Application of Theil Model to Adjustments of Network Densifications
Publication: Journal of Surveying Engineering
Volume 128, Issue 3
Abstract
A new least-squares solution to the Theil model is presented. The proposed solution is particularly suitable for applications of network densifications. By assuming fictitious observations made on the constraints, the pseudoobservation equation is formed and then solved according to the least-squares principle. Instead of the noninteger degrees of freedom as appeared previously, the proposed solution has an integer degree of freedom. Generally, these two solutions are not identical, although statistically both are unbiased and minimum-variance estimates for the parameters. In addition, the proposed method results in a smaller matrix dimension for the corresponding pseudonormal equation. The unknowns to be solved for in the normal equation decrease in such a way that the more the constraints, the less the unknowns will be.
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References
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Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 128 • Issue 3 • August 2002
Pages: 144 - 156
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Feb 8, 2001
Accepted: Oct 3, 2001
Published online: Jul 15, 2002
Published in print: Aug 2002
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