Error analysis of two seven-parameter coordinate conversion methods in GPS positioning

The error of the conversion method is analyzed, and it is pointed out that the accuracy of the two methods is equivalent on the plane coordinate xy, and the accuracy of the spatial rectangular coordinate conversion method is relatively high on the height h.

2 Coordinate system commonly used in GPS surveying Publishingifo not seGP used coordinate system coordinate system t, 1 classification and transformation of the coordinate system 1.1 spatial geodetic coordinate system geodetic coordinates using the ellipsoid as the reference plane v ground point P The location of is represented by the earth longitude L, the earth latitude B, and the earth height H. The longitude of the earth is the angle between the meridian plane and the starting meridian plane passing through the point. The latitude is the angle between the normal line of the point and the equatorial plane. distance.

The origin of the coordinate system of the spatial rectangular coordinate system is located at the center of the ellipsoid, the Z axis points to the north pole of the ellipsoid, the X axis points to the intersection of the starting meridian and the equator, the Y axis is located at the equator, and the right hand system is 90 degrees from the X axis * Angle. The coordinate of a point in space can be transformed from the space geodetic coordinate system to the space rectangular coordinate system under the same ellipsoid datum of the point on each coordinate axis of this coordinate system: Long, engaged in structural engineering research and engineering where: N = a: is the radius of the U-unit; e is the square of the first eccentricity of the ellipsoid; a is the long axis of the earth ellipsoid; b is the earth ellipsoid Short axis.

3 Plane Cartesian Coordinate System Plane Cartesian Coordinate System uses projection transformation to map spatial coordinates (space rectangular coordinates or space geodetic coordinates) to a plane through some mathematical transformation. This transformation is also called projection transformation. There are many methods of projection transformation. The Gauss-Kruger projection, also known as Gaussian projection, is adopted in China.

The Gaussian projection is a horizontal axis, an elliptic cylinder, and an equiangular projection. The elliptic cylinder and the ellipsoid are tangent to the axis meridian (central meridian). It is the vertical axis (x-axis) of the plane rectangular coordinate system, and the equator of the earth. The line intersecting the surface and the elliptic cylinder is orthogonal to the axis meridian, which is the horizontal axis (y-axis) of the plane rectangular coordinate system. Expand the elliptic cylinder to obtain the rectangular coordinates of the Gaussian projection plane with (x, y) coordinates In order to reduce projection distortion, Gaussian projection is divided into 3 * band projection and band projection.

The ephemeris parameters released by GPS are based on this coordinate system. W: The full name of the GS-84 coordinate system is WorldGeodeticSystem-84 (the world's geodetic coordinate system-84). The coordinate origin of the WAGS-84 coordinate system is located at the center of mass of the earth. The intersection of the initiating meridian of BIH1984.0 and the equator, the Y axis forms the right-handed system with the X axis and the Z axis. The parameters of the ellipsoid used in the 1WGS-84 system are: long semi-axis a. The geodetic coordinate system currently widely used in China is the BJ ~ 54 coordinate system. The ellipsoid used in this coordinate system is the Krasovsky ellipsoid. The main parameters of the sphere are: long semi-axis a = 6378245; flatness ratio = 1: 298.33 coordinate system conversion method In actual measurement, the geodetic coordinates BLH (based on WGS-84 ellipsoid) given by the GPS receiver must be converted Into BJ-54 plane rectangular coordinates xyh (based on Krasovsky ellipsoid), there are two ways to achieve this coordinate conversion method 1 Convert the GPS coordinates of the earth BLH (base 84 ellipsoid) given by the GPS receiver to BJ -54 geodetic coordinates L54H54 (based on Krasovsky ellipsoid), and then transform B54L54H54 into BJ-54 plane rectangular coordinates xyh by Gaussian projection Method 2 passes the geodetic coordinates BLH (base 84 ellipsoid) given by GPS receiver Gaussian projection transforms WGS-84 plane rectangular coordinates 1848> force 84, then converts 84 less 84 forces 84 into ugly -54 plane rectangular coordinates xyh (based on Krasovsky ellipsoid) Method 1 uses a different geodetic coordinate system Transformation model, except for 3 translation parameters and 3 rotation parameters In addition to the 7 conversion parameters in one scale parameter, two conversion parameters should be added to consider the changes caused by the different parameters of the earth ellipsoid corresponding to the two geodetic coordinate systems. The conversion formula of the different geodetic coordinate systems is adopted by method 2. The conversion model of the rectangular coordinate system in different spaces is usually a Bursa model with 3 translation parameters, 3 rotation parameters and 1 scale parameter and 7 conversion parameters.

