National University of Uzbekistan
National Centre of Geodesy and Cadastre
Astronomical Institute of the Uzbek Academy of Sciences
Intermediate reference frame for Uzbekistan
topographic maps
Mirmakhmudov E.1, Prenov Sh.1, Magdiev Kh.2, Fazilova D.3
1National
University of Uzbekistan
centre of geodesy and cartography (Uzbekistan)
3Astronomical Institute of the Uzbek Academy of Sciences
2National
phone: (+998-71)234-67-54, (+998-90) 966-38-80 (cell.)
e-mail: erkin_mir@yahoo.com , erkin_mir@mail.ru
United Na*ons/Russian Federa*on Workshop on the Applica*ons of Global Naviga*on Satellite Systems, Krasnoyarsk, 18-­‐22.05.2015 • National University of Uzbekistan
• National Centre of Geodesy and Cadastre
• Astronomical Institute of the Uzbek Academy of Sciences
Contents
1.
2.
3.
4.
5.
6.
7.
GNSS in Uzbekistan
Bessel ellipsoid(1841)
Coordinate system SK32
SK42(Pulkovo, Russia)
Gauss-Kruger Projection
Reference frame
Conclusion
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GNSS EDUCATION SCIENCES INVESTIGATION APPLICATION NCGC,UZGASHLITI NUU,TABI,TIMI AI, SI D =σ 2
σ2 =
∑ (X
2
i
− X)
n
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• National Centre of Geodesy and Cadastre
• Astronomical Institute of the Uzbek Academy of Sciences
Before 1995-­‐2000 CS42 Triangula*on tower BENCH
Now
CS42 In the future WGS84
PZ90(SC95
? CS42
) WGS84
MARK
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National Centre of Geodesy and Cadastre
Astronomical Institute of the Uzbek Academy of Sciences Tashkent coordinate system
Central Asian triangulation measurement were produced in Tashkent coordinate system
(1875). This works are based on the Bessel –ellipsoid (1841), a=6 377 397m., α= 1/299.14
The were measurement and calculated the longitude for 900 points (rms= ± 0s.25).
Gedeonov D.D 1854-1908 In 1950 about 50% of the European triangulation networks and about 20% of
other continents networks (also Russia and Uzbekistan ) were based on the
Bessel ellipsoid.
λ=-4h37m10.80s
1891
φ =410 19/ 31//.48 1895-1896
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Astronomical Institute of the Uzbek Academy of Sciences Origin: Sablino, Russia.1930.
Bessel reference ellipsoid
a=6377397.155m
b=6356078.963 Origin: Bugry, Russia.1942.
Krasovsky reference ellipsoid
a=6378245m b=6356863 f=1/298.3 Bessel F.V. (1784-­‐1846) Resolution of the SU government, №760, 1946.04.07.
Astronomy- geodetic network (87 polygons) of 1 order
Krasovsky 1878-­‐1948 B0=φ0 –ξ0 = 590 46/ 18//.71 – 0//.16 = 590 46/ 18//.55
L0= λ0 –η0secB0 =300 19/ 38//.55+3//.54 =300 19/ 42//.09
A0=α0 - η0tgB0= 1210 40/ 36//.13+2//.66=1210 40/ 38//.79 (Bugry)
f=1:298,3. ΔX=382m.
Δ Y=151m.
Δ Z=574m.
Δ а=739.845
Δ f= 0.10037483
ξ0==-dBo=0,16ʺ″, ηo secB=-dLo==-3,54ʺ″,
ηо=1,78ʺ″.
