Geodetic coordinate positioning simulation method for satellite cross-rail scanning sampling points

Abstract

The invention provides a geodetic coordinate positioning simulation method for a satellite cross-orbit scanning sampling point, and the method comprises the steps: obtaining an observation vector under a satellite coordinate system according to a detector installation matrix, and obtaining an observation vector under an orbit coordinate system based on a satellite attitude matrix; determining a transformation matrix from the orbital coordinate system to the earth-centered earth-fixed coordinate system according to the satellite position vector and the velocity vector, and obtaining an observation vector under the earth-centered earth-fixed coordinate system according to the observation vector under the orbital coordinate system and the transformation matrix; according to the long axis, the short axis and the eccentricity rate of the ellipsoid of the earth, on the basis of an observation vector and a satellite position vector under an earth-centered earth-fixed coordinate system, obtaining geodesic longitude, latitude and height coordinates of a satellite scanning sampling point under a WGS84 coordinate system, and utilizing a terrain database to obtain geodesic longitude, latitude and height coordinates after terrain height correction; and the final geodetic coordinate of the scanning sampling point on the terrain is obtained. The simulation result obtained by the method can provide reference for positioning evaluation of the satellite detector before in-orbit.

Description

Technical Field

[0001] This application belongs to the technical field of satellite detection, and particularly relates to a method for simulating the geodetic coordinate positioning of satellite cross-track scanning sampling points. Background Technique

[0002] Satellite cross-track scanning is a working mode of satellite detectors. In this mode, the detector scans in a direction perpendicular to the satellite flight trajectory. Currently, microwave radiometers on low-Earth orbit satellites (such as ATMS carried on the US Suomi-NPP satellite, MWTS-II and MWHS-II carried on the Chinese FY3D satellite, etc.), and medium-resolution spectral imagers (such as VIIRS carried on the US Suomi-NPP satellite, MERSI-II carried on the Chinese FY3D satellite, etc.) mostly adopt the cross-track scanning mode. Cross-track scanning can obtain more extensive ground information, which helps to comprehensively monitor the Earth. By optimizing the detector design and data processing algorithms, high-resolution image acquisition can be achieved through cross-track scanning. The evaluation of these detectors before being put into orbit is very important. Among them, the positioning evaluation of the scanning sampling points of satellite detectors is a key item. Although the internal structures and detection principles of these different detectors are different, the positioning principle of the observation vector at the outlet of the instrument scanning points on the Earth ellipsoid is the same. Therefore, for any low-Earth orbit satellite, once the satellite orbit, the installation position of the satellite detector, and the scanning angle of the detector scanner are determined, then the geodetic coordinates of the points scanned by the satellite detector on the Earth ellipsoid are also determined. It can be seen that the positioning of the cross-track scanning sampling points of low-Earth orbit satellites is a general method, and its simulation results have important reference significance for the positioning evaluation of detectors before being put into orbit.

[0003] Generally, detectors need to perform positioning evaluation work on scanning sampling points before the satellite is put into orbit. Currently, existing software or algorithms only focus on the simulation of satellite orbits, and lack simulation evaluation of the positioning of cross-track scanning detector scanning sampling points. Regarding the issues of how changes in the scanning angle of the detector, the installation position and angle of the detector, the attitude of the satellite, and orbital parameters affect the positioning change of the detector scanning sampling points after the satellite is in orbit, existing simulation means cannot meet this requirement. Therefore, there is an urgent need for a method for simulating the geodetic coordinate positioning of satellite cross-track scanning sampling points. Summary of the Invention

[0004] In view of this, this application aims to propose a method for simulating the geodetic coordinate positioning of satellite cross-track scanning sampling points to solve the problem that traditional simulation methods lack simulation evaluation of the positioning of cross-track scanning detector scanning sampling points.

