Real-World Applications of COLUMBUS

Triangulation, trilateration and resection in 2D and 3D network adjustments

COLUMBUS is quite capable of adjusting 2D and 3D networks consisting of partial observation sets from each station. Just about any survey consisting of terrestrial observations has the potential for one or more stations to be determined by triangulation, trilateration or resection.

The most important factor when measuring stations in this way is to provide enough information so that there is only one unique coordinate solution for that station.

Methods

• Trilateration: Determining a 2D coordinate position for an unknown station by measuring distances from known stations.

• Triangulation: Determining a 2D coordinate position for an unknown station by measuring horizontal angles from known stations.

• Resection: Determining a 2D coordinate position for an unknown station by occupying that station and measuring horizontal angles to known stations.

where a known station is any station that can be assigned (or computed) an approximate coordinate during the adjustment process.

These three methods yield a 2D position for the unknown station. To establish a 3D position, you must also provide some type of vertical observation, such as height difference, zenith angle, or delta Up.

When integrating any of these field procedure results into an adjustment, it is important to consider a few issues:

1. COLUMBUS may not be able to compute the approximate coordinates of the unknown station during the adjustment process. In this scenario, you will get an error indicating this condition. While the approximate coordinate algorithm is robust, it is not perfect. To remedy this problem, you may need to provide the approximate coordinate (for example, scaled from map) for this station. For more information on doing this, see the Quick Tip Computing approximate coordinates for 2D/3D networks.

2. In order to determine the 2D component of the unknown station using trilateration, triangulation or resection, you must provide enough observations to determine a unique solution.

   For example, if you are using trilateration you would need a measured distance from at least two known stations, plus an orientation for one of those measured lines. Or, you could provide a measured distance from at least three known stations, so long as the known stations are not in a straight line (causing two unique solutions.) There are similar minimum requirements for triangulation and resection.