Erratum for “New First-Order Approximate Precision Estimation Method for Parameters in an Errors-in-Variables Model” by Jie Han, Songlin Zhang, and Jingchang Li

The mean values of the estimated posterior precision for translation parameters with four different SNRs are illustrated in Fig. 3. From the subfigures, we can find that the results of NFOA are slightly higher than results of FOA, namely, the results of NFOA are close to that of MSDTE. From the perspective of quantitative evaluation, the mean improvement ratios comparing the proposed NFOA and FOA with MSDTE are shown in Table 7. The estimated posterior precision of translation parameters increases on average by 0.024%. The results of the other nine rotation parameters are shown in Fig. 4. We can find that the results of NFOA in condition with low SNR noise are superior to that of FOA, but the results of NFOA in condition with high SNR noise are inferior to that of FOA. The difference between estimated posterior precision with FOA or NFOA and MSDTE are unapparent. As reported by Xu et al. (2014) and Amiri-Simkooei et al. (2016), for coordinate transformation parameters, both the posterior precision of weighted LS and FOA of TLS can be used as a good approximation for the covariance matrix of the estimates.