[0005] To achieve the above object, the technical solution of this application is realized as follows: This application provides a method for simulating the geodetic coordinate positioning of satellite cross-track scanning sampling points, including: Given the observation vector of the detector pointing towards the nadir direction, and obtaining the observation vector in the detector coordinate system according to the scan angle, where the scan angle is the angle between the observation vector and the Z-axis of the detector coordinate system; Obtaining the observation vector in the satellite coordinate system according to the detector installation matrix, based on the observation vector in the satellite coordinate system, and obtaining the observation vector in the orbital coordinate system according to the satellite attitude matrix, where the installation matrix is the transformation matrix from the detector coordinate system to the satellite coordinate system; According to the obtained satellite position vector and velocity vector, to determine the transformation matrix between the orbital coordinate system and the Earth-centered Earth-fixed coordinate system, and obtaining the observation vector in the Earth-centered Earth-fixed coordinate system according to the observation vector in the orbital coordinate system and the transformation matrix; According to the major axis, minor axis and eccentricity of the Earth ellipsoid, and based on the observation vector in the Earth-centered Earth-fixed coordinate system and the satellite position vector, obtaining the geodetic longitude, latitude and altitude coordinates of the satellite scan sampling points in the WGS84 coordinate system; Using the DEM terrain database to obtain the geodetic longitude, latitude and altitude coordinates after terrain height correction, and further obtaining the final geodetic coordinates of the scan sampling points on the terrain.

[0006] Furthermore, taking the origin of the detector coordinate system as the starting point, the unit vector along the positive direction of the Z-axis is the given observation vector of the detector pointing towards the nadir direction; Obtaining the observation vector in the detector coordinate system according to different scan angles, specifically: ; In the formula, represents the scan angle, represents the observation vector in the detector coordinate system.

[0007] Furthermore, the observation vector in the satellite coordinate system is: ; The attitude changes of the satellite in orbit include pitch, roll and yaw. The transformation matrix from the satellite coordinate system to the orbital coordinate system is composed of the transformation matrix determined by the pitch angle, the transformation matrix determined by the roll angle and the transformation matrix determined by the yaw angle in sequence product. Then the observation vector in the orbital coordinate system is: ; In the formula, represents the installation matrix, represents the observation vector in the satellite coordinate system, represents the observation vector in the orbital coordinate system, represents the transformation matrix from the satellite coordinate system to the orbital coordinate system, represents the pitch angle, represents the roll angle, represents the yaw angle.

[0008] Further, according to the orbital parameters of the satellite, the velocity vector and position vector of the satellite at each moment on the orbit are obtained, and the transformation matrix between the orbital coordinate system and the Earth-centered Earth-fixed coordinate system is determined from the velocity vector and the position vector, specifically: ; , and are all column vectors of vectors, and their vector calculation formulas are respectively: ; In the formula, and are respectively the satellite position vector and velocity vector in the Earth-centered Earth-fixed coordinate system, is the vector pointing from to , represents the position vector on the Earth ellipsoid corresponding to the nadir scanning direction in the Earth-centered Earth-fixed coordinate system, represents the transformation matrix between the orbital coordinate system and the Earth-centered Earth-fixed coordinate system; Finally, the observation vector in the Earth-centered Earth-fixed coordinate system is: ; In the formula, u represents the observation vector in the Earth-centered Earth-fixed coordinate system.

[0009] Further, according to the major and minor axes and eccentricity of the Earth ellipsoid, the geodetic longitude, latitude and height coordinates of the satellite scanning sampling points in the WGS84 coordinate system are given. The straight line where the observation vector starting from the satellite position intersects the Earth ellipsoid, and the intersection point closest to the satellite position is used as the scanning sampling point on the Earth ellipsoid; According to the major semi-axis and minor semi-axis of the Earth ellipsoid, the vector length is rescaled, and the rescaled observation vector and satellite position vector are: ; Among them, , , and , , are respectively the three components of the observation vector and the satellite position vector in the WGS84 coordinate system, represents the major semi-axis of the Earth ellipsoid, is the minor semi-axis of the Earth ellipsoid; According to the geometric relationship, it can be obtained that: ; The scaling ratio can be obtained by solving the equation: ; Restore the original scanned sampling point position vector using the scaling ratio: ; According to the coordinate transformation, convert the WGS84 rectangular coordinates of the scanned sampling point position vector into WGS84 geodetic longitude, latitude, and altitude coordinates: ; Among them, , , are the three rectangular coordinate components of the original scanned sampling point position vector x, represents the scaled scanned point position vector, represents the observation vector and the satellite position vector the included angle formed between them, represents the scaling ratio.

