easily identifiable significant natural landmarks in the SAR images as the same-name points, and establish equivalent equations for the true geographical locations of the same-name points in different images;

[0014] S22. Estimate the common systematic positioning error between different SAR images in the range and azimuth directions.

[0015] Furthermore, the equivalent equation of the real geographical location of the same-name points between different images in S21 is as follows:

[0016]

[0017] Among them, [i m j m ] and [i n jn ] is the pair of points with the same name between graph m and graph n, r m and a m are the distance positioning error and azimuth positioning error in Figure m, r n and a n are the distance positioning error and azimuth positioning error in Figure n, respectively. are the distance interval and azimuth interval of Figure m and Figure n respectively, C m , D m are the first-order term and constant term coefficient matrices of graph m, respectively, C n , D n are the coefficient matrices of the first-order terms and constant terms of graph n respectively;

[0018] Further, the S22 comprises the following steps:

[0019] S221. Transform the above formula (1):

[0020]

[0021] Where, ΔB nm and ΔL nm The difference between the coarse positioning longitude and latitude of the same name point in Figure n and the coarse positioning longitude and latitude of the same name point in Figure m;

[0022] S222. Further simplify formula (2):

[0023]

[0024] in, and is the estimated value of the positioning error in the range and the estimated value of the positioning error in the azimuth obtained when the system positioning errors between images m and n are equal; at the same time, take K (n,m)

[0025]

[0026] in, Denotes the matrix K (n,m) The elements of the i-th row and j-th column of , we get formula (5) as follows:

[0027]

[0028] Further, the S3 comprises the following steps:

[0029] S31. Determine the weighting coefficients using the error transfer matrix between different images;

[0030] S32. Determine a rough estimate of the range and azimuth positioning error of the reference SAR image system using a weighted approach.

[0031] Further, the S31 includes the following steps:

[0032] S311. For the calculation of the system positioning error of any two images, i.e., image m and image n, an equivalent equation is established based on the real geographical locations of the same-name points:

[0033]

[0034] Pick

[0035] [Δr mn Δa mn ]=[r m a m ]-[r n a n ] (7)

[0036] Among them, r m , a m is the true distance positioning error and true azimuth positioning error of Figure m, Δr mn is the difference between the distance positioning errors of Figure m and Figure n, Δa mn is the difference between the azimuth positioning errors of Figure m and Figure n,

[0037] Substitute formula (7) into formula (6):

[0038]

[0039] S312. Assuming that the system positioning errors of the two images are equal, the error introduced when estimating the image n and image m is as follows:

[0040]

[0041] The error transfer matrix of the error introduced by graph n to graph m satisfies:

[0042]

[0043] Among them, H (n,m) The error transfer matrix of image n to image m is substituted into the above formula (9):

[0044]

[0045] S313. Determine weighting factors for the distance direction and the azimuth direction respectively:

[0046]

[0047] in, is the distance impact factor, is the azimuthal influencing factor;

[0048] S314. Obtain weighting coefficient:

[0049]

[0050] in, for The weighting coefficient of for The weighting coefficient of .

[0051] Furthermore, the rough estimation of the range and azimuth directions of the positioning error of the reference SAR image system determined by the weighted method in S32 is as follows:

[0052]

[0053] Among them, r m (0) Represents a rough estimate of the distance positioning error of Figure m, a m (0) It represents a rough estimate of the azimuth positioning error of Figure m.

[0054] Further, the S4 comprises the following steps:

[0055] S41. Using three images as examples, establish a set of equations

[0056]

[0057] The estimated initial solution is X (0) =[r1 (0) a1 (0) r2 (0) a2 (0) r3 (0) a3 (0) ] T ,make

[0058] Y * =Y-AX (0) =AX-AX (0) =A(XX (0) ) (16);

[0059] S42. The sum of the squares of the differences between the estimated value and the true value satisfies

[0060]

[0061] At this point we can use the MP generalized inverse matrix of the equation to solve the minimum norm least squares solution Z of the system of equations, so that Reaching the minimum,

[0062] Z=A + ·Y * (17)

[0063] Among them, A + is the MP generalized inverse matrix of A. The final estimated value of the positioning error is X * for

[0064] X * =X (0) +Z (18)

[0065] Further, the S5 comprises the following steps:

[0066] S51. Compensate the positioning error solved in step S42 to the longitude and latitude of the four corner points of the SAR image;

[0067] S52.SAR image repositioning, and finally completing SAR image high-precision positioning.

