2009 Mount Stromlo SLR Observatory
Local Tie Survey
Technical Report
GEOSCIENCE AUSTRALIA
RECORD 2013/45
Ryan Ruddick1 and Alex Woods2
1. Geoscience Australia, GPO Box 378, Canberra, ACT, 2601, Australia
2. Office of Surveyor-General Victoria, Land Victoria, Level 17/570 Bourke Street, Melbourne, Victoria, 3000, Australia
Department of Resources, Energy and Tourism
Minister for Industry: The Hon Ian Macfarlane MP
Parliamentary Secretary: The Hon Bob Baldwin MP
Secretary: Ms Glenys Beauchamp PSM
Geoscience Australia
Chief Executive Officer: Dr Chris Pigram
This paper is published with the permission of the CEO, Geoscience Australia
© Commonwealth of Australia (Geoscience Australia) 2013
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ISSN 2201-702X (PDF)
ISBN 978-1-922201-83-6 (PDF)
GeoCat 78503
Bibliographic reference: Ruddick, R. & Woods, A., 2013. 2009 Mount Stromlo SLR Observatory
Local Tie Survey. Record 2013/45. Geoscience Australia: Canberra.
Contents
Executive Summary..................................................................................................................................1
1 Introduction ............................................................................................................................................2
1.1 Methodology ....................................................................................................................................2
1.1.1 Field Observations .....................................................................................................................2
1.1.2 Data Reduction ...........................................................................................................................2
1.1.3 Reporting ....................................................................................................................................2
1.2 Site Description and Contacts .........................................................................................................3
2 Instrumentation ......................................................................................................................................4
2.1 Tachymeters, EDM and Theodolites ...............................................................................................4
2.1.1 Description..................................................................................................................................4
2.1.2 Specification ...............................................................................................................................4
2.1.3 Calibration ..................................................................................................................................4
2.2 Meteorological Sensor .....................................................................................................................4
2.2.1 Description..................................................................................................................................4
2.2.2 Specification ...............................................................................................................................4
2.3 Forced Centring ...............................................................................................................................5
2.3.1 Description..................................................................................................................................5
2.3.2 Specification ...............................................................................................................................5
2.4 Targets and Reflectors.....................................................................................................................5
2.4.1 Description..................................................................................................................................5
2.4.2 Calibration ..................................................................................................................................5
2.5 Precision Levelling ...........................................................................................................................5
2.5.1 Levelling Instruments .................................................................................................................5
2.5.2 Levelling Rods ............................................................................................................................5
2.5.3 Levelling Staff .............................................................................................................................6
2.6 Tripods .............................................................................................................................................6
2.6.1 Description..................................................................................................................................6
3 Measurement Network ..........................................................................................................................7
3.1 Terrestrial Network ...........................................................................................................................7
3.1.1 Primary Survey Control Points ...................................................................................................7
3.2 Representation of Reference Points ................................................................................................8
3.2.1 SLR Reference Point ..................................................................................................................8
3.2.2 GNSS Reference Point ..............................................................................................................8
3.2.3 DORIS Reference Point .............................................................................................................8
4 Observations .......................................................................................................................................10
4.1 Terrestrial Observations.................................................................................................................10
4.1.1 Horizontal Control Survey ........................................................................................................10
4.1.2 Vertical Control Survey.............................................................................................................10
4.2 Indirect Terrestrial Observations ....................................................................................................10
4.2.1 SLR Telescope .........................................................................................................................10
2009 Mount Stromlo Local Survey
iii
4.2.1.1 Azimuth Axis .......................................................................................................................11
4.2.1.2 Elevation Axis .....................................................................................................................11
5 Data and Analysis ................................................................................................................................12
5.1 Process ..........................................................................................................................................12
5.2 Data Reduction ..............................................................................................................................12
5.2.1 Orthometric Levelling ...............................................................................................................12
5.2.1.1 Procedure ...........................................................................................................................12
5.2.1.2 Results ................................................................................................................................12
5.3 Data Processing .............................................................................................................................13
5.3.1 Geodetic Adjustment ................................................................................................................13
5.3.1.1 Procedure ...........................................................................................................................13
5.3.1.2 Results ................................................................................................................................13
5.4 IVP Determination ..........................................................................................................................13
5.4.1 Procedure .................................................................................................................................13
5.4.2 Results......................................................................................................................................15
5.5 Global Alignment ............................................................................................................................15
5.6 Prism Offsets .................................................................................................................................16
5.7 Comparison ....................................................................................................................................16
5.7.1 IVP Coordinate Estimate ..........................................................................................................17
5.7.2 Local Survey Network ..............................................................................................................17
5.7.3 Calibration Prisms ....................................................................................................................18
References .............................................................................................................................................20
iv
2009 Mount Stromlo Local Survey
Executive Summary
The integrity and strength of multi-technique terrestrial reference frames, such as realisations of the
International Terrestrial Reference Frame (ITRF), depend on the precisely measured and expressed
local-tie connections between space geodetic observing systems at co-located observatories.
