Comparison of Posterior Precision Estimation Methods of Weighted Total Least-Squares Solution for Errors-in-Variables Model

This paper summarizes the majority of classic formulae of weighted total least-squares (WTLS) solutions for errors-in-variables (EIV) model and classified them into six categories. Next, the existing approximate posterior precision estimation methods of the WTLS solution are categorized and summarized. Based on the criterion of the orders of Taylor expansion, the current posterior precision estimation methods can be divided into first-order approximate (FOA) and second-order approximate (SOA). From the perspective of formulae, the derivation, comparison, and analysis of FOAs are placed emphasis in theory. Except for the existing FOA methods, four FOA-typed methods from the major variants of WTLS formulations are derived based on error propagation law, which enriched the posterior precision evaluation method of the WTLS solution. Two experimental examples, namely straight-line fitting and three-dimensional (3D) affine transformation, are used to evaluate the cons and pros of these posterior precision estimation methods, and their representation capability are investigated and discussed, with some suggestions being offered.