ISO 17123-5:2012
(Main)Optics and optical instruments — Field procedures for testing geodetic and surveying instruments — Part 5: Total stations
Optics and optical instruments — Field procedures for testing geodetic and surveying instruments — Part 5: Total stations
ISO 17123-5:2012 specifies field procedures to be adopted when determining and evaluating the precision (repeatability) of coordinate measurement of total stations and their ancillary equipment when used in building and surveying measurements. These field procedures have been developed specifically for in situ applications without the need for special ancillary equipment and are purposely designed to minimize atmospheric influences.
Optique et instruments d'optique — Méthodes d'essai sur site des instruments géodésiques et d'observation — Partie 5: Stations totales
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Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 17123-5
Second edition
2012-12-15
Optics and optical instruments —
Field procedures for testing geodetic
and surveying instruments —
Part 5:
Total stations
Optique et instruments d’optique — Méthodes d’essai sur site des
instruments géodésiques et d’observation —
Partie 5: Stations totales
Reference number
ISO 17123-5:2012(E)
©
ISO 2012
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ISO 17123-5:2012(E)
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ISO 17123-5:2012(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 General . 2
4.1 Requirement . 2
4.2 Procedure 1: Simplified test procedure . 2
4.3 Procedure 2: Full test procedure . 2
5 Simplified test procedure . 3
5.1 Configuration of the test field. 3
5.2 Measurement . 3
5.3 Calculation . 4
6 Full test procedure . 5
6.1 Configuration of the test field. 5
6.2 Measurement . 6
6.3 Calculation . 7
6.4 Statistical tests .11
6.5 Combined standard uncertainty evaluation (Type A and Type B) .13
Annex A (informative) Example of the simplified test procedure .15
Annex B (informative) Example of the full test procedure .17
Annex C (informative) Example for the calculation of a combined uncertainty budget (Type A and
Type B) .23
Annex D (informative) Sources which are not included in uncertainty evaluation.26
Bibliography .27
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ISO 17123-5:2012(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International
Standards adopted by the technical committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at least 75 % of the member bodies
casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 17123-5 was prepared by Technical Committee ISO/TC 172, Optics and optical instruments,
Subcommittee SC 6, Geodetic and surveying instruments.
This second edition cancels and replaces the first edition (ISO 17123-5:2005), which has been
technically revised.
ISO 17123 consists of the following parts, under the general title Optics and optical instruments — Field
procedures for testing geodetic and surveying instruments:
— Part 1: Theory
— Part 2: Levels
— Part 3: Theodolites
— Part 4: Electro-optical distance meters (EDM measurements to reflectors)
— Part 5: Total stations
— Part 6: Rotating lasers
— Part 7: Optical plumbing instruments
— Part 8: GNSS field measurement systems in real-time kinematic (RTK)
Annexes A, B and C of this part of ISO 17123 are for information only.
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ISO 17123-5:2012(E)
Introduction
This part of ISO 17123 specifies field procedures for adoption when determining and evaluating the
uncertainty of measurement results obtained by geodetic instruments and their ancillary equipment,
when used in building and surveying measuring tasks. Primarily, these tests are intended to be field
verifications of suitability of a particular instrument for the immediate task. They are not proposed as
tests for acceptance or performance evaluations that are more comprehensive in nature.
The definition and concept of uncertainty as a quantitative attribute to the final result of measurement
was developed mainly in the last two decades, even though error analysis has already long been a part of
all measurement sciences. After several stages, the CIPM (Comité Internationale des Poids et Mesures)
referred the task of developing a detailed guide to ISO. Under the responsibility of the ISO Technical
Advisory Group on Metrology (TAG 4), and in conjunction with six worldwide metrology organizations,
a guidance document on the expression of measurement uncertainty was compiled with the objective
of providing rules for use within standardization, calibration, laboratory, accreditation and metrology
services. ISO/IEC Guide 98-3 was first published in 1995.