[0010] Furthermore, calculate the local ellipsoidal normal unit vector according to the geodetic longitude and latitude at the original scanned sampling point position vector: ; In the formula, represents the local ellipsoidal normal unit vector; Calculate the unit vector from the original scanned sampling point position vector to the satellite position vector: ; Calculate the component of the unit vector in the local vertical direction: ; Calculate the distance from the original scanned sampling point position vector along the unit vector direction to the maximum terrain height: ; Calculate the vector from the original scanned sampling point position vector along the unit vector direction to the maximum terrain height: ; Convert to geodetic coordinates , start from the point define the initial point on the ellipsoid surface, and define a new set of points along the initial point to the original scanned point position vector, denoted as , according to the geometric relationship, we can get: ; Perform terrain cross-iteration and define the initial value as: ; Along the initial point Iteratively solve continuously in the direction of the position vector from the initial point to the original scan point as follows: ; Until , then exit the loop iteration.

[0011] Furthermore, it also includes: Calculate the geodetic longitude, latitude, and altitude coordinates of the corrected scan sampling point position vector based on the results of the last two iterations: ; Wherein, ; In the formula, Represents the result of the last iteration, Represents the result of the penultimate iteration, Represents the height between the minimum terrain height and the terrain surface; The final geodetic coordinates of the scan sampling point position vector on the terrain Is obtained from .

[0012] Compared with the prior art, the geodetic coordinate positioning simulation method for a satellite cross-track scan sampling point described in this application has the following beneficial effects: The geodetic coordinate positioning simulation method for a satellite cross-track scan sampling point described in this application provides a simulation model for the geodetic coordinate positioning of the scan sampling point of a low-orbit satellite cross-track scanner, provides a reference for evaluating the influence of parameters such as the scan angle of the scanner, the installation position and angle of the scanner relative to the satellite, and the attitude angle of the satellite on the geodetic coordinates of the scan sampling point, and solves the positioning evaluation problem of the low-orbit satellite cross-track scanner before it is on orbit. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The accompanying drawings forming a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation of this application. In the drawings: Figure 1 Is a flowchart of the geodetic coordinate positioning simulation method for a satellite cross-track scan sampling point described in an embodiment of this application; Figure 2 Is a schematic diagram of the detector coordinate system and the scan plane described in an embodiment of this application; Figure 3 Is a schematic diagram of the Earth-centered Earth-fixed coordinate system and the orbital coordinate system described in an embodiment of this application; Figure 4 Schematic diagram of the geometric relationship among the observation vector, satellite position vector, and scanning sampling point position vector described in the embodiments of the present application; Figure 5 Schematic diagram of iteratively correcting the geodetic longitude, latitude, and altitude according to the terrain altitude described in the embodiments of the present application; Figure 6 Graph of the simulation test results described in the embodiments of the present application. Detailed implementation manners

[0014] To make the objectives, technical solutions, and advantages of the present application clearer and more understandable, the following further details the present application in conjunction with specific embodiments and with reference to the accompanying drawings.

[0015] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present application should have the ordinary meanings understood by those of ordinary skill in the art to which the present application belongs. The "first", "second", and similar terms used in the embodiments of the present application do not denote any order, quantity, or importance, but are only used to distinguish different components. The terms such as "including" or "comprising" mean that the elements or objects appearing before this term cover the elements or objects listed after this term and their equivalents, without excluding other elements or objects. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left", and "right" are only used to represent relative position relationships, and when the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0016] Please refer to Figure 1 As shown, this embodiment provides a method for simulating the geodetic coordinate positioning of satellite cross-track scanning sampling points, specifically including the following steps: Step S101: Given the observation vector of the detector pointing to the nadir direction, and obtain the observation vector in the detector coordinate system according to the scanning angle, where the scanning angle is the angle between the observation vector and the Z-axis of the detector coordinate system.

[0017] Specifically, in this embodiment, in the detector coordinate system, the origin is a certain point O inside the detector, the X-axis is perpendicular to the scanning plane (YOZ plane), and the positive direction of the Z-axis points to the nadir direction (such as Figure 2 ), starting from the origin of the detector coordinate system, the unit vector along the positive direction of the Z-axis is the given observation vector of the detector pointing to the nadir direction.

[0018] The scan angle is the angle between the viewing vector and the Z-axis of the detector coordinate system. It is stipulated that the scan angle is zero when the viewing vector coincides with the Z-axis of the detector coordinate system. Looking along the positive X-axis of the detector coordinate system, the scan angle is positive when moving counterclockwise away from the Z-axis, and negative when moving clockwise away from the Z-axis. Thus, for different scan angles , the viewing vector is as follows: .

[0019] Step S102: Obtain the viewing vector in the satellite coordinate system based on the detector installation matrix. Based on the viewing vector in the satellite coordinate system and according to the satellite attitude matrix, obtain the viewing vector in the orbital coordinate system, where the installation matrix is the transformation matrix between the detector coordinate system and the satellite coordinate system.

[0020] Specifically, in this embodiment, the detector is installed at a fixed position on the satellite in a certain way. Therefore, there is a distance between the origin of the detector coordinate system and the origin of the satellite coordinate system. The transformation matrix from the detector coordinate system to the satellite coordinate system is called the installation matrix , and thus the viewing vector in the satellite coordinate system is:

[0021] If the position of the detector is disturbed for some reason after the satellite is in orbit, this situation can be simulated by adding perturbations to the installation matrix.

[0022] The attitude changes of the satellite in orbit include pitch, roll, and yaw, which will cause a deviation between the origin of the satellite coordinate system and the origin of the orbital coordinate system. The transformation matrix from the satellite coordinate system to the orbital coordinate system is composed of the transformation matrix determined by the pitch angle , the transformation matrix determined by the roll angle , and the transformation matrix determined by the yaw angle in sequence product. Thus, the viewing vector in the orbital coordinate system is: .

[0023] Step S103: Determine the transformation matrix between the orbital coordinate system and the Earth-centered Earth-fixed coordinate system based on the obtained satellite position vector and velocity vector. Obtain the viewing vector in the Earth-centered Earth-fixed coordinate system based on the viewing vector in the orbital coordinate system and the transformation matrix.

[0024] Specifically, in this embodiment, the satellite position and velocity vectors are obtained by simulating with STK software. The orbital parameters in the two-line element set of the satellite are input into the STK software to obtain the velocity and position of the satellite at each moment on the orbit (vectors in the Earth-Centered Earth-Fixed coordinate system), and the time resolution is based on the time interval of the scanning time sequence (i.e., each moment of the satellite velocity and position vectors in the time series corresponds to the moment of each scanning sampling point).

[0025] From the position vector of the satellite and the velocity vector the transformation matrix between the orbital coordinate system and the Earth-Centered Earth-Fixed coordinate system can be determined :

[0026] , and are all column vectors of the vectors, and their vector calculation formulas are respectively:

[0027] wherein, and are respectively the satellite position vector and velocity vector in the Earth-Centered Earth-Fixed coordinate system, represents the vector pointing from to , represents the position vector on the Earth ellipsoid corresponding to the nadir direction of the scan in the Earth-Centered Earth-Fixed coordinate system (such as Figure 3 ).

