Adjustment Computations Adjustment Computations: Spatial Data Analysis

CHAPTER 14

Adjustment of Horizontal Surveys: Trilateration


Distance Observation Equation Coefficients - Equation 14.9

dxi

dyi

dxj

dyj

Example 14.2

To clarify the computational procedure, a numerical example for to the right is presented. Suppose that the observed distances lAU, lBU, and lCU are 6049.00, 4736.83, and 5446.49 ft, respectively, and the control stations have coordinates in units of feet of


xa = 865.40 ya = 4527.15

xb = 2432.55 yb = 2047.25

xc = 2865.22 yc = 27.15

Given:

SOLUTION: This is a special purpose computation to solve problem at hand. See next example for more generic example.

Determine approximate coordinates for station U.

Build J and K matrices

Loop through three observations

Demonstration on how to call BldMat

Use BldMat to solve problem using least squares method

tolerance to test for convergence

Build matrices

Least squares solution

Update coordinates

Assume done and check

Check tolerance

Compute residuals and S0

break iterations if done

Check for less than 1% change in S0

break if done

Increment iterations counter

Return results

Compute adjusted observations

Tabulated results

The following example was solved using a form that would work for any unweighted trilateration example. See if you can modify this work to solve weighted examples. Finally, create a program that reads a data file.

Example from Section 14.5

Distance observations

From To Distance

Coordinates with unkowns first

Routine to build J and K matrices based on data given in l matrix.

Compute adjusted distances by adding V

Compute standard deviations in x and y

Replace indices with station name in l matrix

and compute standard deviations.

SOLUTION

Distance Observations

 

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