With the introduction of uncertainty in measurement in ISO 17123 (all parts), it is intended to finally
provide a uniform, quantitative expression of measurement uncertainty in geodetic metrology with the
aim of meeting the requirements of customers.
ISO 17123 (all parts) provides not only a means of evaluating the precision (experimental standard
deviation) of an instrument, but also a tool for defining an uncertainty budget, which allows for the
summation of all uncertainty components, whether they are random or systematic, to a representative
measure of accuracy, i.e. the combined standard uncertainty.
ISO 17123 (all parts) therefore provides, for defining for each instrument investigated by the procedures,
a proposal for additional, typical influence quantities, which can be expected during practical use. The
customer can estimate, for a specific application, the relevant standard uncertainty components in
order to derive and state the uncertainty of the measuring result.
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INTERNATIONAL STANDARD ISO 17123-5:2012(E)
Optics and optical instruments — Field procedures for
testing geodetic and surveying instruments —
Part 5:
Total stations
1 Scope
This part of ISO 17123 specifies field procedures to be adopted when determining and evaluating the
precision (repeatability) of coordinate measurement of total stations and their ancillary equipment
when used in building and surveying measurements. Primarily, these tests are intended to be field
verifications of the suitability of a particular instrument for the immediate task at hand and to satisfy
the requirements of other standards. They are not proposed as tests for acceptance or performance
evaluations that are more comprehensive in nature.
These field procedures have been developed specifically for in situ applications without the need for
special ancillary equipment and are purposely designed to minimize atmospheric influences.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in probability
ISO 4463-1, Measurement methods for building — Setting-out and measurement — Part 1: Planning and
organization, measuring procedures, acceptance criteria
ISO 7077, Measuring methods for building — General principles and procedures for the verification of
dimensional compliance
ISO 7078, Building construction — Procedures for setting out, measurement and surveying — Vocabulary
and guidance notes
ISO 9849, Optics and optical instruments — Geodetic and surveying instruments — Vocabulary
ISO 12858-2, Optics and optical instruments — Ancillary devices for geodetic instruments — Part 2: Tripods
ISO 17123-1, Optics and optical instruments — Field procedures for testing geodetic and surveying
instruments — Part 1: Theory
ISO 17123-3, Optics and optical instruments — Field procedures for testing geodetic and surveying
instruments — Part 3: Theodolites
ISO 17123-4, Optics and optical instruments — Field procedures for testing geodetic and surveying
instruments — Part 4: Electro-optical distance meters (EDM measurements to reflectors)
ISO/IEC Guide 98-3.2008, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM: 1995)
ISO/IEC Guide 99:2007, International vocabulary of metrology — Basic and general concepts and
associated terms (VIM)
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ISO 17123-5:2012(E)
3 Terms and definitions
For the purpose of this document, the terms and definitions given in ISO 3534-1, ISO 4463-1, ISO 7077,
ISO 7078, ISO 9849, ISO 17123-1, the GUM and the VIM apply.
4 General
4.1 Requirement
Before commencing the measurements, it is important that the operator ensures that the precision in
use of the measuring equipment is appropriate for the intended measuring task.
The total station and its ancillary equipment shall be in known and acceptable states of permanent
adjustment according to the methods specified in the manufacturer’s reference manual, and used
tripods with reflectors as recommended by the manufacturer.
The coordinates are considered as observables because on modern total stations they are selectable as
output quantities.
All coordinates shall be measured on the same day. The instrument should always be levelled carefully.
The correct zero-point correction of the reflector prism shall be used.
The results of these tests are influenced by meteorological conditions, especially by the gradient of
temperature. An overcast sky and low wind speed guarantee the most favourable weather conditions.
Actual meteorological data shall be measured in order to derive atmospheric corrections, which shall
be added to the raw distances. The particular conditions to be taken into account may vary depending
on where the tasks are to be undertaken. These conditions shall include variations in air temperature,
wind speed, cloud cover and visibility. Note should also be taken of the actual weather conditions at the
time of measurement and the type of surface above which the measurements are made. The conditions
chosen for the tests should match those expected when the intended measuring task is actually carried
out (see ISO 7077 and ISO 7078).
