XV National Conference of Astronomers of Serbia, Belgrade, 2009.

1. 1/11
A Construction of An Advanced
Measuring System for Astro-
Geodetic Determinations
Vukan Ogrizovic
Faculty of Civil Engineering
Chair for Geodesy and Geoinformatics

2. 2/11
Astro-geodetic geoid
• Vertical deflection
ξ = Φ−φ
η = ( Λ − λ ) cos φ
Astronomical levelling
• Geoid undulation difference
dN = − ∫ ( ξ cos α + η sin α ) ds
B
A

3. 3/11
Observation of
zenith stars
• For a zenith star:
LAST = α + t = α + 0 = α
GAST = LAST − Λ
• Co-ordinates of the zenith:
Φ = δz
Λ = α z − GAST

4. 4/11
Connecting scheme

5. 5/11
Components of the
measuring system
• Optical instrument
• Snapshot acquisition
• Time keeping
software integration

6. 6/11
Optical instrument
• Zeiss Zenitlot PZL-100
• Direction of vertical - 2”
• Magnification 30x
• Compensator

7. 7/11
Snapshot acqusition
SBIG ST-2000XMC
• Kodak KAI-2020M
• TI TC-237H
• 1600 px x 1200 px
• 7,4 µm x 7,4 µm
• 11,8 mm x 8.9 mm
• CCDOPS

8. 8/11
Time keeping
• SiRF LX/I
• 12 L1 channels
• 1PPS
• 2 serial ports
notebook

9. 9/11
Results - Face I
Iteration 1 2 3 4 5
xi0 -0,39193 -0,09498 -0,00094 0,00481 0,00054
eta0 0,30169 -0,07087 -0,00532 0,00315 0,00062
Phi 0,7874369 0,7874318 0,7874314 0,7874316 0,7874317
Lambda 0,3716323 0,3716225 0,3716224 0,3716229 0,3716230
DPhi["] 4,525 -1,063 -0,080 0,047 0,009
DLambda["] -8,331 -2,019 -0,020 0,102 0,011
A -0,41076 -0,27311 -0,27300 -0,27300 -0,27300
B 0,08253 0,05657 0,05616 0,05609 0,05612
C 119,31582 78,13306 78,45706 78,56605 78,56783
D 0,06542 0,04319 0,04308 0,04310 0,04311
E 0,39273 0,26261 0,26190 0,26195 0,26198
F -77,33344 -52,03102 -52,27364 -52,21987 -52,21525
K -0,00004 0,00001 0,00000 0,00000 -0,00001
L 0,00062 0,00011 0,00038 0,00039 0,00039
s0 1,10100 0,90136 0,98135 0,95443 0,95383
F 1,21 1,23 1,04 1,10 1,10

10. 10/11
Results - Face 2
Iteration 1 2 3 4 5
xi0 -0,43461 0,08852 -0,06188 0,02116 -0,01040
eta0 0,26652 -0,05651 0,03846 -0,01341 0,00658
Phi 0,7874344 0,7874303 0,7874331 0,7874321 0,7874326
Lambda 0,3716279 0,3716370 0,3716307 0,3716328 0,3716318
DPhi["] 3,998 -0,848 0,577 -0,201 0,099
DLambda["] -9,238 1,882 -1,315 0,450 -0,221
A 0,23148 0,23162 0,23156 0,23157 0,23157
B -0,04566 -0,04545 -0,04577 -0,04563 -0,04570
C -73,05891 -72,66272 -72,73164 -72,68102 -72,69794
D -0,04266 -0,04270 -0,04267 -0,04268 -0,04267
E -0,21906 -0,21932 -0,21912 -0,21919 -0,21916
F 46,75433 46,51308 46,55888 46,52518 46,53720
K -0,00007 -0,00007 -0,00007 -0,00007 -0,00007
L -0,00046 -0,00046 -0,00046 -0,00046 -0,00046
s0 1,10100 1,10448 1,10355 1,10380 1,10378
F 1,21 1,22 1,22 1,22 1,22

11. 11/11
Conclusion
• Portability
• Field session: 30 - 60 min
• GPS: Good reliability of time-keeping
• CCD + GPS => elimination of observer’s error

12. 12/11
Thanks!