On the estimation of variance in unstable condition adjustment models

Eshagh, M. (2011) On the estimation of variance in unstable condition adjustment models. Acta Geodaetica et Geophysica Hungarica, 46 (1). pp. 71-83. ISSN 1217-8977

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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.

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