Adjustment Computations Adjustment Computations: Spatial Data Analysis

CHAPTER 13

Precisions of Indirectly Determined Quantities

13.3 Numerical Examples

The following is the continuation of the unweighted least squares adjustment from Chapter 12 on differential leveling adjustments. The inverse of the normal matrix (Qxx) and the reference standard deviation are derived from this adjustment. This example determines the estimated error in the adjusted elevation differences. Note the symmetry of the level net and the estimated errors in the elevations in the unweighted example and how weights affect this symmetry in the weighted example due to different lengths of lines. This demonstrates the affect weights on an adjustment. In this case, the weights correctly shift uncertainties to thos elevations farther from the control.

Data entry

Solution

In the weighted example of Section 12.4, the Qxx and S0 are

Data entry

Solution

Example 13.1 -- Standard deviations of computed quantities

Consider the linear example in Section 12.3. By Equation 13.25, the estimated standard deviations in th e adjusted elevation differences are

Data entry

Solution

Compute errors in adj. elevations

Determining elevation differences of observation 5 by matrix partitioning.

 

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