Coordinate measurement method of central axis corner reflector

Abstract

The application discloses a coordinate measurement method of a central-axis corner reflector, which comprises the following steps: constructing an office coordinate system with the center point of a servo system spherical ball of the corner reflector as a coordinate origin; obtaining the coordinates of the corner reflector in the office coordinate system, and calculating the coordinates of the office coordinate system mark points by using a rotation matrix equation; obtaining the geographic coordinate system mark point coordinates of the corner reflector; constructing and solving a conversion equation based on the office coordinate system mark point coordinates and the geographic coordinate system mark point coordinates of the corner reflector; and calculating the geographic coordinates of the phase center of the corner reflector according to the conversion equation. The application can complete the conversion between the office and field coordinates of the corner reflector, and can solve the geographic coordinate system coordinates of the corner reflector under any orientation angle and pitch angle.

Description

Technical Field

[0001] The present invention relates to the field of measurement technology, and in particular to a coordinate measurement method of a central axis corner reflector. Background Art

[0002] Synthetic Aperture Radar (SAR) satellites, capable of providing all-day, all-weather Earth imaging, play a vital role in my country's natural resource management and disaster response. To ensure the quality of SAR satellite imaging, after launch, they undergo geometric calibration using ground-based corner reflectors (CRs), achieving extremely high levels of planar positioning accuracy.

[0003] There are basically two ways to measure corner reflectors. One is fixed and the other is rotating. For fixed corner reflectors, after calculating the heading angle and incident angle of the satellite, the layout of the corner reflector is calculated according to the geometric parameters, and then the corner reflector is placed at the calculated position and no longer adjusted. The coordinates of the corner reflector are measured once using GNSS or a total station. For rotating corner reflectors, CORS equipment is often used for observation. However, during the observation process, the independence of the CORS equipment and the SAR equipment is difficult to guarantee, especially for L-band SAR satellites, which use the same frequency band as GNSS positioning. If the GNSS equipment is bound, interference will occur between the two. In addition, for the central axis corner reflector, its rotation point is on the central axis, not at the corner reflector vertex. CORS cannot accurately measure the position coordinates under certain heading and pitch angle conditions during the rotation of the corner reflector, and its accuracy is insufficient.

[0004] The present invention proposes a new coordinate measurement method, namely the feature point control measurement method, which is used to give the coordinate value under any heading angle and pitch angle conditions, providing support for the precise measurement and geometric calibration of the phase center of the corner reflector. Summary of the Invention

[0005] In order to solve the above technical problems, the purpose of the present invention is to provide a coordinate measurement method for a central axis corner reflector. The purpose of this method is to obtain the geodetic coordinate value of the phase center of the corner reflector by calculation by simply inputting the orientation angle and pitch angle of the corner reflector; and solves the problem that the position coordinates of the corner reflector under certain orientation angle and pitch angle conditions cannot be accurately measured during the rotation of the rotating corner reflector.

[0006] The present invention utilizes the heading angle and pitch angle of the input corner reflector to obtain the coordinates of the corner reflector's marker point in the internal coordinate system through calculation, and constructs a conversion equation based on the coordinates of the corner reflector's marker point in the internal coordinate system and the coordinates of the marker point in the measured geographic coordinate system. Finally, the conversion equation is constructed and solved to obtain the coordinate value of the phase center of the corner reflector.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] A coordinate measurement method for a central axis corner reflector, comprising:

[0009] Step S1: construct an indoor coordinate system with the center point of the servo system sphere of the corner reflector as the coordinate origin;

[0010] Step S2 obtains the coordinates of the corner reflector in the internal coordinate system, and uses the rotation matrix equation to calculate the coordinates of the marker point in the internal coordinate system;

[0011] Step S3 obtains the coordinates of the geographic coordinate system marker point of the corner reflector;

[0012] Step S4 constructs and solves a conversion equation based on the coordinates of the marker point in the corner reflector's internal coordinate system and the coordinates of the marker point in the geographic coordinate system;

[0013] Step S5 calculates the geographic coordinates of the phase center of the corner reflector according to the conversion equation.