[0028] Finally, the observation vector in the Earth-Centered Earth-Fixed coordinate system is: .

[0029] Step S104, according to the major axis, minor axis and eccentricity of the Earth ellipsoid, and based on the observation vector and satellite position vector in the Earth-Centered Earth-Fixed coordinate system, obtain the geodetic longitude, latitude and height coordinates of the satellite scanning sampling point in the WGS84 coordinate system.

[0030] Specifically, in this embodiment, the geodetic longitude, latitude and height coordinates of the satellite scanning sampling point in the WGS84 coordinate system are given according to the major axis, minor axis and eccentricity of the Earth ellipsoid, Figure 4 the plane shown is the section formed by the observation vector and the satellite position vector . The straight line where the observation vector starting from the satellite position intersects the Earth ellipsoid surface, and the nearest intersection point to the satellite position is the scanning sampling point on the Earth ellipsoid surface. The position vector of this point in the WGS84 coordinate system (the rectangular coordinate representation of the WGS84 coordinate system is equal to that of the Earth-Centered Earth-Fixed coordinate system) is .

[0031] First, according to the semi-major axis and the semi-minor axis of the Earth ellipsoid, re-scale the vector length so that the position vector of the scan sampling points on the Earth ellipsoid after scaling has a length of 1. The scaled observation vector and satellite position vector are:

[0032] In the formula, , , and , , are the three components of the observation vector and the satellite position vector in the WGS84 coordinate system respectively.

[0033] Then, according to the geometric relationship of Figure 4 , we can get:

[0034] Solving the above equation, we can obtain the scaling ratio :

[0035] Then, use the scaling ratio to restore the original position vector of the scan sampling points:

[0036] Finally, according to the coordinate transformation, convert the WGS84 rectangular coordinates of the scan sampling point position vector into WGS84 geodetic longitude, latitude and height coordinates:

[0037] In the formula, , , are the three rectangular coordinate components of the scan sampling point position vector , and represents the included angle formed between the observation vector and the satellite position vector .

[0038] Step S105: Use the DEM terrain database to obtain the terrain height-corrected geodetic longitude, latitude and height coordinates, and then obtain the final geodetic coordinates of the scan sampling point position on the terrain.

[0039] Specifically, in this embodiment, as Figure 5As shown, the topographic surface of the Earth has height, and the observation vector does not penetrate the terrain to the Earth ellipsoid surface. The actual scan sampling point position will be at the point where the observation vector first intersects the terrain. The longitude, latitude, and height (topographic height) at this point are the geodetic longitude, latitude, and height corrected according to the terrain.

[0040] First, calculate the local ellipsoid normal unit vector at the geodetic longitude and latitude of the original scan sampling point position vector on the Earth ellipsoid:

[0041] Calculate the unit vector from the original scan sampling point position vector on the Earth ellipsoid to the satellite position vector:

[0042] Calculate the component of the unit vector in the local vertical direction:

[0043] Calculate the distance from the original scan sampling point position vector on the Earth ellipsoid along the unit vector to the maximum terrain height :

[0044] Calculate the vector from the original scan sampling point position vector on the Earth ellipsoid along the unit vector to the maximum terrain height :

[0045] Convert to geodetic coordinates , define a point on the ellipsoid starting from point (i.e., Figure 5 in ), and define a new point (i.e., to ) every approximately 500 meters (the spatial resolution of the terrain height data in the DEM topographic database) along the direction from . According to the geometric relationship, we can obtain:

[0046] Next, terrain cross-iteration begins, with the initial values being:

[0047] Among them, represents the terrain height corresponding to the longitude and latitude matched according to the DEM terrain database (it should be noted that the elevation of all grid points less than 0 is modified to 0).

[0048] Along to the direction, continuous iterative solution is carried out as follows:

[0049] Until , the loop iteration is exited.