[0068] By adopting the above technical solution, the present invention has the following advantages:

[0069] The present invention provides an airborne SAR image uncontrolled high-precision positioning method based on multi-viewing angles, which determines weighting coefficients by using the error transfer matrix between airborne SAR images at different angles, uses a weighting method to determine a rough estimate of the positioning error of the multi-angle SAR image system, uses the minimum norm least squares criterion to correct the rough estimate, and uses the result as the system positioning error compensation in SAR image positioning to complete the SAR image high-precision positioning. The airborne SAR image uncontrolled high-precision positioning method effectively solves the problem that the existing two-angle airborne SAR image geometric positioning method is difficult to process three or more multi-angle SAR images, realizes the fusion positioning of three or more multi-angle SAR images, effectively improves the positioning accuracy, and has a more robust and accurate estimation result. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a flow chart of the non-controllable high-precision positioning method of airborne SAR images based on multi-viewing angles of the present invention;

[0071] Figure 2 The multi-angle airborne SAR images of the same area of ​​the present invention;

[0072] Figure 3 The figure is a comparison of the stitching of multi-angle SAR image and optical image before and after correction using the method of the present invention. DETAILED DESCRIPTION

[0073] The technical solution of the present invention is described in detail below in conjunction with the drawings in the specification. It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprises" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0074] Figure 1 The flowchart of the method for high-precision positioning of airborne SAR images without control based on multiple viewing angles of the present invention is shown. The method for high-precision positioning of airborne SAR images without control based on multiple viewing angles of the present invention comprises the following steps: Figure 1 As shown:

[0075] S1. Starting from the initial positioning longitude and latitude of the four corner points of the SAR image, the basic transformation matrix of the SAR image at different angles is calculated;

[0076] S2. Select significant natural landmarks in the SAR images as homonymous points, establish equivalent equations for the true geographical locations of the homonymous points, and estimate the common systematic positioning errors in the range and azimuth directions between different SAR images;

[0077] S2 includes the following specific steps:

[0078] S21. Select the same road intersections, building corners or easily identifiable significant natural landmarks in the SAR images as homonymous points, establish equivalent equations for the true geographic locations of the homonymous points, and estimate the common system positioning errors in the range and azimuth between different SAR images. The specific method is processed by referring to the paper "An Image Planar Position Method Base on Fusion of Dual-View Airborne SAR Data. Remote Sens. 15, 2023, 15, 2499).

[0079] The real geographic coordinates of the same-name points in different images are the same, so the equivalent equations of the geographic locations of the same-name points in different images can be established.

[0080]

[0081] Among them, [i m j m ] and [i n j n] is the pair of points with the same name between graph m and graph n, r m and a m are the distance positioning error and azimuth positioning error in Figure m, r n and a n are the distance positioning error and azimuth positioning error in Figure n, respectively. are the distance interval and azimuth interval of Figure m and Figure n respectively. m , D m are the first-order term and constant term coefficient matrices of graph m, respectively, C n , D n are the first-order term and constant term coefficient matrices of graph n respectively.

[0082] S22. Estimate the common systematic positioning error between different SAR images in the range and azimuth directions.

[0083] S22 includes the following specific steps:

[0084] S221. By transforming formula (1), we can get

[0085]

[0086] Where, ΔB nm and ΔL nm It is the difference between the coarse positioning longitude and latitude of the same-name point in Figure n and the coarse positioning longitude and latitude of the same-name point in Figure m.

[0087] S222. Further simplifying formula (2) yields:

[0088]

[0089] in, and is the estimated value of the positioning error in the range and the estimated value of the positioning error in the azimuth obtained when the system positioning errors between Figure m and Figure n are equal.

[0090]

[0091] in, Denotes the matrix K (n,m) The element in the i-th row and j-th column of .

