Random Error Propagation

Errors in Indirect Quantities Thus far, we have worked with errors in direct measurements Often, we compute other quantities based on our direct measurements (e.g. angles and distances for traverse coordinates) By the method of error propagation, we can assess the impact of the measurements on the computed quantities

Rectangle Example Area of 100x40 rectangle is 4000. A one unit error gives an area of 101x41=4141. The error in area is 141, which is approximately 100x1 + 40x1.

Error Propagation Derivation

Cut to the Chase or Note the variance and covariance terms

In Matrix Form The covariance term shows the interdependence between unknowns. (Covariance matrix is symmetric)

General Matrix Form

For Independent Observations

SLOPOV For Nonlinear Functions

Example – Cylindrical Tank

Horizontal Distance Example