Fitting solution method for center point coordinates of rotary table

Abstract

The invention discloses a fitting solution method for coordinates of a center point of a rotary table, and relates to the technical field of positioning navigation and control. The method comprises the following steps: firstly, setting a turntable to step according to a certain degree to obtain a plurality of position points, and solving a positioning result at each position point; selecting a midpoint of the two symmetrical position points as a reference point, establishing a station center coordinate system at the reference point, and converting coordinates of all the position points to the coordinate system; counting the sky-direction average value of all the position points again to serve as sky-direction coordinates of the center point of the rotary table; and using a least square method to fit the plane coordinates of the center point of the turntable. And obtaining the center point coordinate of the rotary table under the ECEF coordinate system through coordinate conversion. The method is convenient to implement and small in calculation amount, the center point coordinates of the rotary table can be rapidly calculated, and a calculation basis is provided for subsequent GNSS dynamic verification.

Description

Technical Field

[0001] The present invention relates to the technical field of positioning, navigation and control, and particularly to a method for fitting and solving the coordinates of the center point of a turntable. Background Art

[0002] For the dynamic verification of GNSS receiver indicators, it is necessary to obtain the true coordinates of the installation point under the high-speed rotation state of the receiver, and compare and analyze them with the coordinates calculated by the receiver through GNSS satellite navigation signals to obtain the accuracy of the receiver performance indicators.

[0003] The system operation satisfies the following conditions: 1) The load mounting disks at both ends of the turntable cantilever are located in the same horizontal plane. 2) The amplitude during the rotation of the turntable tabletop needs to be controlled at a low level.

[0004] Under the above constraints, if the precise coordinates of the turntable center point are known, the rotation angle of the turntable cantilever is obtained, and the geometric coordinates of the two endpoints of the turntable cantilever relative to the turntable center point can be calculated using the polar coordinate formula. After coordinate transformation, the true coordinates of the receiver antenna installation points at both ends of the turntable cantilever in the Earth-Centered Earth-Fixed coordinate system are finally calculated.

[0005] As can be seen from the above introduction, the precise coordinates of the turntable center point are of great significance for the dynamic verification and evaluation accuracy of GNSS receivers. The coordinates of the turntable center point can be obtained by solving the precise point positioning through continuous observation for 12 hours. This method requires installing a receiver antenna at the turntable center point, and no error can be introduced during the installation process. The error of the turntable center coordinates depends on the precise point positioning accuracy. Summary of the Invention

[0006] In view of this, the present invention proposes a method for fitting and solving the coordinates of the turntable center point. This method does not require installing an antenna at the turntable center point and is not sensitive to the specific installation position on the turntable load mounting disk. The static positioning error of each position point depends on the accuracy of the differential receiver. After using the least squares fitting, the coordinates of the turntable center point are higher than the accuracy of the differential receiver, and it has good engineering application value.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A method for fitting and solving the coordinates of the turntable center point, the turntable includes a central rotating shaft, and a turntable cantilever is respectively arranged on both sides of the central rotating shaft. A load mounting disk is arranged at the end of the turntable cantilever. The two turntable cantilevers are located on the same straight line and are both perpendicular to the central axis of the central rotating shaft, and the two turntable cantilevers perform circular motion with the center point of the central rotating shaft as the center of the circle; the fitting and solving of the turntable center point coordinates specifically includes the following steps:

[0009] Step 1: Install a differential receiver on the load mounting disk on one side of the turntable cantilever, and add a counterweight on the load mounting disk on the other side of the turntable cantilever.

[0010] Step 2: Set the rotation angle step value n of the turntable, and further obtain the geodetic coordinate results of m position points after the differential receiver rotates one circle.

[0011] Step 3: Convert the coordinates of all position points from the geodetic coordinate system to the ECEF coordinate system. Then, select any two position points symmetric about the central axis of the turntable, and calculate the midpoint coordinates of the two position points in the ECEF coordinate system and record them as the reference point coordinates , and then convert the reference point coordinates to the geodetic coordinate system ;

[0012] Step 4: Establish a local coordinate system at the reference point coordinates , and convert the coordinates of all position points to the coordinates in the local coordinate system ;

[0013] Step 5: Calculate the average value of the vertical coordinates of all position points , , and record as the vertical coordinate of the turntable center point;

[0014] Step 6: Use the least squares method in the horizontal plane to fit the plane coordinates of the turntable center point ; Convert to the ECEF coordinate system, and finally obtain the turntable center point coordinates.