[0092]

[0093] S3. Determine the weighting coefficients using the error transfer matrix between different images, and determine a rough estimate of the positioning error of the reference SAR image system using a weighted method;

[0094] S3 includes the following steps:

[0095] S31. Determine the weighting coefficients using the error transfer matrix between different images;

[0096] S31 includes the following specific steps:

[0097] S311. For the calculation of the system positioning error of any two images, i.e., image m and image n, we can establish an equivalent equation based on the real geographical location of the same-name points:

[0098]

[0099] Pick

[0100] [Δr mn Δa mn ]=[r m a m ]-[r n a n ] (7)

[0101] Among them, r m , a m is the true distance positioning error and true azimuth positioning error of Figure m. mn is the difference between the distance positioning errors of Figure m and Figure n, Δa mn is the difference between the azimuth positioning errors of Figure m and Figure n. Substituting formula (7) into formula (6) yields

[0102]

[0103] S312. Assuming that the positioning errors of the two images are equal, the error introduced by image n when estimating image m is

[0104]

[0105] From the above formula, it can be found that due to the difference in the actual system positioning error, the error transfer matrix of the error introduced by Figure n to Figure m satisfies

[0106]

[0107] H (n,m) represents the error transfer matrix of graph n to graph m. At this time, substituting into equation (9), we can know that:

[0108]

[0109] S313. Through analysis, it can be seen that the disturbance effects of atmospheric disturbance and elevation error on the system positioning errors in the range and azimuth directions are consistent, so the weighting factors can be determined for the range and azimuth directions respectively.

[0110]

[0111] in, is the distance impact factor, is the directional influencing factor.

[0112] S314. Therefore, the error introduced by SAR images at different angles to the same SAR image is related to the geometric relationship between the two, and the weighted coefficient can be taken as

[0113]

[0114] in, for The weighting coefficient of for The weighting coefficient of .

[0115] S32. Determine a rough estimate of the range and azimuth positioning error of the reference SAR image system using a weighted approach.

[0116] At this time, the rough estimate of the SAR image positioning error at each angle is obtained as:

[0117]

[0118] Among them, r m (0) Represents a rough estimate of the distance positioning error of Figure m, a m (0) It represents a rough estimate of the azimuth positioning error of Figure m.

[0119] S4. Correct the rough estimate using the minimum norm least squares criterion and use the result as the system positioning error;

[0120] S4 includes the following steps:

[0121] S41. Using three images as examples, establish the equation system:

[0122]

[0123] At this time, the estimated initial solution is X (0) =[r1 (0) a1 (0) r2 (0) a2 (0) r3 (0) a3 (0) ] T ,make

[0124] Y * =Y-AX (0) =AX-AX (0) =A(XX (0) ) (16)

[0125] S42. The sum of the squares of the differences between the estimated value and the true value satisfies

[0126]

[0127] At this point we can use the MP generalized inverse matrix of the equation to solve the minimum norm least squares solution Z of the system of equations, so that Reaching the minimum,

[0128] Z=A + ·Y * (17)

[0129] Among them, A + is the MP generalized inverse matrix of A. The final estimated value of the positioning error is X * for

[0130] X * =X (0) +Z (18)

[0131] S5. Compensate the system positioning error in the SAR image positioning to complete the SAR image high-precision positioning.

[0132] S5 includes the following steps:

[0133] S51. Compensate the positioning error solved in step S42 to the longitude and latitude of the four corner points of the SAR image;

[0134] S52.SAR image repositioning, and finally completing SAR image high-precision positioning.

[0135] Figure 2 In a specific embodiment, the measured data used in the embodiment of the present invention comes from an airborne SAR image of a certain area. Figure 2 As shown, Figure 2 (a) is a SAR image with a track angle of 148.97°. Figure 2 (b) is a SAR image with a track angle of 160.44°. Figure 2 (c) is a SAR image with a track angle of 173.22°.