The conversion formula of the rectangular coordinate system in different spaces is 4 error analysis of the two coordinate conversion methods. For the above two coordinate conversion methods, due to the different calculation processes, the ways and methods of obtaining seven parameters are also different, so the final result is the BJ-54 plane Coordinates will vary. The following is an example to analyze the difference between the calculation results of the two coordinate conversion methods.

The 84 coordinates and BJ-54 plane coordinates are shown in Table 1 and Table 1. The coordinate number of the common point is the point name W. The seven parameters provided by the GS-owner for the conversion of the geodetic coordinate system are: translation amount AX = 9 rotation angle X using 4 common points in Table 1 Calculated to get the plane rectangular coordinate conversion seven 65707; rotation angle X In order to analyze the errors of the two coordinate conversion methods in the construction area and the vicinity of the project, the two coordinate conversion methods were compiled into computer programs, and all variables used double precision. The area formed by the 4 common points in Table 1 and the other 21 calculation points (as shown) was calculated. The calculation results of the two coordinate conversion methods and the difference between the two are shown in Table 2 from Table 2. Coordinate xy, the difference between the two coordinate conversion methods is 1.8mm at the maximum, indicating that the two coordinate conversion methods have two coordinates for the plane coordinate x, one inch, one inch, two inches, two inches, one inch, one inch, one inch, one inch, another inch, and another inch. Yuncun Dad, Cunbu, Cunbu, Cuibu, Cunpan, Cunbu, Tongbu, Chong, Gong, Cun, Cun, C, B, C, C, C, C, C, C, C, C, C, C, C, C, C Cun Ye Gan Cun Yun is called a Cun Cun Cun Ke Cun Cui Cun Biao Cun Cun Yi Cun A certain Bu Min has finished writing differently but differently. He has another writing. Wu has written. Wu has written. Composition analysis and mechanical performance test; finishing and modifying the welding process test report, etc. many times. Contact the owners and consultants by e-mail, fax and telephone to approve the domestic welding rods we selected, the welding process and inspection methods we have developed, and express our satisfaction with our careful drills before going abroad. According to the original regulations, a foreign product must be adopted. Under our recommendation, some modifications were made to use domestic equipment. In order to ensure the success and smoothness of the on-site dredging, we conducted repeated dredging process and equipment tests at the wharf of the five companies, and its dredging effect was better than the design requirements. On this basis, we invited consultants to visit the site to check that there was no problem Afterwards, all the equipment was disassembled and shipped out of the box. 2.5 Seriously claim for changes in the construction process, make timely claims according to the contract and technical documents, and do self-protection. Our construction projects are small, so the amount of the claim is also small, but we have not missed the total of three items of the claim, the total amount of the claim is 87,000 US dollars. 2.6 Efforts to reduce foreign construction management fees in line with the principle of saving and saving, strict Control management expenses. Purchasing transportation vehicles, communication tools, office and daily necessities on the spot are all based on the principle of saving. According to the original budget plan to purchase two living cars, after everyone discussed, only bought an old van, saving costs for the enterprise.

3 Conclusion On January 12, 2000, a grand completion ceremony was held at the Ryan Shipyard in the capital of Freetown, Sierra Leone. Although this project is only a small project of 1.59 million US dollars, due to our serious and responsible, scientific and innovative spirit, the project has been completed with high quality, so that the President, Vice President, Ministers, and parliamentarians of the Republic of Sierra Leone Representatives of the Bank, supervision representatives of international consulting companies, design representatives of the British WSP, ambassadors of some countries in Sierra Leone and the Chinese Embassy in Sierra Leone attended the ceremony, and the participants gave high marks to the project.

