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Table 3 Recovered parameters for Case 1 using the new algorithm and the Felus–Burtch algorithm, respectively

From: WTLS iterative algorithm of 3D similarity coordinate transformation based on Gibbs vectors

Parameters

The new algorithm

The Felus–Burtch algorithm

Iterations

6

–

Scale

 \(\lambda\)

1.0002101164 ± 0.0002001329

1.0002101164

Gibbs vector

 \(a\)

− 0.0381487705 ± 0.0001517110

–

 \(b\)

0.1072667832 ± 0.0001625734

–

 \(c\)

0.2637168674 ± 0.0001124502

–

Rotation angles

 \(\theta_{x}\) (°)

1.0693156620

1.0693156620

 \(\theta_{y}\) (°)

− 12.5193487938

− 12.5193487938

 \(\theta_{z}\) (°)

− 29.4297272328

− 29.4297272328

Translation

 \(t_{x}\) (m)

− 22.9747 ± 0.0074

− 22.9747

 \(t_{y}\) (m)

29.4056 ± 0.0074

29.4056

 \(t_{z}\) (m)

− 2.2626 ± 0.0074

− 2.2626

 \(\sigma\) (m)

0.0165797705

0.0165797705