[0014] Compared with the prior art, one or more embodiments of the present invention may have the following advantages:

[0015] It can accurately provide the geodetic coordinates of the corner reflector phase center under any pitch and heading angle conditions, complete the conversion of the indoor and outdoor coordinates of the corner reflector, and calculate the geographic coordinate system coordinates of the corner reflector under any heading and pitch angle, providing support for the precise measurement and geometric calibration of the corner reflector phase center. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flow chart of the coordinate measurement method of the central axis corner reflector;

[0017] Figure 2a and 2b It is a schematic diagram of the geometric structure of the three-axis rotation servo gimbal corner reflector;

[0018] Figure 3a and 3b It is a geometric diagram constructed based on the office coordinate system;

[0019] Figure 4 This is the viewing angle geometric parameter diagram of the three-axis rotation servo gimbal corner reflector;

[0020] Figure 5a and5b It is a geometric relationship diagram between the incident angle and the lifting angle of the corner reflector. DETAILED DESCRIPTION

[0021] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention will be described in further detail below with reference to embodiments and accompanying drawings.

[0022] like Figure 1 FIG. 1 shows a coordinate measurement method for a central axis corner reflector, comprising the following steps:

[0023] Step S1: construct an indoor coordinate system with the center point of the servo system sphere of the corner reflector as the coordinate origin;

[0024] The center point of the servo system sphere of the artificial corner reflector is used as the coordinate origin O, the east direction (E) as the X-axis, the height direction (H) as the Z-axis, and the south direction (S) as the Y-axis to construct the indoor coordinate system.

[0025] Step S2 obtains the coordinates of the corner reflector in the internal coordinate system, and uses the rotation matrix equation to calculate the coordinates of the marker point in the internal coordinate system;

[0026] like Figure 2a-Figure 5b Specifically, step S2 includes the following:

[0027] S2.1 defines the positive and negative signs of the three-axis rotation angles, taking clockwise rotation as positive, and constructs the rotation matrices of the artificial corner reflector when it rotates around the X axis, Y axis, and Z axis respectively. The rotation matrices when rotating around the X axis, Y axis, and Z axis are R X (θ x ), R Y (θ y ) and R Z (θ z ), the corresponding expressions are:

[0028]

[0029] Among them, θ x ,θ y ,θ z They are the rotation angles around the X, Y, and Z axes respectively.

[0030] Step S2.1 specifically includes the following steps:

[0031] Step S2.1.1, determining the pitch angle, heading angle, and rotation angle around the X-axis of the artificial corner reflector.

[0032] Determine the angle θ of the corner reflector rotating around the Y and Z axes respectively y ,θ z, that is, determine the pitch angle and heading angle of the artificial corner reflector; and determine the angle θ of the corner reflector rotating around the X axis x , usually set to 0; specifically, Figure 5a and Figure 5b As shown, the geometric structure of the corner reflector can be calculated. When the radar beam is incident on the corner reflector, it should be perpendicular to the top surface P2P3P4 of the corner reflector. At this time, the angle between the radar beam P1E and P1P4 is 54.74°. When the radar wave incident angle θ is less than 54.74°, the corner reflector needs to be lifted upward so that the radar wave is perpendicular to the top surface P2P3P4 of the corner reflector. The lifting angle is α, which is expressed as a counterclockwise rotation angle α around the Y axis in the three-dimensional coordinate system. The relationship between the local incident angle of the radar wave and α is:

[0033] α=54.74°-θ (4)

[0034] Step S2.1.2, determining the rotation matrix of the artificial corner reflector when it rotates around the X-axis, Y-axis, and Z-axis.

[0035] From step S2.1, we can see that R Y (θ y ) can be converted to:

[0036]

[0037] Since the north direction of the coordinate azimuth angle β is positive, the corner reflector needs to be rotated 90° clockwise around the Z axis to reach the east zero state, and then:

[0038] θ z =β-90° (6)

[0039] R Z (θ z ) can be converted to:

[0040]

[0041] Step S2.2: Based on the geometric relationship between the artificial corner reflector and the servo rotation system, determine the initial coordinates (X0, Y0, Z0) of the four vertices of the artificial corner reflector when returning to zero in the east direction in the indoor coordinate system: P1 = (-0.4, 0, 0.1); P2 = (0.661, 1.061, 0.1); P3 = (0.661, -1.061, 0.1); P4 = (-0.4, 0, 1.6);

[0042] Step S2.3, using the initial coordinates and rotation matrix of the four vertices of the artificial corner reflector in the internal coordinate system, calculate the coordinates of the marker points in the internal coordinate system of the artificial corner reflector.

[0043] Step S2.3.1: Determine the rotation matrix R of the artificial corner reflector in the internal coordinate system:

[0044] R=R X (θ x )·R Y (θ y )·R Z (θ z ) (8)

[0045] Step S2.3.2: Determine the coordinates of the internal coordinate system marker points, that is, the four vertices of the artificial corner reflector rotate around the X, Y, and Z axes by θ x ,θ y ,θ z The coordinates after the angle are:

[0046]

[0047] In step S2.3.3, since the internal coordinate system takes the south direction as positive, which is opposite to the geodetic coordinate system where the north direction is positive, the sign of the Y-axis coordinate needs to be reversed.

[0048] Step S3 obtains the coordinates of the geographic coordinate system marker point of the corner reflector;

[0049] In this step, the coordinates of the corner reflector's geographic coordinate system marker points are obtained by using two methods: total station eccentricity measurement and GNSS observation.

[0050] Step S4 constructs and solves a conversion equation based on the coordinates of the marker point in the corner reflector's internal coordinate system and the coordinates of the marker point in the geographic coordinate system;

[0051] Specifically, step S4.1 determines the direction cosines of the X, Y, and Z axes of the office coordinate system O-XYZ in the geographic coordinate system:

[0052] The direction cosines of the X-axis, Y-axis, and Z-axis in the geographic coordinate system O'-X'Y'Z' are (a1 b1 c1), (a2 b2c2), and (a3 b3 c3), respectively.

[0053] Step S4.2, determine the scale ratio μ between the internal coordinate system and the geographic coordinate system. In geodetic and engineering surveying, μ is close to 1.

[0054] Step S4.3: Determine the translation of the origin of the internal coordinate system O-XYZ relative to the origin of the geographic coordinate system O'-X'Y'Z'

[0055] Step S4.4: Determine the rotation matrix M for the conversion between the internal coordinate system and the geographic coordinate system.

[0056]

[0057] In step S4.5, the conversion equation between the office coordinate system and the geographic coordinate system is:

[0058]

[0059] The calculation of each parameter is as follows:

[0060] If M satisfies MM T =M T M=E, then M is an orthogonal matrix, and the corresponding coordinate transformation is an orthogonal transformation. If M is an orthogonal matrix, then the following conditions must exist:

[0061]

[0062] Therefore, there are only 3 independent parameters in the M matrix, and the remaining 6 parameters can be deduced from the above conditions. If a2, a3, and b3 are taken as independent parameters, the remaining 6 parameters are:

[0063]

[0064] If there are more than three common points, applying the least squares method to solve Equation (11) yields three translation parameters, three rotation parameters, and one scale parameter. However, since the M matrix in Equation (11) has only three independent parameters and the remaining six parameters are nonlinear functions, directly solving Equation (10) would be very complex. Therefore, the following method is used to solve this problem.

[0065] Assuming that the unknowns are 3 translation parameters, 1 scale parameter, and 9 direction cosine parameters, then Equation (10) can be expanded using Taylor series to obtain:

[0066]

[0067] In the formula, the numbers with superscript 0 are approximate values, and dx', dy', dz', dμ, da1, da2, da3, db1, db2, db3, dc1, dc2, and dc3 are correction numbers. Formula (14) can be written as the error equation as follows:

[0068] V=AX+L (15)

[0069] Where, V=[V X' V Y' V Z' ] T

[0070]

[0071] X=[dx' dy' dz' dμ da1 da2 da3 db1 db2 db3 dc1 dc2 dc3] T

[0072]

[0073] However, a1, a2, a3, b1, b2, b3, c1, c2, and c3 are related. According to formula (12), the conditional equation can be listed as follows:

[0074] BX+W=0 (16)

[0075]

[0076] By solving equations (15) and (16) using the conditional indirect adjustment method, we can obtain X.

[0077] Step S5 calculates the geographic coordinates of the phase center of the corner reflector according to the conversion equation.

[0078] Although the embodiments disclosed herein are as described above, the contents described herein are merely embodiments for facilitating understanding of the present invention and are not intended to limit the present invention. Any person skilled in the art may make any modifications and variations in the form and details of the embodiments without departing from the spirit and scope of the present invention. However, the scope of patent protection of the present invention shall remain subject to the scope defined by the appended claims.