Australia has several observatories which together host the full variety of space geodetic observation
techniques, including Global Navigation Satellite Systems (GNSS), Very Long Baseline Interferometry
(VLBI), Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by
Satellite (DORIS) beacons.
This report documents the technical aspects of the survey undertaken to determine the local-tie
connections at the Mount Stromlo SLR Observatory. The Observatory is located next to the Australian
National University (ANU) Research School of Astronomy and Astrophysics on Mount Stromlo in
Canberra. The Observatory has a Satellite Laser Ranging (SLR) telescope co-located with three
permanent GNSS sites, two of which contribute to the International GNSS Service (IGS) network.
Nearby there is a national gravity observatory at the ANU school and a radio telescope used for Very
Long Baseline Interferometry (VLBI) at the Canberra Deep Space Communication Complex (CDSCC)
which is operated by NASA. The survey was conducted in November 2009 by surveyors from
Geoscience Australia. Precision classical geodetic observations were combined with geodetic GNSS
observations to determine the repeat relationship between the SLR system invariant point (IVP) and
the conventional reference points of the GNSS antennas and the surrounding survey control.
The results of this survey have been provided to the International Earth Rotation Service (IERS) for
inclusion in the next realisation of the ITRF.
2009 Mount Stromlo Local Survey
1
1 Introduction
1.1 Methodology
This report is not written to serve as a manual for precision geodetic surveys and it largely assumes
that the reader has an understanding of the basic concepts of geodetic surveying. Furthermore, this
report does not detail or justify the approach taken, but merely reports the results of each major
computation step. For an in-depth analysis and justification of the approach taken the reader is
referred to Dawson et al, 2007. However for completeness the steps in our approach for observation
and computation of local-ties relationships are as follows:
1.1.1 Field Observations
 The calibration of all geodetic instrumentation,
 The observation of a vertical geodetic network,
 The observation of a horizontal geodetic network,
 The observation of a GNSS network on at least three suitable survey marks,
 The observation of targets located on the observing system during rotational motion about each
of its independent axis, including the observation of zenith angles to a staff on levelled survey
marks for the precise determination of instrument height.
1.1.2 Data Reduction
 The reduction of the terrestrial geodetic observations, including correction for instrument and
target bias, angular set reduction and atmospheric effects,
 The estimation of coordinates and their associated variance-covariance matrix in a local
system, through a classical geodetic least squares adjustment (minimum constraint),
 The estimation of the system IVP, the axes of rotation and associated system parameters, such
as axis orthogonality and offset,
 The analysis of the GNSS observations,
 The transformation (translation and rotation) of the terrestrial network, computed system IVP
and variance-covariance matrix onto a global reference frame defined by the GNSS analysis.
1.1.3 Reporting
 The coordinate estimates and their associated variance-covariance information is provided to
the IERS and made available on-line (ftp.ga.gov.au) in the form of a SINEX file.
2
2009 Mount Stromlo Local Survey
1.2 Site Description and Contacts
The Mount Stromlo Laser Ranging Observatory is located next to the Australian National University
(ANU) Research School of Astronomy and Astrophysics on Mount Stromlo in Canberra. The
Observatory has a Satellite Laser Ranging (SLR) telescope co-located with three permanent GNSS
sites. Nearby there is a national gravity observatory at the ANU school and a radio telescope used for
Very Long Baseline Interferometry (VLBI) at the Canberra Deep Space Communication Complex
(CDSCC) which is operated by NASA. Similar local surveys were undertaken in 2003, after the bush
fire destroyed a large part of the observatory, and in 2006.
Before undertaking the survey the following people should be consulted in regards to site access,
survey timing and interference with observing systems:
Site Contact:
Email
Phone
Chris Moore – EOS Space Systems
cmoore@eos-aus.com.au
+61 2 6222 7979
Gravity Contact:
Email
Phone
Nicholas Dando – Geoscience Australia
nicholas.dando@ga.gov.au
+61 2 6249 9552
GNSS Contact:
Email
Phone
Ryan Ruddick – Geoscience Australia
ryan.ruddick@ga.gov.au
+61 2 6249 9426
2009 Mount Stromlo Local Survey
3
2 Instrumentation
This section provides the specifications and calibration procedures of the equipment used in the
survey.
