Riemann Surface Space Quasi-Orthogonal Ground Imaging Grid Arrangement Method for High-Orbit SAR Imaging

Abstract

The present invention provides a method for arranging a quasi-orthogonal surface imaging grid in the Riemann surface space for high-orbit SAR imaging. The unit vector in the latitude direction, the unit vector in the longitude direction, the azimuth unit vector of the imaging grid, and the range unit vector corresponding to the center point of the scene are calculated; the azimuth angle is calculated; N-point equally spaced sampling is performed, and the coordinates of each sampling point are calculated using the geodesic formula; the longitude and latitude positions of each equally spaced sampling point are obtained according to the longitude and latitude, and then the lines are connected to form the azimuth imaging grid line at the center point of the scene; the range grid lines are arranged; and imaging is performed using the imaging grid to obtain the image after high-orbit SAR imaging. The grid arrangement method proposed by the present invention uses the geodesic method to arrange the quasi-orthogonal grid for the first time, is applicable to high-orbit SAR imaging, realizes high-precision imaging of high-orbit SAR, and provides a reference value for the research on imaging grid arrangement in high-orbit SAR imaging.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and particularly relates to a method for arranging a Riemannian surface space quasi-orthogonal surface imaging grid for high-orbit SAR imaging. Background Art

[0002] A high-orbit SAR system is an active radar located in the geosynchronous orbit. It has an extremely long synthetic aperture time, is not affected by geographical and meteorological conditions, and can achieve long-term reconnaissance of specific areas. Therefore, it plays an important role in target imaging and observation. Although the high-orbit SAR has many advantages, its imaging difficulty is relatively greater. The extremely large imaging swath will cause obvious surface bending phenomenon, making the imaging scene plane approximation invalid. Therefore, it is necessary to arrange a surface imaging grid to avoid this error, otherwise it will affect the imaging result of the SAR and is one of the main limiting factors affecting the image quality.

[0003] Currently, the main methods for arranging imaging grids in the prior art are arranging grids on the ground plane and arranging grids based on the surface curvature. Arranging grids on the ground plane does not consider the azimuth phase error caused by surface bending, which will lead to azimuth defocusing problems. The arranged grids do not fit the actual curved surface, and using such grids in high-orbit SAR imaging cannot meet the imaging accuracy and reduces the imaging quality. The method of arranging a curved surface grid based on the actual surface arranges the imaging grid in the longitude-latitude coordinate system. According to the longitude-latitude direction and the azimuth-range direction of the scene center point, a non-orthogonal longitude-latitude grid is arranged, but the grid accuracy is not high and cannot better guarantee the imaging quality. Summary of the Invention

[0004] Based on the above technical problems, the present invention proposes a method for arranging a Riemannian surface space quasi-orthogonal surface imaging grid for high-orbit SAR imaging, that is, using geodesic lines to arrange grids. The obtained grids fit the surface better, have higher positioning accuracy, and finally achieve accurate imaging of high-orbit SAR, ensure the imaging quality, avoid image blurring, and reduce the spatial sampling rate and the amount of computation.

[0005] The method for arranging a Riemannian surface space quasi-orthogonal surface imaging grid for high-orbit SAR imaging of the present invention includes the following steps:

[0006] Step 1, obtain the satellite position, the coordinates at the scene center point, and the unit normal vector of the corresponding tangent plane, and calculate the unit vector V in the latitude direction corresponding to the scene center point according to the unit normal vector of the corresponding tangent plane at the scene center point and the satellite position la , the unit vector V in the longitude direction lo , the azimuth unit vector A of the imaging grid zi and the range unit vector R zi ;

[0007] (1a) Calculate the cross product of the unit vector in the direction of the Z-axis of the geocentric fixed coordinate system and the vector from the center of the earth to the scene center point to obtain the unit vector V in the latitude direction at the corresponding scene center point. la , and then, according to the unit vector V in the latitude direction at the scene center point la calculate the cross product with the unit normal vector of the tangent plane at the scene center point to obtain the unit vector V in the latitude direction at the scene center point. lo ;

[0008] (1b) Denote the satellite position as S A , where the azimuth unit vector A zi of the imaging grid is ±S A C×n,S A C represents the vector from the satellite position to the scene center point, and n represents the unit normal vector of the tangent plane at the scene center point; then calculate the range unit vector R zi of the imaging grid as ±n×A zi ;

[0009] Step 2, according to the unit vector V in the corresponding longitude direction at the scene center point lo and the azimuth unit vector A zi of the imaging grid at the scene center point, calculate the azimuth angle θ;

[0010] (2a) Define θ as the angle between the vector V lo and A zi , expressed as:

[0011]

[0012] where the operator · represents the inner product of two vectors, and the operator represents the modulus value of the vector.

