Problem (1)

Given the level circuit below, what are the adjusted elevations and their expected errors for points A and B? Compute to both to 0.001 ft.

Obs dElev (ft) Len* (ft)   Obs dElev (ft) Len* (ft)
1 +3.28 625   4 -2.48 1100
2 -11.81 800   5 -11.85 750
3 +14.51 550   6 +8.58 375

*Len is the sum of the backsight and foresite distances for the observation run.

Solution: Least Squares Prob 1


Problem (2)

What are the sizes of the [C] and [K] matrices for the following horizontal network?

Solution: Least Squares Prob 2


Problem (3)

Given the horizontal network below:

The initial coordinates of point W are estimated.

Create the [C] and [K] matrices.

Solution: Least Squares Prob 3


Problem (4)

The following traverse was adjusted by least squares to determine the coordinates of points G and H.

Final coordinates of G and H are:

Point North East
G 4,958.913 917.702
H 5,067.094 1,252.311

Matrices from the final iteration of the adjustment are:



(a) Expected uncertainties of the adjusted coordinates.

(b) Adjusted observations.

(c) Parameters of the standard and 95% CI error ellipsii at each adjusted point.


Solution: Solution: Least Squares Prob 4