New First-Order Approximate Precision Estimation Method for Parameters in an Errors-in-Variables Model

Abstract

To evaluate the posterior precision of weighted total least-squares (WTLS) estimates in an errors-in-variables model, first-order approximate precision estimation (FOA) methods are usually used. However, FOAs might not be valid if the underlying assumption is invalid, and this assumption has not been sufficiently proven. Therefore, this paper investigates the validity of the latent assumption and proposes a new first-order approximate (NFOA) precision estimation method to avoid the underlying assumption and design a corresponding algorithm. The difference between NFOA and FOA is formulated and analyzed. The proposed NFOA method is tested by a simulated classic straight-line fitting example with six scenarios and a simulated three-dimensional (3D) affine transformation experiment with four scenarios, and the mean values of the standard deviation of true errors (MSDTE) and FOA are also calculated for comparison. The results numerically indicate that NFOA works better than FOA and is close to the MSDTE, which means that NFOA can evaluate the precision of estimated parameters more reasonably and accurately.