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## 4.1 Approximate coordinates

For computation of coefficients in system (1) (ie. during linearization) we need, first of all, an estimate of approximate coordinates of points and approximate values of orientations of observed directions sets.

Approximate values of unknown parameters are usually not known and we have to compute them from the available observations. For approximate value of orientation program `gama-local` uses median of all estimates from the given set of directions to the points with known coordinates. Median is less sensitive to outliers than arithmetic mean which is normally used for approximate estimate of orientations

During the phase of computation of approximate coordinate of points, program `gama-local` walks through the list of computed points and for each point gathers all determining elements pointing to points with known or previously computed coordinates. Determining elements are

• outer bearing (oriented half-line) starting from the point with known coordinates and pointing to the computed point

distance between given and computed points

• inner angle with vertex in the computed point and arms intersecting given points

For all combinations of determining elements program `gama-local` computes intersections and estimates approximate coordinates as the median of all available solutions.

If at least one point was resolved while iterating through the list, the whole cycle is repeated.

If no more coordinates can be solved using intersections and points with unknown coordinates are remaining, program tries to compute coordinates of unresolved points in a local coordinates system and obtain their coordinates using similarity transformation. If a transformation succeeds to resolve coordinates at least one computed point and there are still some points without coordinates left, the whole process is repeated. Classes for computation of approximate coordinates have been written by Jiri Vesely.

If program `gama-local` fails to compute approximate coordinates of some of the network points, they are eliminated from the adjustment and they are listed in the output listing.

With the outlined strategy, program `gama-local` is able to estimate approximate coordinates in most of the cases we normally meet in surveying profession. Still there are cases in which the solution fails. One example is an inserted horizontal traverse with sets of observed direction on both ends but without a connecting observed distance. The solution of approximate coordinates can fail when there is a number of gross error for example resulting from confusion of point identifications but in normal situations, leaving computation of approximate coordinates on program `gama-local` is recommended.

## Example

 ```Computation of approximate coordinates of points ************************************************ Number of points with given coordinates: 2 Number of solved points : 2 Number of observations : 4 ----------------------------------------------------- Successfully solved points : 0 Remaining unsolved points : 2 List of unresolved points ************************* 422 424 ```

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