Tests performed in laboratories would provide results which are almost unaffected by atmospheric
influences, but the costs for such tests are very high, and therefore they are not practicable for most
users. In addition, laboratory tests yield precisions much higher than those that can be obtained under
field conditions.
This part of ISO 17123 describes two different field procedures as given in Clauses 5 and 6. The operator
shall choose the procedure which is most relevant to the project’s particular requirements.
To evaluate angle measurement and distance measurement separately, see ISO 17123-3 and ISO 17123-4.
4.2 Procedure 1: Simplified test procedure
The simplified test procedure provides an estimate as to whether the precision of a given total station is
within the specified permitted deviation in accordance with ISO 4463-1.
The simplified test procedure is based on a limited number of measurements. This test procedure
relies on measurements of x-, y- and z-coordinates in a test field without nominal values. The maximum
difference from mean value is calculated as an indicator for the precision.
A significant standard deviation cannot be obtained. If a more precise assessment of the total station
under field conditions is required, it is recommended to adopt the more rigorous full test procedure as
given in Clause 6.
4.3 Procedure 2: Full test procedure
The full test procedure shall be adopted to determine the best achievable measure of precision of a total
station and its ancillary equipment under field conditions.
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ISO 17123-5:2012(E)
This procedure is based on measurements of coordinates in a test field without nominal values. The
experimental standard deviation of the coordinate measurement of a single point is determined from
least squares adjustments.
The full test procedure given in Clause 6 of this part of ISO 17123 is intended for determining the
measure of precision in use of a particular total station. This measure of precision in use is expressed
in terms of the experimental standard deviations of a coordinate measured once in both face positions
of the telescope;
ss,
ISO-TS−XY ISO-TS-Z
Furthermore, this procedure may be used to determine:
the measure of precision in use of total stations by a single survey team with a single instrument
and its ancillary equipment at a given time;
the measure of precision in use of a single instrument over time;
the measure of precision in use of each of several total stations in order to enable a comparison of
their respective achievable precisions to be obtained under similar field conditions.
Statistical tests should be applied to determine whether the experimental standard deviations obtained
belong to the population of the instrumentation’s theoretical standard deviations and whether two
tested samples belong to the same population.
5 Simplified test procedure
5.1 Configuration of the test field
Two target points (T , T ) shall be set out as indicated in Figure 1. The targets should be firmly fixed on
1 2
to the ground. The distance between two target points should be set longer than the average distance
(e.g. 60 m) according to the intended measuring task. Their heights should be as different as the surface
of the ground allows.
Two instrument stations (S , S ) shall be set out approximately in line with two target points. S shall
1 2 1
be set 5 m to 10 m away from T and in the opposite direction to T . S shall be set between two target
1 2 2
points and 5 m to 10 m away from T .
2
T
2
S
2
S
1
T
1
Figure 1 — Configuration of the test field
5.2 Measurement
One set consists of two measurements to each target point in one telescope face at one of the
instrument stations.
The coordinates of the two target points shall be measured by 4 sets (telescope face: I – II – I – II) at the
instrument station S . The instrument is shifted to station S and the same sequence of measurements is
1 2
carried out. Station coordinates and the reference orientation of the station are discretionary in each set.
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ISO 17123-5:2012(E)
On-board or stand-alone software shall be used for the observations. It is preferable to use the same
software which will be used for the practical work.
The sequence of the measurements is shown in Table 1.