2.1 Tachymeters, EDM and Theodolites
2.1.1 Description
A Leica TCA2003 (S/N 439124) total station was used to record all angles and distance
measurements.
2.1.2 Specification
 Electronic Distance Measurement (EDM) (infrared) distance standard deviation of a single
measurement (DIN 18723, part 6): 1.0 mm ± 1 ppm.
 Angular standard deviation of a mean direction measured in both faces (DIN 18723, part 3):
0.15 mgon (≈ 0.49°).
2.1.3 Calibration
The Leica TCA2003 (S/N 439124) was serviced by C.R. Kennedy (Sydney, Australia) in April 2009,
during which the instrument was checked to ensure compliance with manufacture specifications.
2.2 Meteorological Sensor
2.2.1 Description
A NK Kestrel 4000 Pocket Weather Tracker (S/N 516991) was used to record meteorological
observations (temperature, pressure and relative humidity).
2.2.2 Specification
 Temperature is accurate to 1.0°C between -29.0°C and 70.0°C.
 Pressure is accurate to 1.5 mb at 25°C between 750 mb and 1100 mb.
 Relative humidity is accurate to 3.0%.
4
2009 Mount Stromlo Local Survey
2.3 Forced Centring
2.3.1 Description
An FG0L30 (S/N 609030) zenith and nadir optical plummet was used to centre and level all instrument
and target setups.
2.3.2 Specification
 Accuracy is 1:30 000 (1 mm at 30 m).
2.4 Targets and Reflectors
2.4.1 Description
The standard target kit includes:
 4 x Leica GDF21 tribrachs.
 4 x Leica GZR3 prism carriers with optical plummet.
 4 x Leica GPH1P precision prisms.
 6 x Leica GMP101 mini prisms.
2.4.2 Calibration
The additive constant for the Leica GPH1P precision prism is -34.4 mm which was applied directly into
the Leica TCA2003 total station. All prisms were calibrated on a tripod baseline at Geoscience
Australia in July 2009. Prism corrections were applied to observations during data processing.
Leica GMP101 mini prisms were calibrated at Geoscience Australia in July 2009. Approximate prism
corrections of +18.5 mm were applied to observations during data processing.
2.5 Precision Levelling
2.5.1 Levelling Instruments
Refer to section 2.1 for a description of the Leica TCA2003 total station.
2.5.2 Levelling Rods
A fixed height stainless steel rod (ARGN3) approximately 1.5 m in height with Leica style bayonet
mount on top for mounting a precision prism was used with a Leica bi-pod for stability.
A fixed height stainless steel stub (Stub3) approximately 0.2 m in height with Leica style bayonet
mount on top for mounting a precision prism.
2009 Mount Stromlo Local Survey
5
A height offset between the pole (ARGN3) and the stub (Stub3) was determined by observing both on
a low mark. Multi-set, dual face observations were used to eliminate collimation effects. The resulting
height offset was 1.4061 m.
2.5.3 Levelling Staff
A Topcon fibreglass levelling staff was used in the determination of precise instrument heights.
2.6 Tripods
2.6.1 Description
Leica GST20/9 heavy duty timber tripods with adjustable legs were used on all marks with the
exception of the pillars.
6
2009 Mount Stromlo Local Survey
3 Measurement Network
3.1 Terrestrial Network
3.1.1 Primary Survey Control Points
Table 3.1 The primary survey control points observed during the survey.
Name
4-Char ID
AU45
STR2
DOMES
Description
50119M001 The intersection of the top of the stainless steel plate with the vertical
axis of the 5/8 inch Whitworth threaded stainless steel spigot. The pillar
plate is inscribed with “AU045 Fundamental Pillar”.
AU46
The intersection of the top of the stainless steel plate with the vertical
axis of the 5/8 inch Whitworth threaded stainless steel spigot. This is
the north calibration pillar.
AU47
The intersection of the top of the stainless steel plate with the vertical
axis of the 5/8 inch Whitworth threaded stainless steel spigot. This is
the north-east calibration pillar and was re-aligned in September 2009.
AU48
The intersection of the top of the stainless steel plate with the vertical
axis of the 5/8 inch Whitworth threaded stainless steel spigot. This is
the south-east calibration pillar.
AU49
The intersection of the top of the stainless steel plate with the vertical
axis of the 5/8 inch Whitworth threaded stainless steel spigot. This is
the south calibration pillar.
