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Variance component estimation in linear ill-posed problems: TSVD issue
KTH, School of Architecture and the Built Environment (ABE), Transport and Economics, Geodesy.
2010 (English)In: Acta Geodaetica et Geophysica Hungarica, ISSN 1217-8977, Vol. 45, no 2, 184-194 p.Article in journal (Refereed) Published
Abstract [en]

An ill-posed problem which involves heterogonous data can yield good results if the weight of observations is properly introduced into the adjustment model. Variance component estimation can be used in this respect to update and improve the weights based on the results of the adjustment. The variance component estimation will not be as simple as that is in an ordinary adjustment problem, because the result of the solution of an ill-posed problem contains a bias due to stabilizing the adjustment model. This paper investigates the variance component estimation in those ill-posed problems solved by the truncation singular value decomposition. The biases of the variance components are analyzed and the biased-corrected and the biased-corrected non-negative estimators of the variance components are developed. The derivations show that in order to estimate unbiased variance components, it suffices to estimate and remove the bias from the estimated residuals.

Place, publisher, year, edition, pages
2010. Vol. 45, no 2, 184-194 p.
Keyword [en]
biased-corrected estimator, eigenvalues, eigenvector, Gauss-Markov model, non-negative estimator, regularization
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-27520DOI: 10.1556/AGeod.45.2010.2.4ISI: 000278674100004ScopusID: 2-s2.0-77953276353OAI: diva2:384415
QC 20110110Available from: 2011-01-10 Created: 2010-12-13 Last updated: 2011-01-10Bibliographically approved

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Eshagh, Mehdi
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