[0015] Furthermore, the specific method of Step 2 is as follows:

[0016] Record the number of position points of the differential receiver obtained after the turntable rotates one circle as m, , adjust n to make m an even number; Each time the turntable rotates once according to the rotation angle step value, it stops for a period of time. At this time, the differential receiver statistically calculates the geodetic coordinates of the current position point multiple times and calculates their average value, and records the average value as the geodetic coordinate result of the current position point.

[0017] Furthermore, the specific method of Step 6 is as follows:

[0018] Step 601: Set intermediate variables ; And ;

[0019] Among them,

[0020]

[0021] , is the rotation radius of the differential receiver;

[0022] Then there is:

[0023]

[0024] Step 602, transform the center coordinates of the circle into the ECEF coordinate system to obtain the center coordinates of the turntable :

[0025] =S -1 ;

[0026] Wherein,

[0027] S = .

[0028] Due to the adoption of the above technical solution, the beneficial effects of the present invention compared with the prior art are as follows:

[0029] 1. The present invention does not require installing an antenna at the center point of the turntable and is not sensitive to the specific installation position on the load mounting plate of the turntable; moreover, it is easy to implement, has a small calculation amount, can quickly calculate the center coordinates of the turntable, and has good engineering application value.

[0030] 2. In the present invention, the static positioning error of each position point depends on the accuracy of the differential receiver. After using the least squares fitting, the center coordinates of the turntable are higher than the accuracy of the differential receiver, and the center coordinates of the turntable can be accurately solved, providing a calculation basis for subsequent GNSS dynamic verification. Description of the Drawings

[0031] Figure 1 is a schematic diagram of the turntable operation connection for a method of fitting and solving the center coordinates of a turntable in an embodiment of the present invention.

[0032] Figure 2 is a schematic diagram of the fitting process of the center coordinates of the turntable in an embodiment of the present invention. Detailed Embodiment

[0033] The following further describes the content of the present invention in conjunction with the drawings and specific embodiments.

[0034] A method for fitting and solving the center coordinates of a turntable, as Figure 2 shown, includes the following steps;

[0035] Step 1: Set up a high-precision differential receiver, fix the differential receiver at one end of the turntable, and add a counterweight at the other end. Set the turntable to step by a certain number of degrees, and there are a total of m position points in one rotation. For example, stepping by 1°, there are 360 position points from 0° to 359°. After the turntable rotates to each position point, wait for the turntable to stop rotating, count the positioning results several times, and obtain the positioning average value of this position as the positioning result of this position;

[0036] Step 2: Select two symmetric position points, such as the positions of 0° and 180°, calculate the midpoint coordinates as the reference point; establish an ENU coordinate system at the reference point, and convert the previously obtained position point coordinates to this coordinate system;

[0037] Specifically, in Step 2:

[0038] 2.1: Convert the coordinates of all position points from the geodetic coordinate system to the ECEF coordinate system to obtain . Select two symmetric position points, such as the positions of 0° and 180°, and obtain the ECEF midpoint coordinates , where is the symmetric position point. And take this point as the reference point, and convert the ECEF coordinates of the reference point to the geodetic coordinate system through coordinate transformation ;

[0039] 2.2: Establish a local coordinate system at the reference point , and convert the coordinates of all position points to .

[0040] Step 3: Statistically calculate the average value of the celestial direction of all position points , , as the celestial direction coordinate of the center point of the turntable. Use the least squares method in the horizontal plane to fit the plane coordinates of the center point of the turntable . Convert to the ECEF coordinate system to finally obtain the coordinates of the center point of the turntable.

