Free choice of position
With the free choice of position , which is often referred to as free stationing , but should not be designated as such according to DIN 18 709, directions and distances to at least two connection points with known coordinates are measured on the instrument position with an electronic total station . The position can be chosen largely freely according to the local situation, so that both the connection points and the object points ( new points ) are visible from it.
The calculation of the coordinates of the station is based on the measured polar coordinates (directions and distances) to the connection points. It is usually determined with a program in the field computer or in the tachymeter by determining the translation of the instrument position, the rotation of the pitch circle with respect to the coordinate system of the connection points and a scale (unique solution). If the transformation parameters are available, they can be used to determine the coordinates in the coordinate system of the connection points from the polar coordinates of the new points.
If there are measuring elements (directions and horizontal distances) for more than two connection points, an overdetermined Helmert transformation can be used for this. Due to the overdetermination of the transformation parameters (translation, rotation and scale), there are usually deviations (residual gaps v) between the coordinates calculated in the coordinate system from the measuring elements and the coordinates of the connection points given in the system of connection points (fixed position field). The sum of the squares of these residual gaps is minimized by the calculation approach according to Friedrich Robert Helmert ( Gaussian minimum condition : sum vv → min.). The quality of the free choice of viewpoint can be assessed on the basis of the size of the remaining gaps and their distribution.
Alternatively, the calculation of the stationing parameters and the new points can also be carried out by means of a network adjustment .
literature
- Witte / Sparla: surveying and the basics of statistics for the construction industry . 7th edition. Wichmann, 2011, ISBN 978-3-87907-497-6 , pp. 547 ff .
- Kahmen: Applied Geodesy: Surveying . 20th edition. Walter de Gruyter GmbH, 2006, ISBN 3-11-018464-8 , p. 280 ff .