CHAPTER 11
Principles of Least Squares
Example 11.1
Solve the following set of equations using the least squares method.
x + y = 3.0
2x - y = 1.5
x - y = 0.2
Data Entry
SOLUTION
Example 11.2
Find the least squares solution for the following system of nonlinear equations.
F: x + y -2y2 = -4
G: x2 + y2 = 8
H: 2x2 - y2 = 7.7
Create iterating function
Example 11.3 -- Fitting Points to a Straight Line
Find the best-fit straight line for the following points whose x and y coordinates are given in parentheses.
A: (3.00, 4.50) B: (4.25, 4.25) C: (5.50, 5.50) D: (8.00, 5.50)
Example 11.4
A surveyor wishes to use an instrumentreflector combination that has an unknown constant value. Calibration baseline observations were carefully made, and following the manufacturer's recommendations, the necessary corrections were applied for the atmospheric conditions, earth curvature, and slope. Use these corrected distances and their published values listed below to determine the instrument-reflector constant (C) and scaling factor (S) for the system.
Example 11.5
While observing angles at a station, the horizon was closed. The following observations and their standard deviations were obtained. What are the most probable values for the observations?
Adjusted angles
Example from Section 11.14
Use observation equations to solve the data in Example 11.5
Reset A and L
Form matrices for observation equations
Solution