Table 1 — Sequence of the measurements for one series
Instrument
Target point Set
Telescope
station
Seq. No x y z
face
j k
i
1 1 x y z
1,1,1 1,1,1 1,1,1
1 I
2 2 x y z
1,2,1 1,2,1 1,2,1
3 1 x y z
1,1,2 1,1,2 1,1,2
2 II
4 2 x y z
1,2,2 1,2,2 1,2,2
1
5 1 x y z
1,1,3 1,1,3 1,1,3
3 I
6 2 x y z
1,2,3 1,2,3 1,2,3
7 1 x y z
1,1,4 1,1,4 1,1,4
4 II
8 2 x y z
1,2,4 1,2,4 1,2,4
9 2 1 1 I x y z
2,1,1 2,1,1 2,1,1
;
15 1 x y z
2,1,4 2,1,4 2,1,4
2 4 II
16 2 x y z
2,2,4 2,2,4 2,2,4
5.3 Calculation
5.3.1 x-, y-coordinates
The evaluation of the test results is given by the deviation of the horizontal distance of each set from the
mean value of all measured horizontal distances.
Each horizontal distance between two target pointsl is calculated as
ik,
2 2
lx=− xy+− yi ==12,,k 12,,34 (1)
() ()
ik,,ik21,,ik,,ik21,,ik,
Their mean value L is calculated as
2 4
1
Ll= (2)
∑∑ ik,
8
i=1k=1
The half values of the deviation of each distance from its mean value, r are calculated
jk,
l − L
ik,
r = ik==12,,12,,34 (3)
ik,
2
The maximum value d of the r is defined as
ik,
xy
dr==max,ik12 =12,,34, (4)
xy ik,
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ISO 17123-5:2012(E)
5.3.2 z-coordinate
The height differences d between target points are calculated using measured z-coordinate
zi,k
values in each set.
dz=−zi==12,,k 12,,34 (5)
zi,,ki 21,,ki ,k
The mean value a of height difference in all sets is
z
2 4
1
ad= (6)
zz∑∑ ik,
8
i=1k=1
The differences r between height differences of two target points and the mean value a are
zi,k z
r =−d a ik==12,,12,,34 (7)
zi,,k zi,k z
Half of the maximum difference value d is calculated as
z
1
dr= max (8)
zz ik,
2
5.3.3 Evaluation
The differences d and d shall be within the specified permitted deviation,p and p respectively,
xy z xy z
(in accordance with ISO 4463-1 for the intended measuring task). If p andp are not given, they shall
xy
z
be ds≤×25, 2× and ds≤×25, 2× respectively, where s and s are the
xy ISO-TS-XY z ISO-TS-Z ISO-TS-XY ISO-TS-Z
experimental standard deviations of the x,y and z measurements respectively, determined according to
the full test procedure with the same instrument.
6 Full test procedure
6.1 Configuration of the test field
Three target points (T , T , T ) shall be set out at the corner of the triangle (see Figure 2). The targets
1 2 3
should be firmly fixed on to the ground. The distances of target points should be different and at least
one distance should be longer than the average distance (e.g. 60 m) according to the intended measuring
task. Their heights should be as different as the surface of the ground allows.
Three instrument stations (S , S , S ) shall be set out close to each triangular side approximately 5 m to
1 2 3
10 m away from each target point.
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ISO 17123-5:2012(E)
T
2
S
2
S
1
T
1
T
S
3
3
Figure 2 — Example of field configuration for full test
6.2 Measurement
One set consists of three measurements to each target point with a single telescope face at each
instrument station.
From the instrument stations S , S , S , the coordinates of the three target points shall be measured by
1 2 3
four sets of observation sequences (telescope face: I – II – I – II).
The station coordinates and the orientation are discretionary for each station set up. These configurations
should not be changed while measuring four sets of observations from the same station point.
On-board or stand-alone software shall be used for the observations. It is preferable to use the same
software which will be used for the practical work.
The sequence of the measurements is shown in Table 2.