[0136] Figure 3 The comparison diagram of the multi-angle SAR image and the optical image before and after correction using the method of the present invention is shown. Figure 3 (a) is the value before correction using this method Figure 2 (a) is a mosaic of the partially enlarged image and the high-precision optical image; Figure 3 (b) After correction using this method Figure 2(a) is a mosaic of the locally enlarged image and the high-precision optical image. Figure 3 (c) Before correction using this method Figure 2 (b) is a mosaic of the locally enlarged image and the high-precision optical image; Figure 3 (d) is the value after correction using this method Figure 2 (b) is a mosaic of the locally enlarged image and the high-precision optical image. Figure 3 (e) Before correction using this method Figure 2 (c) is a mosaic of the locally enlarged image and the high-precision optical image; Figure 3 (f) is the value after correction by this method Figure 2 (c) is a mosaic of the partially enlarged image and the high-precision optical image. Figure 3 (a) Figure 3 (b) Figure 3 (c) Figure 3 (d) Figure 3 (e) and Figure 3 It can be seen from (f) that when the method of the present invention is not used for correction, there is an obvious break in the splicing with the optical image. After correction by the method of the present invention for airborne SAR image uncontrolled high-precision positioning based on multi-view angles, the splicing quality is effectively improved, which shows that the method of the present invention for airborne SAR image uncontrolled high-precision positioning based on multi-view angles effectively improves the positioning accuracy.

[0137] The comparison of the plane positioning accuracy of the airborne SAR target by the multi-view airborne SAR image uncontrolled high-precision positioning method of the present invention and the two-view method is shown in Table 1 below:

[0138] Table 1: Comparison of the plane positioning accuracy of the proposed method and the two-view method for airborne SAR targets

[0139] Image A Image B Image C Track angle (°) 148.97 160.44 173.22 Positioning accuracy(m) 15.44 15.56 15.21 Positioning accuracy after A+B two-view positioning (m) 3.57 3.99 —— Positioning accuracy after A+C two-view positioning (m) 2.68 —— 2.84 Positioning accuracy after B+C two-view positioning (m) —— 5.97 6.76 A+B+C Positioning accuracy after positioning by this patented method (m) 1.55 1.60 1.29

[0140] It can be seen from Table 1 that the estimation of the SAR positioning error of each airborne SAR target angle of the multi-view airborne SAR image uncontrolled high-precision positioning method of the present invention is better than the existing two-view positioning method under the three airborne SAR target angles. This proves that the multi-view airborne SAR image uncontrolled high-precision positioning method of the present invention is effective, and also proves that the multi-view airborne SAR image uncontrolled high-precision positioning method of the present invention can improve the positioning accuracy of the existing two-angle airborne SAR image geometric positioning method.

[0141] Finally, it should be pointed out that although the present invention has been described with reference to the current specific embodiments, ordinary technicians in this technical field should realize that the above embodiments are only used to illustrate the present invention and are not used as a limitation of the present invention. Various equivalent changes or substitutions can be made without departing from the concept of the present invention. Therefore, as long as the changes and modifications to the above embodiments are within the essential spirit of the present invention, they will fall within the scope of the claims of the present invention.

Claims

1. A high-precision positioning method based on multi-view airborne SAR images without control, characterized in that: The following steps are involved: S1. Starting from the initial positioning longitude and latitude of the four corner points of the SAR image, the basic transformation matrix of the SAR image at different angles is calculated; S2. Select significant natural landmarks in the SAR images as homonymous points, establish equivalent equations for the true geographical locations of the homonymous points, and estimate the common systematic positioning errors in the range and azimuth directions between different SAR images; S3. Determine the weighting coefficients using the error transfer matrix between different images, and determine a rough estimate of the positioning error of the reference SAR image system using a weighting method; The S3 comprises the following steps: S31. Determine the weighting coefficients using the error transfer matrix between different images; S32. Determine a rough estimate of the range and azimuth of the positioning error of the reference SAR image system using a weighted method; S4. Correct the rough estimate using the minimum norm least squares criterion and use the result as the system positioning error; S5. Compensate the system positioning error in the SAR image positioning to complete the SAR image high-precision positioning.

