Document Type

Thesis - University Access Only

Award Date


Degree Name

Master of Science (MS)

Department / School

Mathematics and Statistics

First Advisor

Robert Lacher


A Monte Carlo simulation was used to compare the performance of ten estimators of prediction error as they relate to the positional accuracy of geometrically corrected satellite images. The estimators were evaluated in terms of bias and variability. The simulation design was based on the Landsat TM satellite/sensor system under ideal conditions. Prediction error was defined to be the expected squared error between the geo-corrected (predicted) location of a given point and its known location in a geographically referenced coordinate system. The simulation was designed so that specific values of prediction error could be computed. These values served as the standard against which the ten estimators were compared. The square of RMSE was examined for both the control points (MSE) and an independent set of validation points (VMSE). Three estimators derived from MSE were examined (AASE, CP, BIC}, along with two cross validation estimators (CV, CV2) and three bootstrap estimators (BT, RBT, CST). All estimators, except VMSE, depend only on the original control points. The square of RMSE (MSE), computed for the control points, appeared to be the worst performing estimator in terms of bias. VMSE, the independent estimator, performed the best overall. However, the cost of choosing validation points may be prohibitive to its universal application. The CP estimator derived from MSE, the leave-one-out cross validation estimator (CV), and the most complex bootstrap estimator (CBT) performed quite well overall. However, the bootstrap estimator was extremely variable when used with only 1 O control points. For this reason, and because of its relative complexity, the CBT estimator appears to be slightly inferior to the CP and CV estimators.

Library of Congress Subject Headings

Remote-sensing images -- Mathematical models
Error analysis (Mathematics)
Monte Carlo method




South Dakota State University



Rights Statement

In Copyright