[0013] Step 3, perform N-point equally spaced sampling along the azimuth direction of the imaging grid according to the obtained azimuth angle θ and the coordinates at the scene center point, and calculate the coordinates X i , i = 1, 2,..., N;

[0014] (3a) Perform a mapping operation on the latitude φ of the scene center point on the above ellipsoid to obtain the angular intermediate quantity ψ on the sphere, and the mapping operation ensures that the azimuth angle of the geodesic at any latitude on the sphere is the same as the corresponding azimuth angle on the ellipsoid;

[0015] (3b) Calculate the geodesic length δ on the sphere using the angular intermediate quantity ψ obtained above with the following formula:

[0016]

[0017] Among them, l is the distance between equally spaced sampling points, and C is a constant.

[0018] (3c) Calculate the longitude difference Δλ between the scene center point on the ellipsoid and each equally spaced sampling point according to the geodesic length δ on the sphere and the angular intermediate quantity ψ on the sphere obtained above; then calculate the latitude and azimuth of each equally spaced sampling point according to the spherical triangle formula;

[0019] Step 4: The longitude and latitude positions of each equally spaced sampling point can be obtained according to the above-mentioned longitude difference Δλ and latitude, and then the target X of each sampling point obtained above i is connected to form the azimuth imaging grid line at the scene center point;

[0020] Step 5: For each equally spaced sampling point in the azimuth imaging grid line at the scene center point obtained above, arrange the range grid lines at an azimuth angle of 90° + θ according to the above-mentioned Step 3;

[0021] Step 6: Obtain the imaging grid according to the above-mentioned range grid lines and azimuth grid lines, and use the imaging grid for imaging to obtain the post-imaging image of the high-orbit SAR.

[0022] The grid arrangement method proposed by the present invention first uses the geodesic method to arrange the quasi-orthogonal grid, which is applicable to high-orbit SAR imaging, realizes high-precision imaging of high-orbit SAR, and provides a reference value for the research on imaging grid arrangement in high-orbit SAR imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is the flow chart of the present invention;

[0024] Figure 2 is the 12000KM×12000KM grid of the embodiment;

[0025] Figure 3 is the 500KM×500KM grid of the embodiment;

[0026] Figure 4a-1 is the xyz coordinates and the reciprocal of the difference of the grid line corresponding to the 1000th azimuth sampling point of the embodiment;

[0027] Figure 4a-2 is the xyz coordinates and the second reciprocal of the difference of the grid line corresponding to the 1000th azimuth sampling point of the embodiment;

[0028] Figure 4a-3 is the xyz coordinates and the third reciprocal of the difference of the grid line corresponding to the 1000th azimuth sampling point of the embodiment;

[0029] Figure 4a-4The xyz coordinates of the grid line corresponding to the 1000th azimuth sampling point of the embodiment and the fourth of their differences;

[0030] Figure 4a-5 The xyz coordinates of the grid line corresponding to the 1000th azimuth sampling point of the embodiment and the fifth of their differences;

[0031] Figure 4a-6 The xyz coordinates of the grid line corresponding to the 1000th azimuth sampling point of the embodiment and the sixth of their differences;

[0032] Figure 4b-1 The xyz coordinates of the grid line corresponding to the 10000th azimuth sampling point of the embodiment and the first of their differences;

[0033] Figure 4b-2 The xyz coordinates of the grid line corresponding to the 10000th azimuth sampling point of the embodiment and the second of their differences;

[0034] Figure 4b-3 The xyz coordinates of the grid line corresponding to the 10000th azimuth sampling point of the embodiment and the third of their differences;

[0035] Figure 4b-4 The xyz coordinates of the grid line corresponding to the 10000th azimuth sampling point of the embodiment and the fourth of their differences;

[0036] Figure 4b-5 The xyz coordinates of the grid line corresponding to the 10000th azimuth sampling point of the embodiment and the fifth of their differences;

[0037] Figure 4b-6 The xyz coordinates of the grid line corresponding to the 10000th azimuth sampling point of the embodiment and the sixth of their differences;

[0038] Figure 4c-1 The xyz coordinates of the grid line corresponding to the 20000th azimuth sampling point of the embodiment and the first of their differences;

[0039] Figure 4c-2 The xyz coordinates of the grid line corresponding to the 20000th azimuth sampling point of the embodiment and the second of their differences;

[0040] Figure 4c-3 The xyz coordinates of the grid line corresponding to the 20000th azimuth sampling point of the embodiment and the third of their differences;

[0041] Figure 4c-4 The xyz coordinates of the grid line corresponding to the 20000th azimuth sampling point of the embodiment and the fourth of their differences;

[0042] Figure 4c-5 The xyz coordinates of the grid line corresponding to the 20000th azimuth sampling point of the embodiment and the fifth of their differences;

[0043] Figure 4c-6 The xyz coordinates and their differences of the grid line corresponding to the 20,000th azimuth sampling point of the embodiment, six of them;

[0044] Figure 5a For point target imaging using an imaging grid arranged by traditional methods;

[0045] Figure 5b For point target imaging using the imaging grid proposed by this invention. Detailed implementation manners

[0046] The flowchart of the present invention is as Figure 1 shown.

