Gross error detection in survey networks by L(1)-norm minimization
Abstract
The purpose of this study was to develop a statistical method for finding mistakes and gross errors in land surveying data/observations using L1-norm minimization. The motivation for examining L1-norm minimization is that reasonable parameter estimates can be obtained in the face of single and multiple large-magnitude gross errors which may prevent existing least squares methods from providing a solution. The L1-norm yields these parameter estimates with minimal computational cost and time. This study's theoretical contributions are based on a systematic exploitation of the linear programming solution to the L1-norm minimization problem. Foremost among these contributions is the single and joint statistical distributions associated with L1-norm residuals since these statistical distributions are used to generate common land surveying measures such as redundancy numbers, marginally detectable errors, as well as post-analysis measures such as critical values and test statistics. Also, the linear programming solution reveals the systematic behavior of the signs of L1-norm residuals which may be exploited in both pre-analysis and post-analysis of survey networks. To ground the theoretical developments of this thesis, several of the developed L1 pre-analysis measures are compared to existing least squares measures in the disciplines of land surveying, photogrammetry, and regression. While these comparisons show that least squares methods are superior for detecting small-magnitude gross errors, L 1-norm minimization effectively accommodates large-magnitude gross errors which cannot be accommodated by least squares methods.
Degree
Ph.D.
Advisors
Gelder, Purdue University.
Subject Area
Civil engineering|Statistics|Earth
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