Example of Calculating Transformation Model Parameters

Feature Description

SuperMap supports calculating commonly used four-parameter and seven-parameter values through operations such as selecting common points, coordinate transformation models, and accuracy evaluation. Users can utilize these parameter values to transform the coordinate system of data products.

Preparations

Example Description

A user has vector data in the Xi'an 1980 coordinate system for a certain area and now wishes to convert it to the 2000 National Geodetic Coordinate System. The user has measured some control points within the survey area, which have both Xi'an 1980 coordinates and 2000 National Geodetic coordinates. The following details the steps using this data conversion as an example.

Preparations

Select control points with Xi'an 1980 coordinate system coordinates and 2000 National Geodetic Coordinate System coordinates as the common points file.

Common Points

Selection of Common Points is crucial for calculating transformation parameters. Users need to select control points that have coordinate results in both coordinate systems as common points.

  • Basic Principles for Selecting Common Points: High grade, high accuracy, uniform distribution, covering the entire transformation area, and small local deformation.
  • Requirements for the Number of Common Points: Generally, for conversion to the 2000 system, the selection of common points should be no less than 6, with no less than 6 external check points, all uniformly distributed to cover the entire transformation area. Considering possible gross errors, it is necessary to prepare several additional common points as backups. In summary, common points should be selected as many as possible.
    Figure: Data Common Points

Feature Entry

In the Start tab -> Data Processing group -> Project drop-down button -> Calculate Transformation Model Parameters.

Steps

  1. Model Settings:: Select the transformation model method. Click the drop-down button to the right of the "Model Method" label. The pop-up drop-down menu lists five transformation models provided by the program, including Position Vector (7-para) (Position Vector Transformation), Coordinate Frame (7-para) (Coordinate Frame Rotation Transformation), China_3D_7P (7-para) (3D Seven-Parameter Transformation Model), China_2D_7P (7-para) (2D Seven-Parameter Transformation Model), and China_2D_4P (7-para) (2D Four-Parameter Transformation Model).

    Since the selection of the transformation model is influenced by the coordinate system of the control points and the transformation area, the choice of model method depends on the specific situation. The Technical Specification for Geodetic Measurement Control Point Coordinate Transformation provides the scope of application for transformation models. Users can select the transformation model based on the coordinate system to which the source data control points belong, according to the applicable area range of the transformation model. For details on transformation models and their scope of application, please refer to Transformation Models .

    Figure: "Calculate Transformation Model Parameters" Dialog
  2. Set the Coordinate System Types for Mutual Transformation, i.e., the source coordinate system and target coordinate system. The program supports geographic coordinate systems, projected coordinate systems, and mutual conversion between them:
    • Source Coordinate System Settings: Set the coordinate system of the source data at the source coordinate system. Coordinate system settings can be done in two ways:
      • Projection Settings: Select the Projection Settings radio button, click the Settings... button, choose a geographic coordinate system or projected coordinate system provided by the program that matches the source point data, and set it as the current coordinate system. For specific operations on setting projections, refer to Projection Settings.
      • Import Projection File: Select the import projection file radio button, click the Select button, choose the projection information file, and import it.
    • Target Coordinate System Settings: Set the coordinate system type for the converted data.
  3. Common Point Settings: Input common points with coordinates in the source coordinate system and target coordinate system. The coordinate format of the common points must be consistent with the source coordinate system and target coordinate system set in the previous step; otherwise, the program will prompt an error in the control point coordinate format.

    Common points can be added in three ways: Create a Matching Dot String, Import Common Points File, and Manual Input:

    • Create a Matching Dot String: When common points exist as datasets in the data source, you can separately specify the select fields for common points in the source data and target dataset, establishing a connection between them through specified field values. Click the Create a Matching Dot String button in the superposition point settings toolbar to perform operations in the Create a Matching Dot String dialog.
    • Import Common Points: Click the import button in the superposition point settings toolbar to import a common points file (.txt). The format of the common points file (.txt) is as shown below:
      Figure: Common Points (.txt) File
    • Manual Input: Click the "Add Data" button in the superposition point settings toolbar to add a new record in the common points list box, where you can manually input the corresponding coordinates of the common points.
  4. After importing common points, you can view their details in the list box. By checking the checkbox in the Apply column, you can set which points participate in the calculation of coordinate transformation parameters. Control point pairs should not be fewer than 6 groups.
  5. Calculate Coordinate Transformation Parameters: Click the "Calculate" button to perform the calculation of coordinate transformation parameters, yielding the following results:

    ① The program substitutes the common points into the transformation model and uses the least squares method to calculate the transformation parameters, including Offset X, Offset Y, Offset Z, Rotation X, Rotation Y, Rotation Z, and Scale Difference. The units for Offset X, Offset Y, and Offset Z are "meters"; for Rotation X, Rotation Y, and Rotation Z, the units are "arcseconds"; and Scale Difference is in parts per million (ppm).

    ② The residual errors of common point coordinates (Dx, Dy, DH) and the root mean square error of points are calculated. The program identifies common points with residual errors greater than 3 times the root mean square error as unusable, displaying No in the Usable column; otherwise, they meet the accuracy requirements.

    Note: To improve the accuracy of transformation parameters, users can remove unusable common points or set them as not adopted, then update the transformation parameters.

    Related Error Calculation Formulas: 

    • Residual error of common points (Dx, Dy, DH) = Transformed coordinate value of common point - Known coordinate value of common point
    • Root mean square error calculation formula:
    • Planar root mean square error:
  6. Calibrate Precision: Click the calibrate precision button to open the calibrate precision dialog. Import common points not used in calculating transformation parameters as external check points, with no fewer than 6 points uniformly distributed. Use internal and external precision assessments to evaluate coordinate transformation accuracy based on the root mean square error of residual errors from common points used in the calculation. Points with residual errors less than 3 times the root mean square error meet the accuracy requirements.
  7. Export Transformation Parameters: After passing the precision calibration, click the export button in the coordinate transformation parameters combo box to export the calculated transformation parameters as a projection transformation parameters file (*.ctp).
  8. Apply the exported projection transformation parameters file (*.ctp) to reproject the entire dataset in the control point area. For details on reprojecting datasets, refer to Reproject Dataset. In the "Parameter Settings" dialog, import the calculated transformation parameters to achieve reprojection of the entire dataset.
  9. Overlay the converted data with the original data for comparison, as shown below:

Related Topics

Reproject Dataset

Batch Reproject

Transform Coordinates

Calculate Transformation Model Parameters