TriangulaRon line 1ord Pulkovo TriangulaRon line 2ord Base-­‐line Astronomical points United Na*ons/Russian Federa*on Workshop on the Applica*ons of Global Naviga*on Satellite Systems, Krasnoyarsk, 18-­‐22.05.2015 6 National University of Uzbekistan
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Astronomical Institute of the Uzbek Academy of Sciences THE GAUSS-­‐KRUGER PROJECTION 10 11 12 13 Gauss К F (1777 – 1855) Z O N E S UZBEKISTAN J. Krüger 1853-­‐1923 l2
l4
r SinB + r Cos 2 B SinB (5 − t 2 + 9η 2 + 4η 4 );
2
24
3
l
l5
y = lr + r Cos 2 B(1 − t 2 + η 2 ) +
r Cos 4 B (5 − 18t 2 + t 4 − 14η 2 − 58η 2 t 2 );
6
120
2
2
m = n = 1 + 0,000152l Cos B; p = m 2 ; w = 0; t = tgB; η 2 = eʹ′ 2 Cos 2 B,
x=S+
X
0
О
1
6 12 2
3
18
equator
354 0
Y
60
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SK42(Pulkovo)
B0=φ0 –ξ0
L0= λ0 –η0secB0
A0=α0 - η0tgB0
SK42,
WGS84
ywgs84 –ysk42=64m. , Lwgs84 –Lsk42 = 2.90 arcsec
xwgs84 –xsk42=9m. , Bwgs84 –Bsk42 = 0.23 arcsec
Scale 1:100 000 1:50 000 1:25 000 1:10 000 1:5 000 ΔXwgs84-sk42 0.09mm 0.18mm 0.30mm 0.9mm 1.8mm hwgs84 –hsk42=109m ΔYwgs84-sk42 0.64mm 1.28mm 2.56mm 6.40mm 12.8mm United Na*ons/Russian Federa*on Workshop on the Applica*ons of Global Naviga*on Satellite Systems, Krasnoyarsk, 18-­‐22.05.2015 National University of Uzbekistan
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The first geoid
Prof.Pomeranzev
1847-1921
GIS Panorama Ferghana valley The geoid of Ferghana valley (1897).
B-φ=12.73'' , L-λ=16.31 '‘, Rms= ±0.30 '‘
33 points.
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Fragment of Uzbekistan geoid
.
)
CATS network (Uzbekistan)(1992-1996
№ст 1 2 3 4 6 9 10 16 40 54 55 56 58 59 79 N,м -37.73 -36.71 -40.14 -41.37 -36.96 -41.60 -42.90 -50.97 -35.64 -40.41 -42.86 -46.79 -37.90 -43.85 -43.16 United Na*ons/Russian Federa*on Workshop on the Applica*ons of Global Naviga*on Satellite Systems, Krasnoyarsk, 18-­‐22.05.2015 10 National University of Uzbekistan
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Z
ω
Zcs42
z
ZZ
cs42
CS42
ω =0
CS42
z
WGS84
Y
ω
xcs42
ω
WGS84
ω
Y
y
ω
ycs42
x
X⎡ X ⎤
X
ωZ − ωY ⎤⎡ X ⎤
⎡ X ⎤
⎡TX ⎤ ⎡ m
⎢ Y ⎥
⎢ Y ⎥
⎢T ⎥ + ⎢− ω
⎥⎢ Y ⎥
=
+
m
ω
Y
Z
X
⎢ ⎥
⎢ ⎥
⎢ ⎥ ⎢
⎥⎢ ⎥
⎢⎣ Z ⎥⎦ SК −42 ⎢⎣ Z ⎥⎦WGS −84 ⎢⎣TZ ⎥⎦ ⎢⎣ ωY − ω X m ⎥⎦⎢⎣ Z ⎥⎦WGS −84
x
DATUM ∆X ∆Y ∆Z Method Comments CS42-­‐WGS84 +28 -­‐130 -­‐95 Molodensky NIMA CS42-­‐WGS84 +25 -­‐141 -­‐80 Helmert GOST(RU) CS42-­‐WGS84 +22 -­‐123 -­‐83 Molodensky Bazlov(RU) CS42-­‐WGS84 +23 -­‐125 -­‐87 Molodensky Fazilova(UZ) United Na*ons/Russian Federa*on Workshop on the Applica*ons of Global Naviga*on Satellite Systems, Krasnoyarsk, 18-­‐22.05.2015 11 y
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International Latitude station (1899)
IGS
Kit3
Network
Kitab, Uzbekistan CHAMP DORIS
Change of the north pole coordinate
NETWORK
Tashkent DORIS MAID Kitab Maidanak φ*- φ = x cosλ – y sinλ;
λ* - λ = (x sinλ – y cosλ)tgφ;
η* - η = (λ* - λ)cosB;
A* - A = (x sinλ – y cosλ)cosφ.
