Table 3 Computed transformation parameters (identical 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 | 1 | 1 | 2 | 2 | 1 | 1 |
\(\theta_{x}\) (″) | − 0.998502912 | − 0.998502948 | − 0.998502968 | − 0.998502645 | − 0.998502985 | − 0.998502912 | − 0.998501973 | − 0.998501973 |
\(\theta_{y}\) (″) | 0.893693386 | 0.893693331 | 0.893693483 | 0.893692963 | 0.893693803 | 0.893693386 | 0.893690956 | 0.893690956 |
\(\theta_{z}\) (″) | 0.993092526 | 0.993092564 | 0.993092561 | 0.993092355 | 0.993092530 | 0.993092526 | 0.993092056 | 0.993092056 |
\(t_{x}\) (m) | 641.8804 | 641.8806 | 641.8804 | 641.8804 | 641.8804 | 641.8804 | 641.8804 | 641.8804 |
\(t_{y}\) (m) | 68.6554 | 68.6554 | 68.6554 | 68.6554 | 68.6554 | 68.6554 | 68.6553 | 68.6553 |
\(t_{z}\) (m) | 416.3981 | 416.3983 | 416.3981 | 416.3981 | 416.3981 | 416.3981 | 416.3982 | 416.3982 |
\(\lambda\) | 1.000005583 | 1.000005583 | 1.000005583 | 1.000005583 | 1.000005583 | 1.000005583 | 1.000005583 | 1.000005583 |
\(rmse\) (m) | 0.077233661 | 0.077233748 | 0.077233663 | 0.077233668 | 0.077233683 | 0.077233661 | 0.077233661 | 0.077233661 |