Adjustment of Level Net (ALN)

When constructing the model matrix, the parameters (unknowns) of the system of linear equations are the elevations of all non-control points in the network. The equations used describe the elevation differences, including all but the ones between two control points. The following observation equation is defined:

Then, the value of the righthand vector for the th elevation difference is:

When one of the two points, between which an elevation difference is used, is marked as a 1D control point, it is put on the other side of the equation (in the vector, with a reversed sign). Let be a control point, and have be the th elevation difference, then

Likewise, have be the th elevation difference, then

Note that the elevation difference equation is linear, so the terms of the A matrix can only have the values 1, -1 and 0. For example:

When it comes to weighing the adjustment, Geolyth provides two different weighing models:

• Reciprocal of theoretical variance

• Reciprocal of horizontal distance

The value used for the horizontal distance is rounded up to the nearest integer, as higher accuracy than that has little to no effect on the weight value. When the horizontal distance is not measured using a total station, an approximate value is put together using the sum of the distances between the level and the level rods. Also important to note is that the values for the a-posteriori standard deviation have no meaning if this weighing model is picked, mathematically the method used to find them only makes sense when the first weighing model is used. This also means the statistic for each observation is not an accurate measure for determining outliers.

After carrying out the adjustment, the values of the matrix are the adjusted point elevations, from which the adjusted elevation differences are calculated.