AU52
STR1
50119M002 The intersection of the top of the stainless steel prism holder with the
vertical axis of the 5/8 inch Whitworth threaded stainless steel spigot.
The prims holder is attached directly to AU46. The offset between
AU46 and AU52 is 0.182 m.
AU54
The intersection of the top of the stainless steel plate with the vertical
axis of the 5/8 inch Whitworth threaded stainless steel spigot.
AU60
The intersection of the top of the stainless steel plate with the vertical
axis of the 5/8 inch Whitworth threaded stainless steel spigot. This pillar
is located on the western edge of the roof of the SLR building.
AU61
The intersection of the top of the stainless steel plate with the vertical
axis of the 5/8 inch Whitworth threaded stainless steel spigot. This pillar
is located on the eastern edge of the roof of the SLR building.
STR3
STR3
DORIS
MSPB
50119S004
The intersection of the DORIS antenna with the plane coinciding with
the base of the reference height line marked on the DORIS antenna.
7825
50119S003
The intersection of the estimated azimuth axis and elevation axis of
rotation of the SLR telescope.
SLR IVP
The intersection of the top of the stainless steel prism holder with the
vertical axis of the 5/8 inch Whitworth threaded stainless steel spigot.
This is the north-west calibration pillar.
TRIG
The original Mount Stromlo geodetic survey mark. A .303 cartridge set
in concrete beneath a steel quadrapod.
1586
Levelling benchmark located to the north-east of the observatory. It
consists of a stainless steel rod with a centre punch mark at the top.
2009 Mount Stromlo Local Survey
7
Name
4-Char ID
DOMES
Description
AU45 RM1
and RM2
Stainless steel reference pins with a centre punch mark on top.
….R
An “R” as the suffix denotes the SLR calibration targets on the
calibration pillars.
3.2 Representation of Reference Points
3.2.1 SLR Reference Point
There is one SLR telescope used for geodetic observations at the Mount Stromlo Observatory. The
telescope is an azimuth-elevation style and was established in 2003. The reference point of the
telescope, referred to as the system invariant point (IVP), is a theoretical point defined by the
intersection of the azimuth axis with the common perpendicular of the azimuth and elevation axes. An
indirect survey was used to determine this point.
3.2.2 GNSS Reference Point
There are three permanent GNSS antennas at the Observatory. The antennas are mounted on pillars
attached to bedrock with the antennas aligned to true north. The conventional reference point for the
antennas is described as the intersection of the top of the stainless steel pillar plate with the vertical
axis of the 5/8 inch Whitworth threaded spigot. For STR1 this point corresponds with the antenna
reference point (ARP). All of the antennas were removed during this survey.
3.2.3 DORIS Reference Point
There is one DORIS beacon at the Observatory. The conventional reference point of the beacon is
described as the intersection of the beacon with the plane coinciding with the base of the reference
height line marked on the beacon.
8
2009 Mount Stromlo Local Survey
Figure 3.1 Mount Stromlo SLR Observatory terrestrial survey network.
2009 Mount Stromlo Local Survey
9
4 Observations
4.1 Terrestrial Observations
4.1.1 Horizontal Control Survey
A terrestrial network survey was conducted between the permanent survey marks within the Mount
Stromlo Observatory. Five sets of observations were completed at each standpoint; a set consists of a
round of face left observations, followed by a round of face right observations to each of the visible
survey marks. For each observation a horizontal direction, zenith angle and slope distance was
recorded. At each instrument set-up atmospheric conditions (temperature, pressure and relative
humidity) were recorded. Atmospheric conditions were applied during post-processing and not directly
into the total station. Instrument and target heights were measured using an offset tape.
During the survey the GNSS antennas were removed and direct observations made to and from the
survey pillars.
4.1.2 Vertical Control Survey
Precise levelling was conducted between the survey pillars and reference marks using the EDM height
traversing technique (Reuger and Brunner 1981). Height difference observations were made using a
Leica TCA2003 total station to a prism mounted on a fixed height stainless steel pole and to a fixed
height stainless steel stub. Atmospheric conditions (temperature, pressure and relative humidity) were
recorded every 30 minutes and entered directly into the total station.
Levelling loops to all monuments in the survey network were completed in both directions. Each
instrument set-up involved reading three rounds of face left and face right observations to a single
prism set-up over two marks.
