Robust Total Least Squares with reweighting iteration for three-dimensional similarity transformation

Abstract

To resist the influence of gross errors in observations on the adjusted parameters, the robust Least Squares (LS) adjustment has been extensively studied and successfully applied in the real applications. However, in the LS adjustment, the design matrix is treated as non-random even if its elements come from the real observations that are in general inevitably error-contaminated. Such assumption will lead to the incorrect solution if the gross error exists in the observations of design matrix. In this paper, we study the robust Total Least Squares (TLS) adjustment, where observation errors in design matrix are taken into account. The reweighting iteration robust scheme is applied to detect and identify the blundered observation equations as well as reweight them, obtaining the reliable TLS solution. The example of three-dimensional similarity coordinate transformation is carried out to demonstrate the performance of the presented robust TLS. The result shows that the robust TLS can indeed resist the gross errors to achieve the reliable solution.