Observation Equations - MDT26

Observation Equations

Each observation making up a survey can generate several equations among of the following:

• Distance equations

• Azimuth equation

• Angle equation

• Vertical equation.

Each equation is determined from an observation's data or from the relationship between two observations, as is the case with angle equations. The program determines which of the equations can be generated on the basis of the data available. For instance, if an observation is just of distance, only such an equation will be created. If the observation is angular, the angle and azimuth equations will be created. In this way, better use is made of the data gathered.

Each equation affects the coefficient, residual and weighting matrices. The values of the A coefficient matrix depend on the type of equation and are based on linearization using Taylor series non-linear equations generated by the observations.

The L vector residual values are calculated by simply finding the difference between the observed and calculated values for each observation. This coincides with the data displayed in the program's information windows.

L~i~ = V~o~ - V~c~

where:

L~i~ = Residue

V~o~ = Observed value

V~c~ = Calculated value

Finally, the diagonal matrix P for weightings contains a factor which affects each equation and determines its fitness or precision. In the following section "Measurements uncertainties" detailed information is provided on how it is constructed.