4.2 Indirect Terrestrial Observations
4.2.1 SLR Telescope
The SLR telescope was observed from two instrument standpoints (AU45 and STR3). From each
standpoint one set of observations was made to each of the visible targets. Each set of observations
consists of a round of face left observations, followed by a round of face right observations. For each
observation a horizontal direction, zenith angle and slope distance was recorded. Every 60 minutes
atmospheric conditions (temperature, pressure and relative humidity) were recorded. Atmospheric
conditions were applied during the post-processing and not directly into the total station. After each set
of observations the telescope was rotated in set increments for first azimuth and then elevation, until
the telescope was rotated through 360° for azimuth and 180° for elevation.
10
2009 Mount Stromlo Local Survey
At each standpoint the height of instrument was determined before and after each observation session
using the technique described by Reuger and Brunner (1981). The measurement technique involved
the observation of a single round of face left and face right vertical angles to specific graduations on a
levelling staff (in this case 2.0, 1.6, 1.2 and 0.8 m) placed on two nearby, levelled survey marks.
4.2.1.1 Azimuth Axis
For the azimuth axis:
 Observations were made from the standpoints AU45 and STR3.
 Three mini prisms were mounted to the substructure of the telescope using magnetic mounts.
 The elevation axis was fixed.
 The azimuth axis was rotated in 20° increments through 360°.
4.2.1.2 Elevation Axis
For the elevation axis:
 Observations were made from the standpoints AU45 and STR3.
 Four mini prisms were mounted to the substructure of the telescope using magnetic mounts.
 The azimuth axis was fixed at 91° and 355° for the standpoints respectively.
 The elevation axis was rotated from 0° to 180° in 10° increments.
2009 Mount Stromlo Local Survey
11
5 Data and Analysis
5.1 Process
The data analysis can be split into five steps:
 Data Reduction – angular sets reduced, prism offsets and atmospherics applied,
 GNSS Analysis – coordinates estimated in a global reference frame,
 Classic Geodetic Adjustment – coordinates estimated in a local reference frame,
 IVP Determination – system reference points and tie vectors estimated,
 Transformation – alignment of the survey to a global reference frame.
5.2 Data Reduction
5.2.1 Orthometric Levelling
5.2.1.1 Procedure
The levelling observations were reduced using Geoscience Australia’s levelling reduction application.
Height differences were determined between all survey marks. The misclosure was noted as being
well within zero order specifications. The results were added into the survey adjustment with a
precision of 0.0002 m.
5.2.1.2 Results
Table 5.1 Orthometric heights (in metres) derived with respect to AU45 (STR2) from the 2009 survey compared
with the 2003 (post-fire) and 2006 surveys.
AU45 to …
2003
2006
2009
σ (m)
AU46
-2.7314
-2.7315
-2.7311
0.0003
AU47
4.6889
4.6876
4.6882
0.0003
AU48
-0.9367
-0.9363
-0.9351
0.0003
AU49
-7.9697
-7.9693
-7.9688
0.0003
AU54
-3.7628
-3.7628
-3.7638
0.0003
AU60
-
0.8962
0.8961
0.0003
AU61
-
1.8059
1.8055
0.0003
STR3
-
-3.4452
-3.4452
0.0003
1586
-
-5.4965
-5.4975
NA
TRIG
1.0846
1.0839
1.0838
NA
12
2009 Mount Stromlo Local Survey
5.3 Data Processing
5.3.1 Geodetic Adjustment
5.3.1.1 Procedure
The geodetic adjustment was undertaken using Dynanet (v 3.08) (Fraser et al, 2013). In the
adjustment AU45 (STR2) was minimally constrained to its ITRF2000 coordinates and AU46 was
minimally constrained in a longitudinal direction. The angular observations were given a precision of
1.0” and the slope distances given a base precision of 1.0 mm. The estimated coordinates and
associated variance-covariance matrix in a local topocentric system was output as a SINEX file.
5.3.1.2 Results
Table 5.2 Local topocentric vectors (in metres) between AU45 and the surrounding survey control from 2009.
AU45 to …
de
dn
du
AU46
-9.2911
69.6446
-2.7315
AU47
25.6967
21.8581
4.6880
AU48
49.3484
-88.6286
-0.9359
AU49
-67.4328
-30.0221
-7.9691
AU52
-9.2911
69.6446
-2.5491
AU54
-43.4766
8.6562
-3.7638
AU60
-28.5237
9.3048
0.8960
AU61
-15.7924
6.4620
1.8054
MSPB
-15.8578
6.1397
2.4314
STR3
-25.5947
51.7637
-3.4454
5.4 IVP Determination
5.4.1 Procedure
The geometrical modelling and adjustment processes were undertaken in Axis (v 1.08) (Dawson et al,
2007). The SINEX file containing the estimated coordinates and variance-covariance matrix in a local
topocentric reference frame was used as input for Axis.
