Free and Constrained Adjustments

The adjustment of a network is usually subdivided into two separate steps or phases:

The adjustment of a network is usually subdivided into two separate steps or phases:

This approach is intended to separate the statistical testing of observations and known stations.

See also:

See also:

Statistical Testing

Free adjustments:

Free adjustments:

A free network is a network in which the geometrical layout is determined by the observations only. The position, scale and orientation of the network are fixed by a minimum number of constraints. The control coordinates of known stations do not impose any extra constraints on the adjustment solution, yet. In a free network adjustment the emphasis is on the quality control of the observations rather than on the computation of coordinates. Selecting other stations to fix the position, scale and orientation changes the coordinates but not the results of statistical testing.

Constrained adjustments:

Constrained adjustments:

Having eliminated possible outliers in the observations by running a free adjustment, the network can be connected to the known stations. This does impose extra constraints on the solution. Now the emphasis is on the analysis of the known stations and on the computation of the final coordinates.

There are two types of constrained adjustments:

There are two types of constrained adjustments:

Absolutely constrained.
Weighted constrained.

The difference between these two types lies in the way coordinates are computed:

The difference between these two types lies in the way coordinates are computed:

In an absolutely constrained adjustment the coordinates of the known stations are kept at their original value, that is, they do not get a least squares correction. An absolutely constrained adjustment is sometimes called a pseudo least squares adjustment.
In a weighted constrained adjustment however, the known stations do get corrections.

Your decision whether to compute the adjustment absolutely or weighted constrained leaves the testing results unchanged.