[0041] Specifically, in Step 3:

[0042] Set the rotation radius as r, and now there are coordinate points , . The center coordinates are . The basic equation of the least squares fitting curve is

[0043]

[0044] Expand

[0045] Let

[0046] After transformation, there is

[0047]

[0048] Generalizing to the existing coordinate points, there is

[0049]

[0050] Denote:

[0051]

[0052] Then according to the least squares method, there is

[0053]

[0054] Finally, it can be obtained that .

[0055] Transform the center coordinates of the circle into the formula in the ECEF coordinate system as follows.

[0056] =S -1

[0057] Wherein,

[0058] S = .

[0059] Specifically, as Figure 1 shown. The GNSS receivers to be calibrated include two types: integrated machines and split machines. As Figure 1 shown in the red frame, when installing the GNSS integrated receiver, the receiver to be measured needs to be fixedly installed on the load mounting plate at one end of the turntable cantilever, and the load mounting plate at the other end is counterweighted. When installing the GNSS split receiver, only the receiver antenna needs to be fixed on the load mounting plate at one end of the turntable cantilever, and the RF signal and communication data cables are connected to the receiver host placed outside the turntable through a slip ring. During the test, the receiver or the receiver antenna rotates at high speed with the turntable cantilever. Therefore, the accurate coordinates of the turntable center point are of great significance for the dynamic calibration and evaluation accuracy of the GNSS receiver.

[0060] In summary, the present invention does not require installing an antenna at the turntable center point and is not sensitive to the specific installation position on the turntable load mounting plate. The static positioning error of each position point depends on the accuracy of the differential receiver. After using the least squares fitting, the coordinates of the turntable center point are higher than the accuracy of the differential receiver, having good engineering application value.

[0061] Those skilled in the art will realize that the described embodiments are provided to assist the reader in understanding the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to the described embodiments. For those skilled in the art, various modifications and variations can be made to the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A fitting and solving method for the coordinates of the center point of a turntable. The turntable includes a central rotating shaft, and a turntable cantilever is provided on each side of the central rotating shaft. A load mounting disk is provided at the end of the turntable cantilever. The two turntable cantilevers are located on the same straight line and are both perpendicular to the central axis of the central rotating shaft, and the two turntable cantilevers perform circular motion around the center point of the central rotating shaft. It is characterized in that, The fitting solution of the coordinates of the center point of the turntable specifically includes the following steps: Step 1: Install a differential receiver on the load mounting plate on one side of the turntable cantilever, and add counterweights to the load mounting plate on the other side of the turntable cantilever; Step 2: Set the rotation angle step value n of the turntable, and further obtain the geodetic coordinate results of m position points after the differential receiver rotates one circle; Step 3: Convert the coordinates of all position points from the geodetic coordinate system to the ECEF coordinate system. Then, arbitrarily select two position points that are symmetric about the center axis of the turntable, and calculate the midpoint coordinates of the two position points in the ECEF coordinate system, which are recorded as the reference point coordinates , and then convert the reference point coordinates to the geodetic coordinate system ; Step 4, establish a station-centered coordinate system at the reference point coordinates and convert the coordinates of all position points into coordinates in the station-centered coordinate system ; Step 5, calculate the average value of the celestial coordinates of all position points , , and record it as the celestial coordinate of the center point of the turntable; Step 6, use the least squares method to fit the planar coordinates of the turntable center point in the horizontal plane ; Convert to the ECEF coordinate system, and finally obtain the coordinates of the turntable center point.

2. The fitting and solving method for the coordinates of the center point of a turntable according to claim 1, characterized in that, The specific method of Step 2 is: The number of differential receiver position points obtained after rotating the turntable one full circle is denoted as m. , adjust n so that m is an even number; each time the turntable rotates once according to the rotation angle step value, it stops for a period of time. At this time, the differential receiver statistically calculates the geodetic coordinate of the current position point multiple times and calculates its average value, and records the average value as the geodetic coordinate result of the current position point.

3. The fitting and solving method for the coordinates of the center point of a turntable according to claim 1, characterized in that, The specific method of Step 6 is: Step 601, set intermediate variables ; and ; Among them, , is the rotation radius of the differential receiver; Then there is: Step 602, transform the center coordinates of the circle into the ECEF coordinate system to obtain the coordinates of the center point of the turntable : =S -1 ； Among them, S= 。

Images