# Survey 2

## Horizontal survey by trilateration

The task is to use trilateration to measure given area described by wooden stakes and to determine coordinates of these points. Trilateration is based on measuring merely the distances (by a tape or EDMI).

### Recommended procedure

For trilateration we have to establish network of triangles. Sharp triangles are usually sources of large errors. It is recommended to establish one or two additional temporary points and measure sides of each triangle.

### Data reduction (processing the values measured)

We may assume that there will be always error of closure. That is because the system is indeterminate, there are more measurements than unknowns. The most
appropriate way to process data reduction is to use the least-square method.
This method finds corrected positions while the **sum of squares of
corrections is kept at minimum**. The least-square method needs experience in
related mathematical background.

We will use a simplified method:

- It is recommended to process data graphically in CAD. Firstly, draw
the data as they were taken from the field. Then apply correction of errors by your
guess in such way, that the
*sum of changes*(applied corrections) to the field values*will be minimum.* - Alternative: use software for geodetic engineers (LISCAD by Leica), which provides module
*Adjustment*(least square adjustment of field data).

### Important notes

- Do care to keep the
**tape in horizontal and vertical line**during measurements. - The distances to measure are larger than the tape is. You need to hold the point where measurement has to continue.

### Evaluation

Make data reduction by

- the least square adjustment (software LISCAD by Leica) or
- by guess/intuition using CAD.

Make a table with a row for each distance measured and with 3 columns:

- The first column shows the distance measured: d
_{i} - The second column shows the distance after it is fixed: d
_{f,i} - The last column is the change (fix) squared: Δ
_{i}^{2}= (d_{i}- d_{f,i})^{2}

Express Σ Δ_{i}^{2}. When this term is the lowest possible, then the best fit is found.

Finally transform coordinates into local coordinate system where A = (0,0) and azimuth AD = 90°. That can be done easily in CAD and will be useful for comparison the results between the teams.