Abstract
In this contribution, non-typical errors-in-variables (EIV) model is introduced as a more general form of the so-called EIV model which is highly relevant for geodetic data processing. Total least-squares (TLS) algorithms within a typical EIV model cannot deal with the non-typical EIV models since the first order moment/mean of the random design matrix in a non-typical EIV model is not linear. In this paper, we propose a new algorithm besides a standard solution to deal with this model. To achieve this goal, first we review a classic algorithm in order to solve this problem using traditional non-linear least-squares method within a non-linear mixed model. Then by comparison, weighted TLS algorithm within the typical EIV model can be replaced by the proposed approach after some slight modifications which results in an excellent approximate solution. This foundation is important because there is no need for linearization in the TLS algorithms. The proposed way is not sensitive to the approximate initial values of the unknown parameters and it is applicable to curve fitting, surface reconstruction or other non-typical EIV models. Here we employ it to the curve fitting. Also two examples convincingly demonstrate that the standard TLS solution of the non-typical EIV model is not admissible when it is incorrectly considered as a typical EIV model; i.e., the non-linear relationships of the elements of the random design matrix are neglected.
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I confirm that Dr. A. A. Ardalan and Dr. S. Ebrahimzadeh are the co-authors for this manuscript. Thank you for your assistance. Yours sincerely Vahid Mahboub.
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Mahboub, V., Ardalan, A.A. & Ebrahimzadeh, S. Adjustment of non-typical errors-in-variables models. Acta Geod Geophys 50, 207–218 (2015). https://doi.org/10.1007/s40328-015-0109-5
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DOI: https://doi.org/10.1007/s40328-015-0109-5