Coordinate Transformation Parameter Solving Online

Online coordinate transformation parameter solving tool, input a set of known point coordinates, and solve the parameters used for coordinate transformation. Coordinate conversion types support three parameter, four parameter, and seven parameter coordinate conversions.

1. Input Coordinates Type ： Supports the input of Cartesian spatial rectangular coordinate system coordinates (ECEF coordinates, XYZ) and geodetic coordinates (geodetic longitude, geodetic latitude, geodetic height, LBH). Use comma-separated values to enter one set of coordinates per line. Multiple lines are supported. The spatial Cartesian coordinate format is X , Y , Z, the unit is the meter (m). The geodetic coordinate format is L , B , H, longitude and latitude are in degrees and elevation is in meters.
2. Coordinate System 1 Coordinate : The coordinates of a known point in coordinate system 1. The format of XYZ and LBH coordinates is supported. If LBH coordinates are entered, the ellipsoid of coordinate system 1 must be selected. When the parameter is calculated, the LBH coordinates are automatically converted to XYZ coordinates for calculation.
3. Coordinate System 2 Coordinate : The coordinates of a known point in coordinate system 2. The format of XYZ and LBH coordinates is supported. If LBH coordinates are entered, the ellipsoid of coordinate system 2 must be selected. When the parameter is calculated, the LBH coordinates are automatically converted to XYZ coordinates for the calculation.
4. Convert Type : The tool supports three-parameter, four-parameter, four-parameter Helmert, seven-parameter, and seven-parameter Bursa-wolf coordinate conversions. The calculation formula, known point coordinate requirements and output conversion parameter information corresponding to each conversion type are shown in the following.
5. Three-parameter coordinate conversion:
   1. Description of three-parameter coordinate conversion : Uses x-axis translation, y-axis translation, and z-axis translation for coordinate conversion, with no coordinate rotation or scale scaling involved.
   2. Input coordinate type : Requires the input of 3D coordinates and at least 1 set of known point coordinates.
   3. Output parameter results : x-axis translation (x), y-axis translation (y), z-axis translation (z) in meters m.
   4. Transformation Formula :
6. Four-parameter coordinate transformation:
   1. Description of the four-parameter coordinate transformation : Uses x-axis translation, y-axis translation, r rotation angle, and d scaling factor for planar coordinate conversions; no Z-axis coordinate conversions are involved.
   2. Input coordinate type : Requires input of 2D/3D coordinates and at least 2 sets of known point coordinates. It is recommended to input at least 4 sets of known point coordinates, obtain conversion parameters, and based on the displayed residual data of known points, remove known points with residuals greater than 3 times the unit weight root mean square error.
   3. Output parameter results : x-axis translation (x), y-axis translation (y) in meters m . r Angle of rotation in arcseconds, d Scaling factor in ppm .
   4. Transformation Formula :
7. Four-parameter Helmert coordinate transformation:
   1. Description of the four-parameter Helmert coordinate transformation : Uses x-axis translation, y-axis translation, r rotation angle, and d scaling factor for planar coordinate conversions; no Z-axis coordinate conversions are involved.
   2. Input coordinate type : Requires input of 2D/3D coordinates and at least 2 sets of known point coordinates. It is recommended to input at least 4 sets of known point coordinates, obtain conversion parameters, and based on the displayed residual data of known points, remove known points with residuals greater than 3 times the unit weight root mean square error.
   3. Output parameter results : x-axis translation (x), y-axis translation (y) in meters m . r Angle of rotation in arcseconds, d Scaling factor in ppm .
   4. Transformation Formula :
8. Seven-parameter coordinate transformation:
   1. Description of seven-parameter coordinate conversion : Use x-axis translation, y-axis translation, z-axis translation, d scaling factor, x-axis rotation angle, y-axis rotation angle, and z-axis rotation angle for 3D coordinate conversion.
   2. Input coordinate type : Requires the entry of 3D coordinates, with at least three sets of known point coordinates. It is recommended to input at least 6 sets of known point coordinates, obtain conversion parameters, and based on the displayed residual data of known points, remove known points with residuals greater than 3 times the unit weight root mean square error.
   3. Output parameter results : x-axis translation (x), y-axis translation (y), z-axis translation (z) in meters m . d Scaling factor in ppm . x-axis rotation (rx), y-axis rotation (ry), and z-axis rotation (rz) in arc-seconds.
   4. Transformation Formula : When the angle of rotation is small,
      
