Differential leveling observations are used to determine differences in elevations between stations. As with all observations, these measurements are subject to random errors that can be adjusted using the method of least squares. In this chapter, the observation equation method for adjusting differential leveling observations by least squares is developed, and several examples are given to illustrate the adjustment procedures.
12.2 OBSERVATION EQUATION
To apply the method of least squares in leveling adjustments, a prototype observation equation is first written for any elevation difference. Figure 12.1 illustrates the functional relationship for an observed elevation difference between two stations I and J. The equation is expressed as
This prototype observation equation relates the unknown elevations of any two stations, I and J, with the differential leveling observation ΔElevij and its residual . This equation is fundamental in performing least squares adjustments ...
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To apply the method of least squares in leveling adjustments, a prototype observation equation is first written for any elevation difference. Figure 12.1 illustrates the functional relationship for an observed elevation difference between two stations I and J. The equation is expressed as
. This equation is fundamental in performing least squares adjustments ...