2. The method for high-precision positioning based on multi-view airborne SAR images without control according to claim 1, characterized in that: The S2 comprises the following steps: S21. Select the same road intersections, building corners or easily identifiable significant natural landmarks in the SAR images as the same-name points, and establish equivalent equations for the true geographical locations of the same-name points in different images; S22. Estimate the common systematic positioning error between different SAR images in the range and azimuth directions.

3. The method for high-precision positioning based on multi-view airborne SAR images without control according to claim 2, characterized in that: The equivalent equation of the real geographical location of the same-name points between different images in S21 is as follows: Among them, [i m j m ] and [i n j n ] is the pair of points with the same name between graph m and graph n, r m and a m are the distance positioning error and azimuth positioning error in Figure m, r n and a n are the distance positioning error and azimuth positioning error in Figure n, respectively. are the distance interval and azimuth interval of Figure m and Figure n respectively, C m , D m are the first-order term and constant term coefficient matrices of graph m, respectively, C n , D n are the first-order term and constant term coefficient matrices of graph n respectively.

4. The method for high-precision positioning based on multi-view airborne SAR images without control according to claim 3, characterized in that: The S22 comprises the following steps: S221. Transform the above formula (1): Where, ΔB nm and ΔL nm The difference between the coarse positioning longitude and latitude of the same name point in Figure n and the coarse positioning longitude and latitude of the same name point in Figure m; S222. Further simplify formula (2): in, and is the estimated value of the positioning error in the range and the estimated value of the positioning error in the azimuth obtained when the system positioning errors between images m and n are equal; at the same time, take K (n,m) in, Denotes the matrix K (n,m) The elements of the i-th row and j-th column of , we get formula (5) as follows:

5. The method for high-precision positioning based on multi-view airborne SAR images without control according to claim 1, characterized in that: The S31 comprises the following steps: S311. For the calculation of the system positioning error of any two images, i.e., image m and image n, an equivalent equation is established based on the real geographical locations of the same-name points: Pick [Δr mn Δa mn ]=[r m and m ]-[r n and n ] (7) Among them, r m , a m is the distance positioning error and azimuth positioning error in Figure m, Δr mn is the difference between the distance positioning errors of Figure m and Figure n, Δa mn is the difference between the azimuth positioning errors of Figure m and Figure n, Substitute formula (7) into formula (6): S312. Assuming that the system positioning errors of the two images are equal, the error introduced when image n estimates image m is as follows: The error transfer matrix of the error introduced by graph n to graph m satisfies: Among them, H (n,m) The error transfer matrix of image n to image m is substituted into the above formula (9): S313. Determine weighting factors for the distance direction and the azimuth direction respectively: in, is the distance impact factor, is the azimuthal influencing factor; S314. Obtain weighting coefficient: in, for The weighting coefficient of for The weighting coefficient of .

6. The method for high-precision positioning based on multi-view airborne SAR images without control according to claim 5, characterized in that: The rough estimation of the range and azimuth directions of the positioning error of the reference SAR image system determined by the weighted method in S32 is as follows: Among them, r m (0) Represents a rough estimate of the distance positioning error of Figure m, a m (0) It represents a rough estimate of the azimuth positioning error of Figure m.

7. The method for high-precision positioning based on multi-view airborne SAR images without control according to claim 6, characterized in that: The S4 comprises the following steps: S41. Using three images as examples, establish a set of equations Y=AX The estimated initial solution is X (0) =[r1 (0) a1 (0) r2 (0) a2 (0) r3 (0) a3 (0) ] T ,make Y * =Y-AX (0) =AX-AX (0) =A(X-X (0) ) (16); S42. The sum of the squares of the differences between the estimated value and the true value satisfies At this point we can use the MP generalized inverse matrix of the equation to solve the minimum norm least squares solution Z of the system of equations, so that Reaching the minimum, Among them, A + is the MP generalized inverse matrix of A; the final estimated value of the positioning error is X * for X * =X (0) +Z (18)。 8. The method for high-precision positioning based on multi-view airborne SAR images without control according to claim 7, characterized in that: The S5 comprises the following steps: S51. Compensate the positioning error solved in step S42 to the longitude and latitude of the four corner points of the SAR image; S52.SAR image repositioning, and finally completing SAR image high-precision positioning.

Images