Preprocessing of Planimetric Net (PPN)

This module produces data for planimetric traverse misclosures and approximate plane coordinate values. This module must be ran prior to a 2D adjustment, as it requires approximate values for its parameters.

Azimuth computations. Angular misclosure

For the traverse to have an orientation in 2D space, it must begin with 2 control points, so that the azimuth from the first to the latter can be computed:

After computing the initial azimuth, the rest are computed as:

Subsequently, an azimuth's standard deviation is computed as:

For a traverse to have angular control, it must either end in a different pair of control points (making it a link traverse):

or form a closed polygon (making it a polygonal traverse):

In the future, perhaps direct azimuth observations may be added, making it possible for traverses to be oriented while having only one datum point. The maximum angular misclosure value is calculated similarly to the maximum misclosure value of a level traverse, though for this module only one coefficient model is provided:

This also happens to be the accumulated value for the last azimuth's standard deviation.

Coordinate computations. Linear misclosure

Coordinate differences can be computed using simple trigonometry:

For a traverse to have linear control, it must either end in a control point (making it a link traverse):

or form a closed polygon (making it a polygonal traverse):

The linear misclosure is then the magnitude of . The computation of the maximum threshold for this misclosure is a degree more involved.

Let be the number of coordinate differences, used in computing the coordinate misclosure. The model matrices and and the covariance matrix are constructed:

From there, the following covariance matrices are computed, the latter of which contains only one element, the variance for the linear misclosure.