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
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VIEW THE CORRECTED ARTICLEPublication: Journal of Surveying Engineering
Volume 148, Issue 1
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 -axis labels in Fig. 1 should be changed from to . All -axes in Fig. 2 should be changed from to .
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.
Evaluation index | Parameter item | SNR (dB) | |||
---|---|---|---|---|---|
3.01 | 13.01 | 23.01 | 33.01 | ||
Mean improved ratio (%) | Translation parameters | 0.098 | 0.011 | 0.024 | |
Rotation parameters | 0.001 | 0.016 | |||
Resource coordinate | 0.082 | 0.009 | 0.003 | 0.001 | |
Target coordinate | 2.820 | 1.303 | 6.507 | 7.886 |
In 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.”
To preserve the published version of record, these details have been corrected only in this erratum.
References
Amiri-Simkooei, A. R., S. Mortazavi, and J. Asgari. 2016. “Weighted total least squares applied to mixed observation model.” Surv. Rev. 48 (349): 278–286. https://doi.org/10.1179/1752270615Y.0000000031.
Xu, P., J. Liu, W. Zeng, and Y. Shen. 2014. “Effects of errors-in-variables on weighted least squares estimation.” J. Geod. 88 (7): 705–716. https://doi.org/10.1007/s00190-014-0716-x.
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© 2021 American Society of Civil Engineers.
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Received: May 25, 2021
Accepted: Aug 11, 2021
Published online: Sep 22, 2021
Published in print: Feb 1, 2022
Discussion open until: Feb 22, 2022
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