Calculation routines for external reliability

The starting point for calculating external reliability is the largest remaining gross error \(\nabla_0\), calculated under internal reliability. These errors are too uncertainly determined for the observations to be rejected in gross error detection. The errors therefore remain in the observation material and can cause significant damage to the network.

Calculation process

For each observation, the largest remaining gross error \(\nabla_0\) is found, and what impact they have on the already mentioned quantities in the network. Then the standard's requirements for the impact are calculated, and the ratio (factor) is calculated.

The largest ratio is continuously recorded, and after all observations have been processed, we have our measure for external reliability: the largest impact of a remaining gross error \(q_{DD}\). This is a measure that depends on both the network's geometry, the observation quality, and possibly the quality of control points (constraint).

Handling large networks

For large networks, the number of distance and direction combinations becomes very large. We must therefore limit ourselves so that external reliability is only calculated for the most interesting and critical distances and directions.

The area around each point is therefore divided into sectors, and a defined number of the nearest points in each sector is defined as neighbors. A table of the neighborhood is then created: For each point follows a list of all points, known and unknown, that are neighbors to this point.

Technical calculation

The technique used to calculate coordinate impact involves replacing the right side of the error equation with the largest remaining gross error for the relevant observation. For the first direction observation, this becomes as shown below.

This results in us getting a new constant term column in the normal equation system. This must be reduced in the usual way, and we find the coordinate impacts through back-solution of the unknowns.