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On the estimation of variance in unstable condition adjustment models

On the estimation of variance in unstable condition adjustment models 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Geodaetica et Geophysica Springer Journals

On the estimation of variance in unstable condition adjustment models

Acta Geodaetica et Geophysica , Volume 46 (1) – Mar 1, 2011

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Publisher
Springer Journals
Copyright
Copyright © Akadémiai Kiadó 2011
ISSN
2213-5812
eISSN
1587-1037
DOI
10.1556/ageod.46.2011.1.6
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Acta Geodaetica et GeophysicaSpringer Journals

Published: Mar 1, 2011

Keywords: adjustment; minimum variance property; nonlinear condition model; Tikhonov regularization; unbiased quadratic estimator; variance components

References