Geoscience Reference
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where,
xy½
= Coordinates of the target in the scanner coordinate system
3
R
3
¼ Components of rotation matrix between the two coordinate systems for the
ith scanner station
X
j
½
Y
j
Z
j
= Coordinates of the jth target in the global coordinate system
½
X
Si
Y
Si
Z
Si
= Coordinates of the ith scanner station in the global coordinate
system.
4 Systematic Error Models
According to Lichti (
2010
), error models which are consisted in TLSs can be
classified into two groups, either physical or empirical parameters. The first group
can be considered as basic calibration parameters which have been derived from
the total station systematic error models. This group includes the constant, cyclic,
collimation, vertical circle index errors and others as described by Lichti and Licht
(
2006
). The other group of error models may appear due to the geometric defects
in construction or electrical cross-talk and may be system dependent. These are
inferred from systematic trends visible in the residuals of a highly-redundant and
geometrically strong, minimally-constrained least-square adjustment.
However, this study focuses on the most significant systematic error models
which are categorised under physical parameters as follows:
• Systematic error model for range.
Dr ¼ a
0
ð
9
Þ
• Systematic error model for horizontal direction.
Du ¼ b
0
sec h
þ
b
1
tan h
ð
10
Þ
• Systematic error model for vertical angle.
Dh ¼ c
0
ð
11
Þ
where,
a
0
¼ Constant rangefinder offset error
:
b
0
¼ Collimation axis error
:
b
1
¼ Trunnion axis error
:
c
0
¼ Vertical circle index error
:
Lichti et al. (
2011
) have mentioned that systematic error models for panoramic
scanner can be recognised based on the trends in the residuals from a bundle
