CIVIL ENGINEERING 365 ALL ABOUT CIVIL ENGINEERING



The authors regret a careless error caused by the cofactor matrix Q being substituted with the weight matrix P of Example 2 in the implemented code. Therefore, we must make the following corrections to the experimental results, including figures, table, and the corresponding depiction.All x-axis labels in Fig. 1 should be changed from u to v. All x-axes in Fig. 2 should be changed from v to u.The fourth paragraph of the “Example 2: 3D Affine Transformation” section should be discarded and replaced with the following: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.Table 7. Mean improvement ratio between proposed algorithm and FOATable 7. Mean improvement ratio between proposed algorithm and FOAEvaluation indexParameter item3.0113.0123.0133.01Mean improved ratio (%)Translation parameters0.0980.011−0.0010.024Rotation parameters0.0010.016−0.001−0.078Resource coordinate0.0820.0090.0030.001Target coordinate2.8201.3036.5077.886In the penultimate paragraph of the “Example 2: 3D Affine Transformation” section, the third sentence should read, “Some abnormal values even exist in Fig. 6, like the 9th index in Fig. 6(a), the 13th index in Fig. 6(b), the 3rd index in Fig. 6(c), and the 18th index in Fig. 6(d).” The final sentence should read, “As the last row of Table 7 shows, the largest mean improved ratio is as high as 7.886%, and averages 4.629%, which suggests the effectiveness of the NFOA.”Revised versions of Figs. 1–6 and Table 7 are provided herein.To preserve the published version of record, these details have been corrected only in this erratum.



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