[0050] Then, based on the results of the last two iterations, the corrected geodetic longitude, latitude, and altitude coordinates of the scanning sampling points are calculated:

[0051] Among them,

[0052] In the formula, represents the result of the last iteration, represents the result of the penultimate iteration. If is less than 0, then is changed to 0.

[0053] Finally, the final geodetic coordinates of the scanning sampling point on the terrain are given by .

[0054] The method described in this embodiment provides a simulation model for the geodetic coordinate positioning of the scanning sampling points of the cross-track scanning detector of a low-orbit satellite, and provides a reference for the evaluation of the influence of parameters such as the scanning angle of the detector, the installation position and angle of the detector relative to the satellite, and the attitude angle of the satellite on the geodetic coordinates of the scanning sampling points, and solves the problem of the positioning evaluation of the cross-track scanning detector of a low-orbit satellite before orbit.

[0055] Embodiment 1 Figure 6The spatial distribution map (using Mercator projection) of the geodetic coordinate results of the satellite cross-track scanning sampling points simulated by the above method is given. The simulation time period is from 04:00:00.000 seconds (UTC) on December 20, 2024 to 06:00:00.000 seconds (UTC) on December 20, 2024; the orbital parameters are orbital inclination 97.54°, right ascension of the ascending node 62.5894°, orbital eccentricity 0, argument of perigee 105°, mean anomaly 0, number of orbits around the Earth per day 15.094, installation matrix is the identity matrix, all three satellite attitude angles are 0, the semi-major axis and eccentricity of the Earth ellipsoid are taken as 6378137 meters and 0.081819191 respectively; the DEM terrain database used is the GEBCO grid released in July 2024, which is a global terrain model of the ocean and land, providing elevation data in meters on a grid at 15 arc-second intervals (where all grid points with heights less than 0 are changed to 0). The simulation results have important reference significance for the positioning evaluation of the satellite pre-orbit scanning sampling points.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered by the scope of the claims and the description of the present invention.

[0057] The embodiments of the present application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the embodiments of the present application shall be included within the protection scope of the present application.

Claims

1. A geodetic coordinate positioning simulation method for satellite cross-track scanning sampling points, characterized in that: include: Given an observation vector pointing to the nadir direction of the detector, the observation vector in the detector coordinate system is obtained according to the scanning angle, wherein the scanning angle is the angle between the observation vector and the Z axis of the detector coordinate system; Obtaining an observation vector in the satellite coordinate system according to the detector installation matrix, and obtaining an observation vector in the orbital coordinate system based on the observation vector in the satellite coordinate system and according to the satellite attitude matrix, wherein the installation matrix is ​​a conversion matrix between the detector coordinate system and the satellite coordinate system; Determine a transformation matrix from the orbital coordinate system to the Earth-centered Earth-fixed coordinate system based on the acquired satellite position vector and velocity vector, and obtain an observation vector in the Earth-centered Earth-fixed coordinate system based on the observation vector in the orbital coordinate system and the transformation matrix; According to the major and minor axes and eccentricity of the earth ellipsoid, and based on the observation vector and satellite position vector in the earth-centered earth-fixed coordinate system, the geodetic longitude, latitude and altitude coordinates of the satellite scanning sampling point in the WGS84 coordinate system are obtained; The DEM terrain database is used to obtain the geodetic longitude, latitude and altitude coordinates after terrain height correction, and then the final geodetic coordinates of the scanning sampling points on the terrain are obtained.

2. The method according to claim 1, characterized in that: Taking the origin of the detector coordinate system as the starting point, the unit vector along the positive Z axis is the observation vector of a given detector pointing in the nadir direction; The observation vector in the detector coordinate system is obtained according to different scanning angles, specifically: ； In the formula, represents the scanning angle, represents the observation vector in the detector coordinate system.