Claims

1. A coordinate measurement method for a central axis corner reflector, characterized in that: The method comprises the following steps: Step S1: construct an indoor coordinate system with the center point of the servo system sphere of the corner reflector as the coordinate origin; Step S2 obtains the coordinates of the corner reflector in the internal coordinate system, and uses the rotation matrix equation to calculate the coordinates of the marker point in the internal coordinate system; Step S3 obtains the coordinates of the geographic coordinate system marker point of the corner reflector; Step S4 constructs and solves a conversion equation based on the coordinates of the marker point in the corner reflector's internal coordinate system and the coordinates of the marker point in the geographic coordinate system; Step S5 calculates the geographic coordinates of the corner reflector phase center according to the conversion equation; Step S2 specifically includes: Step S2.1 defines the positive and negative signs of the three-axis rotation angles, taking clockwise rotation as positive, and constructs the rotation matrices of the corner reflector when it rotates around the X axis, Y axis, and Z axis respectively. The rotation matrices when it rotates around the X axis, Y axis, and Z axis are R X (θ x ), R Y (θ y ) and R Z (θ z ), the corresponding expressions are: Among them, θ x ,θ y ,θ z They are the angle values ​​of rotation around the X, Y, and Z axes respectively; Step S2.2: Based on the geometric relationship between the corner reflector and the servo rotation system, determine the initial coordinates (X0, Y0, Z0) of the four vertices of the corner reflector when returning to zero in the east direction in the internal coordinate system: P1=(-0.4,0,0.1); P2=(0.661,1.061,0.1); P3=(0.661,-1.061,0.1); P4=(-0.4,0,1.6); Step S2.3 uses the initial coordinates of the four vertices of the corner reflector in the internal coordinate system and the rotation matrix to calculate the coordinates of the corner reflector's internal coordinate system marker points; The step S2.1 specifically includes: Determine the angle θ of the corner reflector rotating around the Y, Z, and X axes respectively y ,θ z ,θ x , where θ x Set to 0, and calculated through the geometric structure of the corner reflector, when the radar beam is incident on the corner reflector, it is perpendicular to the top surface P2P3P4 of the corner reflector. At this time, the angle between the radar beam P1E and P1P4 is 54.74°; when the radar wave incident angle θ is less than 54.74°, the corner reflector is lifted upward so that the radar wave is perpendicular to the top surface P2P3P4 of the corner reflector. At this time, the lifting angle is α, which is expressed as a counterclockwise rotation angle α around the Y axis in the three-dimensional coordinate system. The relationship between the radar wave incident angle and α is: α=54.74°-θ Determine the rotation matrix R when the corner reflector rotates around the X, Y, and Z axes X (θ x ), R Y (θ y ) and R Z (θ z ), from step S2.1, R Y (θ y ) is converted to: Since the north direction of the coordinate azimuth angle β is positive, the corner reflector needs to be rotated 90° clockwise around the Z axis to reach the east zero state, and then: i z =β-90° R Z (θ z ) is converted to:

2. The coordinate measurement method of the central axis corner reflector according to claim 1, characterized in that: In step S1, the coordinate origin is O, and the internal coordinate system is constructed with the east direction E as the X axis, the height direction H as the Z axis, and the south direction S as the Y axis.

3. The coordinate measurement method of the central axis corner reflector according to claim 1, characterized in that: The step 2.3 specifically includes: Determine the rotation matrix R of the corner reflector in the indoor coordinate system: R=R X (i x )·R Y (i y )·R Z (i z ) Determine the coordinates of the internal coordinate system marker points, that is, the four vertices of the corner reflector rotate around the X, Y, and Z axes by θ x ,θ y ,θ z The coordinates after the angle are: Since the internal coordinate system takes the south direction as positive, which is opposite to the geodetic coordinate system where the north direction is positive, the sign of the Y-axis coordinate is reversed.

4. The coordinate measurement method of the central axis corner reflector according to claim 1, characterized in that: In step S3, the coordinates of the geographic coordinate system marker points of the corner reflector are obtained by using two methods: total station eccentricity measurement and GNSS observation.

5. The coordinate measurement method of the central axis corner reflector according to claim 1, characterized in that: The step S4 specifically includes: Step S4.1 Determine the direction cosines of the X, Y, and Z axes of the office coordinate system O-XYZ in the geographic coordinate system: The direction cosines of the X-axis, Y-axis, and Z-axis in the geographic coordinate system O'-X'Y'Z' are: (a1 b1 c1), (a2 b2 c2), (a3 b3 c3); Step S4.2 determines the scale ratio μ between the office coordinate system and the geographic coordinate system; Step S4.3 Determine the translation of the origin of the internal coordinate system O-XYZ relative to the origin of the geographic coordinate system O'-X'Y'Z' Step S4.4 Determine the rotation matrix M for the conversion between the internal coordinate system and the geographic coordinate system In step S4.5, the conversion equation between the office coordinate system and the geographic coordinate system is: The coordinates of the marker points in the internal coordinate system, that is, the four vertices of the corner reflector rotate around the X, Y, and Z axes respectively by θ x ,θ y ,θ z The coordinates after the angle; The coordinates are in the geographic coordinate system.

Images