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ISO 17123-5:2012(E)
Table 2 — Sequence of the measurements for one series
Instrument
Target point Set
Telescope
station
Seq. No x y z
face
j k
i
1 1 x y z
1,1,1 1,1,1 1,1,1
2 2 1 I x y z
1,2,1 1,2,1 1,2,1
3 3 x y z
1,3,1 1,3,1 1,3,1
4 1 x y z
1,1,2 1,1,2 1,1,2
5 2 2 II x y z
1,2,2 1,2,2 1,2,2
6 3 x y z
1,3,2 1,3,2 1,3,2
1
7 1 x y z
1,1,3 1,1,3 1,1,3
8 2 3 I x y z
1,2,3 1,2,3 1,2,3
9 3 x y z
1,3,3 1,3,3 1,3,3
10 1 x y z
1,1,,4 1,1,4 1,1,4
11 2 4 II x y z
1,2,4 1,2,4 1,2,4
12 3 x y z
1,3,4 1,3,4 1,3,4
13 2 1 1 I x y z
2,1,1 2,1,1 2,1,1
34 1 x y z
3,1,4 3,1,4 3,1,4
35 3 2 4 II x y z
3,2,4 3,2,4 3,2,4
36 3 x y z
3,3,4 3,3,4 3,3,4
6.3 Calculation
6.3.1 x-, y-coordinates
Construction of the mathematical model of the triangle is carried out as follows.
Calculate the horizontal distances between T and T ; l between T and T ; between T
l 1 2 2 3 l 3
ik,,1
ik,,3 ik,,2
and T respectively by measured coordinates xy, .
1 ()
ij,,ki,,jk
2 2
lx=− xy+− y (9)
() ()
ij,,ki,,jk−+11ij,,ki,,jk−+11ij,,k
i = 1, 2, 3; j = 1, 2, 3 (if j −1 is 0 or j+1 is 4, then replace it by 3 or 1 respectively); k = 1, 2, 3, 4.
The mean length of each sideL :
j
3 4
1
L = l j =12,,3 (10)
∑ ∑
j ij,,k
12
i=1k =1
The coordinates of the mathematical model of the triangle M (i = 1,2,3) is defined based on M = (0,0)
i 1
and the line from M to M as the x-axis.
1 2
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ISO 17123-5:2012(E)
Coordinates of M :
1
M (X , Y ) = (0, 0)
1 1 1
(11)
Coordinates of M :
2
M (X , Y ) = (L , 0)
2 2 2 3
(12)
Coordinates of M :
3
2
2 2 2 2 2 2
− LL++ L − LL++ L
() ()
1 2 3 1 2 3
2
MX ,,Y = L − (13)
()
33 3 2
22L L
3 3
x
M
2
M
3
y
M (0,0)
1
Figure 3 — Mathematical model of the triangle
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ISO 17123-5:2012(E)
The coordinates of the centre of gravity of the mathematical model, XY, :
()
gg
3 3
XY
∑∑j j
j==1 j 1
(,XY ),= (14)
gg
33
The coordinates of the centre of gravity of the triangle obtained at each instrument station, xy, :
()
gi,,gi
3 4 3 4
xy
∑∑∑ ij,,k ∑ ij,,k
j==1k=1 j=1k 1
xy,,= i =12,,3 (15)
()
gi,,gi
12 12
Shift the coordinates to coincide the centre of gravity of the mathematical model on the centre of gravity
of the measured triangle.
The coordinates of the centre of gravity of the mathematical model (,XY ) after the shift are
ti,,jk,,ti,,jk
calculated as
XX=+ xX− ,,YY=+ yY− ij==12,,31,,23,,k =12,,34, (16)
() ()
ti,,jk,,jg ig,,it ij,,kj gi,,gi
Rotate the mathematical model around the centre of gravity to minimize residuals of the apex coordinates
between the mathematical model and respective measured triangles.
