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On the estimation of variance in unstable condition adjustment models
Royal Institute of Technology Division of Geodesy .
2011 (English)In: Acta Geodaetica et Geophysica Hungarica, ISSN 1217-8977, E-ISSN 1587-1037, ISSN 1217-8977, Vol. 46, no 1, p. 71-83Article in journal (Refereed) Published
Abstract [en]

Estimation of variance in an ordinary adjustment model is straightforward, but if the model becomes unstable or ill-conditioned its solution and the variance of the solution will be very sensitive to the errors of observations. This sensitivity can be controlled by stabilizing methods but the results will be distorted due to stabilization. In this paper, stabilizing an unstable condition model using Tikhonov regularization, the estimations of variance of unit weight and variance components are investigated. It will be theoretically proved that the estimator of variance or variance components has not the minimum variance property when the model is stabilized, but unbiased estimation of variance is possible. A simple numerical example is provided to show the performance of the theory.

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Place, publisher, year, edition, pages
Budapest, 2011. Vol. 46, no 1, p. 71-83
Keywords [en]
adjustment; minimum variance property; nonlinear condition model; Tikhonov regularization; unbiased quadratic estimator; variance components
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:hv:diva-5638DOI: 10.1556/AGeod.46.2011.1.6OAI: oai:DiVA.org:hv-5638DiVA, id: diva2:657000
Available from: 2013-10-17 Created: 2013-10-17 Last updated: 2017-12-06Bibliographically approved

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Eshagh, Mehdi
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