The Business Section of the Chinese Embassy in Sierra Leone wrote in a letter to the China Hong Kong Group Corporation: "Our Department congratulates the Group Corporation on its impressive performance."

Sierra Leone President Kaba delivered a warm speech at the completion ceremony. He praised us for completing the task with high quality and high level, supporting the construction of Sierra Leone, and enhancing the friendship between the people of Sierra Leone and the people of Sierra Leone. The error of the calculation method at the common point (continued from page 26) y calculation results are consistent. For the height h, the maximum difference is 43.7mm, it can be seen that the difference between the two coordinate conversion methods for the elevation is still relatively large relative to the plane coordinates.

In order to analyze the error of the two calculation methods on the common point, the calculation results of method 1 and method 2 in four common points in Table 2 are subtracted from the corresponding values ​​in Table 1, and the results are listed in Table 3 and visible from Table 3 At the common point, the maximum error of Method 1 on xy is 1. 7mm, the maximum error of Method 2 on xy is 0.9mm; on the height h, the maximum error of Method 1 is 36.4mm, the maximum error of Method 2 It is 11.2mm, and the sum of the absolute values ​​of the four elevation errors of Method 1 is 5.9 times that of Method 2. This further shows that, in the plane coordinate xy, the calculation accuracy of the two methods is equivalent, while in the elevation hi, the accuracy of method 2 is relatively high.

It should be pointed out that when two different coordinate systems are converted, the accuracy of the coordinate conversion depends not only on the mathematical model of the coordinate conversion and the coordinate accuracy of the common point for solving the conversion parameters, but also on the number of common points and the geometry structure. In view of the fact that there may be certain systematic errors in the ground network, and it is not exactly the same in different regions, the conversion parameters are solved by partitions, and the coordinate conversion by partitions can improve the accuracy of coordinate conversion.

5 Conclusion GPS measurement is carried out in the WGS-84 geodetic coordinate system. The coordinate data of the spatial point is described by the geodetic longitude, latitude and geodetic height. However, the BJ-54 plane coordinate system or the independent engineering coordinate system is used in the construction of China, so it is necessary to convert the WGS-84 coordinates to the BJ-54 coordinate system or the independent coordinate system.

When the owner provides the high-precision BJ-54 plane coordinate control network of the surrounding area of ​​the construction and the WGS-84 geodetic coordinates of the corresponding common points, if the owner provides the conversion parameters of WGS-84 geodetic coordinates and BJ-54 geodetic coordinates, the method in the text can be used. 1 Obtain the BJ-54 plane coordinates; if the owner does not provide the conversion parameters of WGS-84 geodetic coordinates and BJ-54 geodetic coordinates, you can use the method 2 in the article to obtain the BJ-54 plane zongfeng standard. When the construction surrounding area has only high precision For BJ-54 plane coordinate control points or independent engineering coordinate system coordinates, a GPS positioning system can be used to perform long-term static observations at multiple known points at the same time, thereby obtaining high-precision 84 geodetic coordinates of these points, and then using the existing Application programs such as TOP-CON's GPS random static post-processing software Pinnacle can be used to obtain seven parameters by forced fitting, which can be used to obtain BJ-54 plane coordinates or independent engineering coordinates by method 2 in the article. The necessary condition for solving the seven conversion parameters is that at least three common points have high-precision WGS-84 geodetic coordinates and BJ-54 plane coordinates or independent engineering coordinates v. When calculating conversion parameters, pay attention to: (1) the most known points It is better to choose evenly around the construction area and the center, which can effectively control the construction area; (2) In order to improve the accuracy, it is best to choose more than 3 common points to solve the conversion parameters using the least square method; (3) In order to verify the conversion parameters After calculating the conversion parameters, the coordinates of the common point need to be substituted into formula (3) for verification calculation. Only the conversion parameters that have been verified to meet the requirements can be considered reliable.

It should be pointed out that, on the plane coordinate xy, the calculation accuracy of the two seven-parameter coordinate conversion methods is equivalent, while on the elevation h, the precision of the spatial rectangular coordinate conversion method is relatively high. In the preparation of measurement and control software, the two methods can be verified with each other, or choose to use according to the actual situation.

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