      Since D is usually small, The formula can be approximated as
      
9. Seven-parameter Bursa-Wolf coordinate transformation:
   1. Description of the seven-parameter Bursa-Wolf coordinate transformation : Use x-axis translation, y-axis translation, z-axis translation, d scaling factor, x-axis rotation angle, y-axis rotation angle, and z-axis rotation angle for 3D coordinate conversion.
   2. Input coordinate type : Requires the entry of 3D coordinates, with at least three sets of known point coordinates. It is recommended to input at least 6 sets of known point coordinates, obtain conversion parameters, and based on the displayed residual data of known points, remove known points with residuals greater than 3 times the unit weight root mean square error.
   3. Output parameter results : x-axis translation (x), y-axis translation (y), z-axis translation (z) in meters m . d Scaling factor in ppm . x-axis rotation (rx), y-axis rotation (ry), and z-axis rotation (rz) in arc-seconds.
   4. Transformation Formula : When the angle of rotation is small,
      
      Since D is usually small, The formula can be approximated as
      
10. Precision Evaluation :
    1. The tool lists X residual, Y residual, Z residual, X residual root mean square error, Y residual root mean square error, Z residual root mean square error, point root mean square error and unit weight root mean square error in the calculation results for evaluating the accuracy of the coordinate conversion parameters.
    2. Residual Formula : V = Known point transformation coordinate values - Known point coordinate system 2 coordinate values .
    3. X residual root mean square error formula :
    4. Y residual root mean square error formula :
    5. Z residual root mean square error formula :
    6. Point residual root mean square error formula : 2D plane coordinates - , 3D spatial coordinates -
    7. Unit weight root mean square error formula : , Among them, V is the residual vector, P is the weight matrix, n is the total number of observations (including components), and t is the number of unknown parameters.
11. The coordinate transformation parameters solved by this tool can be verified using the Coordinate Frame Convert Online tool on this site with the following parameter filling rules:
    1. Three-parameter coordinate transformation : Just fill in the corresponding parameters directly.
    2. Four-parameter coordinate transformation : x, y are filled in directly, s is filled in with d, and theta is filled in with -r.
    3. Four-parameter Helmert coordinate transformation : x, y are filled in directly, s is filled in by d, theta is filled in by r .
    4. Seven-parameter coordinate transformation : x, y, z, rx, ry, rz fill in directly, s fill in d, Convention select position_vector.
    5. Seven-parameter Bursa-Wolf coordinate transformation : x, y, z, rx, ry, rz fill in directly, s fill in d, Convention select coordinate_frame. Since the tool already inverts Rx, Ry, Rz in the formula for the seven-parameter Bursa-Wolf coordinate transformation, the Convention needs to be coordinate_frame.
12. The angle of rotation r is reversed in the results of the four-parameter and four-parameter Helmert transformations, and the rest of the parameters are identical. In the calculation results of seven-parameter coordinate conversion and seven-parameter Bursa-Wolf coordinate conversion, the rotation angles rx, ry ,rz are reversed, and the rest of the parameters are exactly the same. In actual use, the parameter values should be selected according to the formula and the usage scenario.
13. Open File : Support for opening UTF-8 encoded text files.
14. This tool has a certain frequency limit, please use this tool reasonably. Anonymous : 3/IP*Hour, Normal user : 3/Hour, VIP : 360/Hour, Senior VIP : 360/Hour.