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Table 13 Transformation residuals of coordinates (m)

From: A dual quaternion algorithm of the Helmert transformation problem

Point no.

Identical weight situation

Point-wise weight situation

\({\text{d}}x\)

\({\text{d}}y\)

\({\text{d}}z\)

\({\text{d}}x\)

\({\text{d}}y\)

\({\text{d}}z\)

1

− 0.02258

− 0.02006

0.02540

− 0.02302

− 0.01738

0.02667

2

0.03615

− 0.01216

0.01080

0.03619

− 0.01426

0.01390

3

− 0.00017

0.01748

− 0.02705

− 0.00004

0.01115

− 0.02406

4

− 0.00189

0.03076

0.02746

− 0.00168

0.03320

0.03082

5

0.02870

0.00602

− 0.01572

0.02895

0.00434

− 0.01283

6

− 0.01192

0.01675

0.00412

− 0.01183

0.01122

0.00554

7

− 0.00390

− 0.00201

− 0.00916

− 0.00299

0.00014

− 0.00347

8

− 0.03124

0.00145

− 0.00674

− 0.03115

0.00073

− 0.00599

9

0.00684

− 0.03822

− 0.00912

0.00681

− 0.04283

− 0.00963

 

\({\text{rmse}}\) = 0.022510349

\({\text{rmse}}\) = 0.017848379