The method of IVP determination involves the derivation of independent axes of rotation of the
telescope through a process of 3-dimensional circle fitting to the 3-dimensional coordinates of targets
observed at points on the telescope during rotational sequences. A least squares method was used
for the computation of the axes of rotations and the system IVP. The method works on the basis that a
target located on a rigid body, rotating about one independent axis can be fully expressed as a circle
in 3-dimensional space and described by seven parameters:
 A circle centre (3 parameters),
2009 Mount Stromlo Local Survey
13
 A unit normal vector, perpendicular to the circle (3 parameters),
 A circle radius (1 parameter).
The method of IVP determination makes assumptions that:
 During a rotational sequence target paths scribe a perfect circular arc in 3-dimensional space,
 There is no deformation of the targeted structure during rotational sequence,
 There is no wobble error,
 The axis of interest can be rotated independently of the other axis.
No assumptions of axis orthogonality, verticality / horizontality or the precise intersection of axes are
made.
The indirect geometrical model includes a number of conditions, including:
 Target paths during rotations about an independent axis scribe a perfect circle in space,
 Circle centres derived from targets observed while being rotated about the same axis are forced
to lie along the same line in space,
 Normal vectors to each circle derived from targets observed while being rotated about the same
axis are forced to be parallel,
 The orthogonality of the primary axis to the secondary axis remains constant over all
realisations of the secondary axis,
 Identical targets rotated about a specific realisation of an axis will scribe 3-dimensional circles of
equal radius,
 The offset distance between the primary and the secondary axis remains constant over all
realisations of the secondary axis,
 The distance between 3-dimensional circle centres for all realisations of the secondary axis are
constant over all realisations of the secondary axis,
 The IVP coordinate estimates remain constant over all realisations (combinations) of the
primary/secondary axis.
In addition, a constraint that the unit normal vector perpendicular to the plane of the circle must have a
magnitude of one applied and a minimum of three rotational sequences for each target was required
to enable the solution of the equation of a circle.
The linearized equations take the form of twos sets of equations, namely conditions and constraints
with added parameters:
Av  B  f
(1)
D1  D2 '  h
(2)
Where 𝑣 is the parameter vector of residuals of the input classical adjustment results, ∆ is the
parameter vector of the circle parameters, ∆′ is the parameter vector of the parameters associated
with IVP estimates, 𝑓 and ℎ are the constant vectors associated with the evaluation of the conditions
14
2009 Mount Stromlo Local Survey
and constraints respectively and 𝐴, 𝐵, 𝐷1 and 𝐷2 are matrices of coefficients. The least squares
solution is obtained from the following system of normal equations:
 W

 A
 0

 0
 0

At
0
Bt
0
0
0
B
0
D1
0
0
0
D1t
0
D2t
0  v   0 
   
0  k   f 
0      0 
   
D2  k c   h 
0    0 
(3)
Where 𝑊 is the weight matrix of the input coordinates derived from the classical adjustment and 𝑘 and
𝑘𝑐 are vectors of the Lagrange multipliers required to satisfy the least squares criteria.
The solution to the normal equation is iterated as required for non-linear condition and constraint
equations. An updated estimate of the input coordinates and their variance-covariance matrix is
obtained together with an estimate of the IVP coordinate their variance-covariance matrix and the
inter-relating covariance matrix.
The solution for the IVP included 747 observations to 14 targets. There were two estimates of the IVP
for the point 7825 50119S003 which were constrained together through 30 separate constraints. The
resultant linear system for the network was 747 x 747 with 1203 degrees of freedom. The computed
variance factor was 0.185. The maximum circle fit residual was 1.2 mm.
5.4.2 Results
Along with the coordinate estimates and associated variance-covariance matrix in a local reference
frame, the following system parameters specific to the telescope were determined:
 The azimuth axis deflection of the vertical is 0°00’30.55”.
 The orthogonality of the azimuth to elevation axis is 89°59’42.88”.
 The offset distance between the azimuth and elevation axis is 0.0002 m.
Table 5.3 Local topocentric vectors (in metres) between AU45 and the surrounding survey control from 2009.
7825 to …
de
dn
du
AU45 (STR2)
24.9531
-2.0066
-2.4997
AU52 (STR1)
15.6626
67.6383
-5.0488
STR3
-0.6413
49.7576
-5.9451
MSPB (DORIS)
9.0953
4.1333
-0.0683
5.5 Global Alignment
The estimated coordinates in a local topocentric reference frame were not aligned to a global
reference frame. Instead the ITRF2000 coordinate of AU45 and the azimuth to AU46, as obtained
from the 2003 survey, were used to align the survey.
