An iterative solution of weighted total least-squares adjustment |
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Authors: | Yunzhong Shen Bofeng Li Yi Chen |
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Institution: | (1) Department of Surveying Engineering, Ferris State University, Big Rapids, MI 49307-2291, USA |
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Abstract: | Total least-squares (TLS) adjustment is used to estimate the parameters in the errors-in-variables (EIV) model. However, its
exact solution is rather complicated, and the accuracies of estimated parameters are too difficult to analytically compute.
Since the EIV model is essentially a non-linear model, it can be solved according to the theory of non-linear least-squares
adjustment. In this contribution, we will propose an iterative method of weighted TLS (WTLS) adjustment to solve EIV model
based on Newton–Gauss approach of non-linear weighted least-squares (WLS) adjustment. Then the WLS solution to linearly approximated
EIV model is derived and its discrepancy is investigated by comparing with WTLS solution. In addition, a numerical method
is developed to compute the unbiased variance component estimate and the covariance matrix of the WTLS estimates. Finally,
the real and simulation experiments are implemented to demonstrate the performance and efficiency of the presented iterative
method and its linearly approximated version as well as the numerical method. The results show that the proposed iterative
method can obtain such good solution as WTLS solution of Schaffrin and Wieser (J Geod 82:415–421, 2008) and the presented numerical method can be reasonably applied to evaluate the accuracy of WTLS solution. |
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