3. The method according to claim 2, characterized in that The observation vector in the satellite coordinate system is: ； The attitude changes of the satellite in orbit include pitch, roll and yaw. The transformation matrix from the satellite coordinate system to the orbital coordinate system is composed of the transformation matrix determined by the pitch angle, the transformation matrix determined by the roll angle and the transformation matrix determined by the yaw angle in sequence. The observation vector in the orbital coordinate system is: ； In the formula, represents the installation matrix, represents the observation vector in the satellite coordinate system, represents the observation vector in the orbital coordinate system, Represents the transformation matrix from the satellite coordinate system to the orbital coordinate system, represents the pitch angle, represents the roll angle, Indicates the yaw angle.

4. The method according to claim 3, characterized in that: The velocity vector and position vector of the satellite at each moment in orbit are obtained according to the orbital parameters of the satellite, and the transformation matrix between the orbital coordinate system and the Earth-centered Earth-fixed coordinate system is determined by the velocity vector and the position vector, which is specifically: ； , and They are all column vectors of vectors, and their vector calculation formulas are: ； In the formula, and are the satellite position vector and velocity vector in the Earth-centered Earth-fixed coordinate system, Is point to The vector of It represents the position vector on the Earth ellipsoid surface corresponding to the nadir direction of the scan in the Earth-centered Earth-fixed coordinate system. Represents the transformation matrix between the orbital coordinate system and the Earth-centered Earth-fixed coordinate system; The final observation vector in the Earth-centered Earth-fixed coordinate system is: ； Where u represents the observation vector in the Earth-centered Earth-fixed coordinate system.

5. The method according to claim 4, characterized in that: The geodetic longitude, latitude and altitude coordinates of the satellite scanning sampling point in the WGS84 coordinate system are given according to the major and minor axes and eccentricity of the earth ellipsoid. The straight line where the observation vector starting from the satellite position intersects with the earth ellipsoid surface, and the intersection point closest to the satellite position is taken as the scanning sampling point on the earth ellipsoid surface; Rescale the vector length according to the major and minor axes of the earth ellipsoid. The scaled observation vector and satellite position vector are: ； in, , , and , , The observation vectors are and the satellite position vector The three components in the WGS84 coordinate system are: represents the semi-major axis of the Earth ellipsoid, is the semi-minor axis of the Earth ellipsoid; According to the geometric relationship, we can get: ； Solving the equation gives the scaling factor: ； Use the scaling factor to restore the original scan sampling point position vector: ； According to the coordinate transformation, the WGS84 rectangular coordinates of the scanning sampling point position vector are converted into WGS84 geodetic longitude, latitude and altitude coordinates: ； in, , , are the three rectangular coordinate components of the original scan sampling point position vector x, represents the scaled scan point position vector, Represents the observation vector and the satellite position vector The angle formed between Indicates the zoom ratio.

6. The method according to claim 5, characterized in that: Calculate the local ellipsoid normal unit vector based on the geodetic longitude and latitude at the original scanning sampling point position vector: ； In the formula, represents the local ellipsoid normal unit vector; Calculate the unit vector from the raw scan sample point position vector to the satellite position vector: ； Calculating the unit vector Component in the local vertical direction: ； Calculate the position vector from the original scan sample point along the unit vector Distance from the direction to the maximum terrain height: ； Calculate the position vector from the original scan sample point along the unit vector Vector direction to the maximum terrain height: ； Will Convert to geodetic coordinates , from point Start by defining the initial point on the ellipsoid , a set of new points are defined along the position vector from the initial point to the original scan point, expressed as According to the geometric relationship, we can get: ； Perform terrain cross iteration and define the initial value as: ； Along the initial point The direction of the original scanning point position vector is iterated and solved as follows: ； until , then exit the loop iteration.

7. The method according to claim 6, characterized in that Also includes: Calculate the corrected longitude, latitude and altitude coordinates of the scan sampling point position vector based on the results of the last two iterations: ； in, ； In the formula, represents the result of the last iteration, represents the result of the second-to-last iteration, Indicates the height between the minimum terrain height and the terrain surface; The final geodetic coordinates of the position vector of the scanned sampling point on the terrain Depend on get.

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