2009 Mount Stromlo Local Survey
15
Table 5.4 Final Cartesian coordinates (in metres) with 1σ precision estimates, aligned to the ITRF2000 coordinate
of AU45 (STR2) orientated to the ITRF coordinate of AU46.
Station ID
X
Y
Z
AU45 50119M001
-4467074.6878 ± 0.0005
2683011.8687 ± 0.0005
-3667007.8238 ± 0.0005
AU61 50119M004
-4467071.0218 ± 0.0005
2683028.0889 ± 0.0005
-3667003.5946 ± 0.0005
MSPB 50119S004
-4467071.2663 ± 0.0005
2683028.3120 ± 0.0006
-3667004.2194 ± 0.0005
7825 50119S003
-4467064.5827 ± 0.0005
2683034.9074 ± 0.0005
-3667007.6315 ± 0.0005
STR3 50119M005
-4467084.7522 ± 0.0005
2683047.7698 ± 0.0005
-3666963.5938 ± 0.0005
STR1 50119M002
-4467102.6350 ± 0.0005
2683039.4920 ± 0.0005
-3666949.5217 ± 0.0005
AU46
-4467102.5074 ± 0.0005
2683039.4154 ± 0.0005
-3666949.4163 ± 0.0005
AU47
-4467102.0302 ± 0.0005
2682998.3155 ± 0.0005
-3666992.6983 ± 0.0005
AU48
-4467055.5198 ± 0.0006
2682942.7914 ± 0.0006
-3667079.6017 ± 0.0005
AU49
-4467019.5152 ± 0.0006
2683057.3923 ± 0.0006
-3667027.7137 ± 0.0006
5.6 Prism Offsets
The SLR system at Mount Stromlo Observatory regularly ranges to terrestrial targets located on five of
the surrounding pillars. The terrestrial laser observations are used to calibrate the system, including
calculation of the system delay.
The prism offsets were calculated using a two pillar baseline between AU45 and STR3. Repeat face
left and face right observations were made between the pillars to each of the calibration prisms. The
prisms offsets were calculated and added to the IVP to calibration pillar baselines.
Table 5.5 Local topocentric vectors between the SLR IVP and the calibration prisms.
7825 to …
de
dn
du
Range (m)
AU46 R (N)
15.6572
67.6136
-5.1303
69.5921
AU47 R (NE)
50.6310
19.8438
2.2847
54.4290
AU48 R (SE)
74.2838
-90.6151
-3.3396
117.2190
AU49 R (SW)
-42.4598
-32.0126
-10.3652
54.1763
STR3 R (NW)
-0.6410
49.7323
-5.8451
50.0787
5.7 Comparison
Local surveys have previously been carried out in 2003 (post-fire) (Johnston et al 2004) and 2006
(Woods 2007). This section shows the comparisons between the previous survey results with the
2009 survey.
16
2009 Mount Stromlo Local Survey
5.7.1 IVP Coordinate Estimate
Table 5.6 shows the estimates of the system IVP coordinates from the three surveys. There is good
agreement the 2006 and 2009 surveys. The differences are well within the expected error bounds of
the survey.
Table 5.6 Comparison of the Cartesian coordinates of the system IVP (in metres) with the 1σ precision estimates
aligned to the ITRF2000 coordinates of AU45 (STR2), AU52 (STR1) and AU61.
Station ID
X
Y
Z
2009
-4467064.5827 ± 0.0005
2683034.9074 ± 0.0005
-3667007.6315 ± 0.0005
2006
-4467064.5844 ± 0.0001
2683034.9069 ± 0.0001
-3667007.6316 ± 0.0001
2003
-4467064.5807 ± 0.0001
2683034.9070 ± 0.0001
-3667007.6305 ± 0.0001
5.7.2 Local Survey Network
Tables 5.7 to 5.9 show the residuals in the local vectors from the system IVP between the individual
surveys and the mean of the three surveys. The results indicate good agreement in the horizontal
(east and north) components. Again the agreement between the 2006 and 2009 surveys is relatively
good. One point of concern is the possible instability of AU61 which has been used in all surveys as
an alignment point to the global reference frame. In future surveys, the alignment of the survey should
be made using the three permanent GNSS sites.
Table 5.7 Residuals (mm) in the local vectors from the system IVP between the 2003 survey and the mean of the
three surveys.
