Adjustment of Planimetric Net (APN)

Adjustments of 2D nets are constructed differently from 1D nets, due to the fact that their observation equations are not linear and must be linearized first. The unknowns in the system are the corrections to the plane coordinates of non-control points. The equations used are derived from horizontal angle and distance observations.

APN can only be ran with one weighing model:

Horizontal distance observation equation

The function is defined to return the horizontal distance between points and :

Then:

Evaluating the partial derivative coefficients yields:

Then the observation equation and righthand vector value become:

Horizontal angle observation equation

The function is defined to return the horizontal angle between points , and :

The partial derivatives for this function are defined as:

Then, the observation equation and righthand vector value become:

Posterior analysis of 2D network adjustments

After a successful adjustment, Geolyth proceeds to calculate error ellipses for each adjusted point. The relevant terms of the covariance matrix are defined:

The orientation angle of the error ellipse is defined as:

Then, the semi-axes of the ellipse are defined as: