Adjustment Computations Adjustment Computations: Spatial Data Analysis

CHAPTER 19

Error Ellipses

The error ellipse provides the orientation of the largest error at a given station in a horizontal adjustment. As given in Chapter 19 of Adjustment Computations: Spatial Data Analysis, it is computed from the 2 by 2 submatrix that defines the unknowns for the station in question. The process of transforming the original submatrix to the matrix used to compute the error ellipse is known as orthogonalization. In mathematics this process produces eignevalues and eigenvectors. This worksheet demonstrates the process of computing error ellipses using the method presented in the textbook and eigenvalues.

Functions

Set matrix

Compute t and place in proper quadrant

By Eq. (19.19):

By Eq. (19.20):


Example from Section 19.3

Station Wisconsin

Using eigenvalues

Note: The direction of the positive U axis is 180° opposite of the t angle computed using the equations. Since the direction of the positive axis is not important in error ellipse analysis, this does not present a problem.

Station Badger

Using eigenvalues

 

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