[0047] The effects of the present invention are verified through the following simulation experiments.

[0048] I. Simulation parameter settings

[0049] Table 1 Simulation parameter table

[0050]

[0051] II. Simulation content

[0052] Under the above parameters, using the method proposed by the present invention and using a new grid for imaging to prove the feasibility of the present invention. The results are as follows. Figure 2 For a grid layout of 12,000 KM × 12,000 KM, in Figure 2 where the solid line 21 represents a grid line at the center of the scene determined using geodesics, and the solid line 22 represents the range grid line arranged. Figure 3 For a grid layout of 500 KM × 500 KM, Figures 4a-1 to 4c-6 which shows the xyz coordinates and their differences of the grid lines corresponding to different azimuth sampling points.

[0053] In Figure 5a For point target imaging using an imaging grid arranged by traditional methods, Figure 5b For point target imaging using the imaging grid proposed by this invention. It can be seen that the image obtained by imaging using the imaging grid proposed by this invention is more focused and the imaging quality accuracy is higher.

[0054] From the above analysis, it can be seen that the proposed grid layout method fits better with the ground surface, has higher coordinate accuracy, and the image quality accuracy obtained by imaging using the proposed grid is higher.

Claims

1. A method for arranging quasi-orthogonal surface imaging grids in Riemann surface space for high-orbit SAR imaging, characterized in that: The following steps are involved: Step 1: Get the satellite position, the coordinates of the scene center point, and the unit normal vector of the corresponding tangent plane, and calculate the unit vector of the meridian direction corresponding to the scene center point based on the unit normal vector of the tangent plane corresponding to the scene center point and the satellite position. , the azimuth unit vector of the imaging grid ; Step 2: According to the unit vector of the meridian direction corresponding to the center point of the scene Unit vector to the imaging grid at the center of the scene , calculate the azimuth ; Step 3: According to the azimuth angle obtained above The coordinates of the scene center point are sampled at N points at equal intervals along the azimuth of the imaging grid, and the coordinates of each sampling point are calculated using the geodesic formula. ; Step 4: Based on the longitude difference The latitude and longitude positions of each equally spaced sampling point are obtained by the difference in latitude and longitude; then the target position of each sampling point obtained above is Connect the lines to form an azimuth imaging grid line at the center point of the scene; Step 5: For each equally spaced sampling point in the imaging grid line of the scene center point obtained above, the azimuth angle Arrange the distance grid lines according to step 3 above; Step 6: Obtain an imaging grid according to the above-mentioned distance grid lines and azimuth grid lines, and use the imaging grid to perform imaging to obtain a high-orbit SAR imaging image.

2. The method for arranging quasi-orthogonal ground imaging grids in Riemann surface space for high-orbit SAR imaging according to claim 1, characterized in that: Step 1 includes the following sub-steps: (1a) The unit vector in the Z-axis direction of the Earth-fixed coordinate system and the vectors at the center of the Earth and the scene are calculated by performing the outer product calculation to obtain the corresponding unit vector in the latitude direction at the center of the scene: , and then according to the unit vector in the latitude direction at the center of the scene The unit vector in the meridian direction at the center of the scene is obtained by performing an outer product calculation with the unit normal vector of the tangent plane at the center of the scene. ; (1b) The satellite position is recorded as , where the azimuth unit vector of the imaging grid is for , Represents the vector from the satellite position to the center point of the scene, Represents the unit normal vector of the tangent plane at the center point of the scene; then calculate the distance unit vector of the imaging grid for .

3. The method for arranging quasi-orthogonal ground imaging grids in Riemann surface space for high-orbit SAR imaging according to claim 1, characterized in that: Step 2 Calculate the azimuth The method is: definition Representation vector and The angle between them is expressed as: ， where operator Indicates the inner product of two vectors. The operator Indicates the modulus of the orientation quantity.

4. The method for arranging quasi-orthogonal ground imaging grids in Riemann surface space for high-orbit SAR imaging according to claim 1, characterized in that: Step 3 includes the following sub-steps: (3a) The latitude of the scene center point on the ellipsoid Perform a mapping operation to obtain the intermediate angle on the sphere , the mapping operation ensures that the azimuth of the geodesic at any latitude on the sphere is the same as the azimuth on the corresponding ellipsoid; (3b) Substitute the median angle on the sphere obtained above The length of the geodesic on the sphere is calculated using the following formula: : ， in, is the distance between equally spaced sampling points, and C is a constant; (3c) According to the geodesic length on the sphere obtained above , the median angle on the sphere Calculate the longitude difference between the center point of the scene on the ellipsoid and each equally spaced sampling point and latitude difference.

Images