Table 5 Calculated transformation parameters (point-wise weight)
From: A dual quaternion algorithm of the Helmert transformation problem
Parameters | DQA | OMA | PA | |||||
|---|---|---|---|---|---|---|---|---|
Solution 1 (\(\lambda_{H}\)) | Solution 2 (\(\lambda_{Z1}\)) | Solution 3 (\(\lambda_{Z2}\)) | Solution 4 (\(\lambda_{Z3}\)) | Solution 5 | Solution 6 | – | – | |
\(\lambda_{ 0}\) | 1.000005421 | 1.000004788 | 1.000005583 | 1.000005583 | 10 | 100 | – | – |
Iterative times | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 |
\(\theta_{x}\) (″) | − 0.997716767 | − 0.997716882 | − 0.997716767 | − 0.997716882 | − 0.997716767 | − 0.997716767 | − 0.997716185 | − 0.997716186 |
\(\theta_{y}\) (″) | 0.896086322 | 0.896087012 | 0.896086322 | 0.896087012 | 0.896086322 | 0.896086322 | 0.896085615 | 0.896085615 |
\(\theta_{z}\) (″) | 0.985885473 | 0.985885475 | 0.985885473 | 0.985885475 | 0.985885473 | 0.985885473 | 0.985885069 | 0.985885070 |
\(t_{x}\) (m) | 641.8395 | 641.8395 | 641.8395 | 641.8395 | 641.8395 | 641.8395 | 641.8395 | 641.8395 |
\(t_{y}\) (m) | 68.4729 | 68.4729 | 68.4729 | 68.4729 | 68.4729 | 68.4729 | 68.4729 | 68.4729 |
\(t_{z}\) (m) | 416.2155 | 416.2155 | 416.2155 | 416.2155 | 416.2155 | 416.2155 | 416.2156 | 416.2156 |
\(\lambda\) | 1.000005611 | 1.000005611 | 1.000005611 | 1.000005611 | 1.000005611 | 1.000005611 | 1.000005611 | 1.000005611 |
\({\text{rmse}}\) (m) | 0.114082157 | 0.114082183 | 0.114082157 | 0.114082183 | 0.114082157 | 0.114082157 | 0. 114082157 | 0.114082157 |