7825 to …
de
dn
du
AU45
-0.9
0.2
-1.1
AU61
-2.4
-0.9
-1.3
STR3
-
-
-
STR1
-1.2
0.6
-1.3
AU46
-1.1
0.5
-1.0
AU47
0.4
-0.5
-2.2
AU48
-1.8
1.7
-0.8
AU49
-1.4
0.6
0.7
Table 5.8 Residuals (mm) in the local vectors from the system IVP between the 2006 survey and the mean of the
three surveys.
7825 to …
de
dn
du
AU45
-0.6
-0.1
-0.8
AU61
1.0
-0.2
0.5
STR3
0.0
0.5
-0.2
2009 Mount Stromlo Local Survey
17
7825 to …
de
dn
du
STR1
1.0
0.4
0.8
AU46
1.0
0.5
0.7
AU47
2.6
-2.0
1.7
AU48
0.2
-0.8
1.9
AU49
0.0
-0.1
-0.2
Table 5.9 Residuals (mm) in the local vectors from the system IVP between the 2009 survey and the mean of the
three surveys.
#
7825 to …
de
dn
du
AU45
0.0
-0.3
0.2
AU61
1.5
1.1
0.8
STR3
0.0
-0.5
0.2
STR1
0.1
-0.9
0.5
AU46
0.2
-0.9
0.4
AU47#
-3.0
2.5
0.4
AU48
1.5
-0.9
-1.0
AU49
1.4
-0.4
-0.6
The pillar AU47 was re-aligned between the 2006 and 2009 surveys.
5.7.3 Calibration Prisms
Tables 5.10 to 5.12 show the local vectors between the system IVP and the calibration prisms. Good
agreement is shown between the 2003 and 2006 surveys. The 2009 survey indicates a significant
difference in the vertical (up) component. This is most likely attributed to the methodology used. In the
2003 and 2006 surveys the calibration prisms were taken to the Watson baseline for calibration. In
2009 the prisms were calibrated on site using a two pillar baseline. Until a new survey is undertake the
suggestion would be to use the local vectors from the 2006 survey for any SLR system calibrations.
Table 5.10 Local vectors between the system IVP and the calibration prisms from the 2003 survey.
7825 to …
de
dn
du
Range (m)
AU46 R (N)
15.6583
67.6127
-5.1257
69.5912
AU47 R (NE)
50.6243
19.8456
2.2953
54.4237
AU48 R (SE)
74.2868
-90.6180
-3.3310
117.2230
AU49 R (SW)
-42.4574
-32.0131
-10.3644
54.1747
STR3 R (NW)
-
-
-
-
18
2009 Mount Stromlo Local Survey
Table 5.11 Local vectors between the system IVP and the calibration prisms from the 2006 survey.
7825 to …
de
dn
du
Range (m)
AU46 R (N)
15.6561
67.6130
-5.1267
69.5911
AU47 R (NE)
-
-
-
-
AU48 R (SE)
74.2853
-90.6154
-3.3357
117.2202
AU49 R (SW)
-42.4593
-32.0134
-10.3636
54.1761
STR3 R (NW)
-0.6409
49.7322
-5.8410
50.0781
Table 5.12 Local vectors between the system IVP and the calibration prisms from the 2009 survey.
7825 to …
de
dn
du
Range (m)
AU46 R (N)
15.6572
67.6136
-5.1303
69.5921
AU47 R (NE)
50.6310
19.8438
2.2847
54.4290
AU48 R (SE)
74.2838
-90.6151
-3.3396
117.2190
AU49 R (SW)
-42.4598
-32.0126
-10.3652
54.1763
STR3 R (NW)
-0.6410
49.7323
-5.8451
50.0787
2009 Mount Stromlo Local Survey
19
References
Dawson, J., Sarti, P., Johnston, G., Vittuari, L., 2007. Indirect approach to invariant point
determination for SLR and VLBI systems: an assessment. Journal of Geodesy. June 2007, Vol. 81,
Issue 6-8. pp 433-441.
Fraser, R., Leahy, F., Collier, P., 2013. Dynanet User’s Guide Version 3.0. Dynamic Network
Adjustment Software.
Johnston, G., Dawson, J., Naebkhil, S., 2004. The 2003 Mount Stromlo Local Tie Survey. Record
2004/020. Geoscience Australia: Canberra.
Rueger, J. M., Brunner, F. K., 1981. Practical Results from EDM-Height Traversing. The Australian
Surveyor. June 1981, Vol. 30, No 6.
Woods, A., 2007. The 2006 Mount Stromlo Local Tie Survey. Record 2007/018. Geoscience Australia:
Canberra
20
2009 Mount Stromlo Local Survey