Rotation angle θ is
ik,
q
ik,
−1
θ =tan, ik==12,,31,,23,4 (17)
ik,
p
ik,
3
Xx− ×−yy −−Yy ×−x xx
()() () () ()
∑ ti,,jk,,gi ij,,kg,,it ij,,kg,,ii jk, gi,
j=1
q = (18)
ik,
3
22
Xx− +−Yy
() ()
∑ ti,,jk,,gi ti,,jk,,gi
j=1
3
Xx− ×−xx +−Yy ×−y yy
() () () ()
()ti,,jk,,gi ij,,kg,,it ij,,kg,,ii jk, gi,
∑
j=1
p = (19)
ik,
3
22
Xx− +−Yy
() ()
ti jk gi ti jk gi
∑ ,, ,, ,, ,,
j=1
Apex coordinates of mathematical model(,XY ) after the rotation:
mi,,jk,,mi,,jk
Xx=+coss¸X×−x¸−×in Yy−
() ()
mi,,jk,,gi ik,,ti,,jk gi,,ik ti,,jk,,g ii
(20)
Yy=+sinc¸X×−x¸+×os Y −− yi==12,,31,,jk23,, =12,,34,
() ()
mi,,jk,,gi ik,,ti,,jk gi,,ik ti,,jk, gi,
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ISO 17123-5:2012(E)
Residuals (,rr )of the coordinates of the measured triangles from those of the rotated
xi,,jk,,yi,,jk
mathematical model are
rx=−Xi==12,,31jk,,23 =12,,34, (21)
xi,,jk,,ij,,km ij,,k
r =−y Y ij==12,,31,,23 k =12,,34, (22)
yi,, jk,,ij,,k mi,,jk
The sum of squares of residuals is
3 3 4
2 22
rr=+r (23)
xy ()xi,,jk,,yi,,jk
∑∑∑∑
i=1 j=1k=1
Since there are 3 sides of the mathematical model, 6 [= 2 (components) × 3 (instrument stations)] centre of
gravity points of the measured triangle and 12 [= 4 (sets) × 3 (instrument stations)] rotation parameters,
the number of unknown parameters v = 3 + 6 + 12 = 21. Thus the number of degrees of freedom is
ν =−72 21=51 (24)
XY
The experimental standard deviation is
2
r
∑ xy
s = (25)
XY
51
Finally, the standard uncertainty of x-, y-coordinates is:
us= (26)
ISO-TS-XY XY
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ISO 17123-5:2012(E)
6.3.2 z-coordinate
The height difference between T and T (and T ) is calculated using measured z-values for each set.
1 2 3
dz=−z
zi,, jk,,ij,,ki 1,k
(27)
ij==12,,32,,31k= 23,,4
The mean values of d and d are
z,ik,,2 z3,,ik,
3 4
1
ad==j 23, (28)
zj ∑∑ zi,,jk,
12
i=1k=1
The residuals r of the height differences dd, from obtained mean values for each set of
zi,,jk zi,,23kzik,,
measurements are calculated as
rd=−ai==12,,32,,jk31,,= 23,,4 (29)
zi,,jk,,zi,,jk zj,
The sum of the squares of the residuals is obtained by
3 3 4
22
rr= (30)
∑ z ∑∑∑ zi,,jk,
i=1 j=2k=1
The number of degrees of freedom is
ν =−24 22= 2 (31)
Z
Finally, the standard deviation of z-coordinate is
2
r
∑ Z
s = (32)
Z
22
Its standard uncertainty is
us=
ISO-TS-Z Z
6.4 Statistical tests
6.4.1 General
Statistical tests are applicable for the full test procedure only.
For the interpretation of the results, statistical tests shall be carried out using the experimental
standard deviation of a coordinate measured on the test triangle in order to answer the following
questions (see Table 3).
a) Is the calculated experimental standard deviation, s, smaller than or equal to a corresponding value,
σ, stated by the manufacturer or smaller than another predetermined value, σ?
b) Do two experimental standard deviations, s and s , as determined from two different samples of
measurements, belong to the same population, assuming that both samples have the same number
of degrees of freedom, v?
The experimental standard deviations, s and s , may be obtained from
two samples of measurements by the same instrument but different observers;
two samples of measurements by the same instrument at different times; or
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ISO 17123-5:2012(E)
two samples of measurements by different instruments.
For the following tests, a confidence level of 10−=α ,95 and, according to the design of meas
...
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