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Transformation of coordinate system B, L,Н, WGS84
x =(N+H) cosB cosL
y=(N+H) cosB sin L
z=(N(1-e 2)+H) sinB
⎡ X ⎤
⎡ X ⎤
⎡T X ⎤ ⎡ µ
⎢ Y ⎥ = ⎢ Y ⎥ + ⎢ T ⎥ + ⎢− ω
⎢ ⎥
⎢ ⎥
⎢ Y ⎥ ⎢ Z
⎢⎣ Z ⎥⎦84 ⎢⎣ Z ⎥⎦ 42 ⎢⎣ TZ ⎥⎦ ⎢⎣ ωY
L = arctg
ωZ
µ
− ωX
X,Y,Z (WGS84)
− ωY ⎤⎡ X ⎤
ω X ⎥⎥⎢⎢ Y ⎥⎥
µ ⎥⎦⎢⎣ Z ⎥⎦ 42
X,Y,Z (CS42)
B, L,Н, СS-42
Y
Z + N ( i −1 )e2 sin B( i −1 )
B( i ) = arctan
rp
X
l2
l4
r SinB +
r Cos 2 B SinB (5 − t 2 + 9η 2 + 4η 4 );
2
24
l3
l5
y = lr + r Cos 2 B (1 − t 2 + η 2 ) +
r Cos 4 B (5 − 18t 2 + t 4 − 14η 2 − 58η 2 t 2 );
6
120
m = n = 1 + 0,000152l 2 Cos 2 B; p = m 2 ; w = 0; t = tgB; η 2 = eʹ′ 2 Cos 2 B,
x=S+
ywgs84 =ysk42+ Δy
xwgs84 =xsk42+Δx
х,у(CS42)
G-К projection
Intermediate
G-К projection
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REFERENCE FRAME NATIONAL
Nukus
Urgench
LOCAL(1+2 regions)
TOSHKENT
Namangan
Andijon
Farg’ona
Guliston
Navoi
Buhoro
Jizzax
Samarqand
Qarshi
Termiz
region
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NaRonal ellipsoid of Uzbekistan ? Central-Asian
ellipsoid ?
?
Reference-ellipsoid(SK42)
Global ellipsoid(WGS84)
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Sheglov, V. P.100 Anniversary of the Astronomical InsRtute of the Uzbek Academy of Sciencies .Tashkent.Fan.
1974. Reigber, Ch, Angermann, D., Michel, G. W. Klotz, J., Galas, R., & the CATS-­‐Team, GPS constraints on the distribuRon of deformaRon of the Tien Shan, N-­‐Pamirs and behavior of the Tarim, 14th Himalaya-­‐Karakorum-­‐
Tibet Workshop, Terra Nostra, 127,1999. Moritz, H. (2000): GeodeRc Reference System 1980. J. Geod. 74: 128–133. Gunter Seeber . Satellite Geodesy. 2nd completely revised and extended ediRon. New York 2003. Fazilova D., Mirmakhmudov E. WGS-­‐84 and SC-­‐42: current realizaRons of geodeRc network of Uzbekistan and transformaRon parameters. Proceeding of conference. France.2002. Mirmakhmudov E., Safarov E. Improvement of the ellipsoid height for maps of Uzbekistan based on of GPS data. Abstract. United NaRons/United Arab Emirates/United States of America Workshop on the ApplicaRons of Global NavigaRon Satellite Systems, Dubai, 16-­‐20 January 2011. Mirmakhmudov E., Safarov E. Fazilova D. ModificaRon of verRcal reference frame. Abstract. United NaRons/
Riga /United States of America Workshop on the ApplicaRons of Global NavigaRon Satellite System, Latvia, Riga, 14 –18 May 2012. Mirmakhmudov E., Safarov E., Fazilova D. and Fan H. (2013). DeterminaRon okransformaRon parameters between CS42 and WGS84 for Uzbekistan territory.UN/CroaRa Workshop on the Global NavigaRon Satellite Systems, April 21-­‐25, 2013,Baska Krk Island. Mirmakhmudov E., Fazilova D. ConverRng between CS42 and WGS84. New Technologies and EducaRon. Tashkent-­‐2013. P.89-­‐104. Akylbek CHYMYROV. GNSS applicaRon trends in Central Asia. Megfelelni az új kihívásoknak * GISopen konferencia.2014. United Na*ons/Russian Federa*on Workshop on the Applica*ons of Global Naviga*on Satellite Systems, Krasnoyarsk, 18-­‐22.05.2015 National University of Uzbekistan
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Thank you for your aden*on! The author is very thankful
for financial support of the United Nations
(Office for Outer Space Affairs)
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