Determination of the reference frames deflections from optical observations of GNSS satellites
Optical observations of navigation satellites were carried out at Terskol observatory during 2007-2010 with the aim to determine the deffection angles between GPS and GLONASS dynamical reference frames. There were three different observations strategies: celestial equator crossing, intersection of v...
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Головна астрономічна обсерваторія НАН України
2011
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| Cite this: | Determination of the reference frames deflections from optical observations of GNSS satellites / V.Ya. Choliy, V.P. Zhaborovskyy, V. Taradiy, L. Rykhlova // Advances in Astronomy and Space Physics. — 2011. — Т. 1., вип. 1-2. — С. 99-101. — Бібліогр.: 7 назв. — англ. |
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Choliy, V.Ya. Zhaborovskyy, V.P. Taradiy, V. Rykhlova, L. 2017-06-03T20:14:19Z 2017-06-03T20:14:19Z 2011 Determination of the reference frames deflections from optical observations of GNSS satellites / V.Ya. Choliy, V.P. Zhaborovskyy, V. Taradiy, L. Rykhlova // Advances in Astronomy and Space Physics. — 2011. — Т. 1., вип. 1-2. — С. 99-101. — Бібліогр.: 7 назв. — англ. 987-966-439-367-3 https://nasplib.isofts.kiev.ua/handle/123456789/119092 Optical observations of navigation satellites were carried out at Terskol observatory during 2007-2010 with the aim to determine the deffection angles between GPS and GLONASS dynamical reference frames. There were three different observations strategies: celestial equator crossing, intersection of visible satellite paths, occultation of astrometric stars with the satellite. We present methodology of observation, data processing and the first results. Authors kindly acknowledge M. Andreev from Terskol observatory for his help in optical observations. en Головна астрономічна обсерваторія НАН України Advances in Astronomy and Space Physics Determination of the reference frames deflections from optical observations of GNSS satellites Article published earlier |
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Determination of the reference frames deflections from optical observations of GNSS satellites |
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Determination of the reference frames deflections from optical observations of GNSS satellites Choliy, V.Ya. Zhaborovskyy, V.P. Taradiy, V. Rykhlova, L. |
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Determination of the reference frames deflections from optical observations of GNSS satellites |
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Determination of the reference frames deflections from optical observations of GNSS satellites |
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Determination of the reference frames deflections from optical observations of GNSS satellites |
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Determination of the reference frames deflections from optical observations of GNSS satellites |
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determination of the reference frames deflections from optical observations of gnss satellites |
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Choliy, V.Ya. Zhaborovskyy, V.P. Taradiy, V. Rykhlova, L. |
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Choliy, V.Ya. Zhaborovskyy, V.P. Taradiy, V. Rykhlova, L. |
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2011 |
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Advances in Astronomy and Space Physics |
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Головна астрономічна обсерваторія НАН України |
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Optical observations of navigation satellites were carried out at Terskol observatory during 2007-2010 with the aim to determine the deffection angles between GPS and GLONASS dynamical reference frames. There were three different observations strategies: celestial equator crossing, intersection of visible satellite paths, occultation of astrometric stars with the satellite. We present methodology of observation, data processing and the first results.
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https://nasplib.isofts.kiev.ua/handle/123456789/119092 |
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Determination of the reference frames deflections from optical observations of GNSS satellites / V.Ya. Choliy, V.P. Zhaborovskyy, V. Taradiy, L. Rykhlova // Advances in Astronomy and Space Physics. — 2011. — Т. 1., вип. 1-2. — С. 99-101. — Бібліогр.: 7 назв. — англ. |
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2025-11-24T04:20:24Z |
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Determination of the reference frames de�ections from optical
observations of GNSS satellites
Choliy V. Ya.1, Zhaborovskyy V. P.1, Taradiy V.2, Rykhlova L.2
1 Taras Shevchenko National University of Kyiv, Glushkova ave., 4, 03127, Kyiv, Ukraine
2INASAN, Pyatnizkaya st., 48, 119017, Moscow, Russia
charlie@univ.kiev.ua
Optical observations of navigation satellites were carried out at Terskol observatory during 2007-2010
with the aim to determine the de�ection angles between GPS and GLONASS dynamical reference frames. There
were three di�erent observations strategies: celestial equator crossing, intersection of visible satellite paths,
occultation of astrometric stars with the satellite. We present methodology of observation, data processing
and the �rst results.
Introduction
During seasons of 2007-2010 optical observation of navigation (GPS and GLONASS) satellites were carried
out at Terskol observatory (3128 m above sea level, Northern Caucasus, Russia). In total, more than 3000
raw satellite images were caught. The �rst testing images have 5 sec exposure while the most of others �
1 sec. Raw images served as a sources of combined ones. Examples are presented in Fig. 1.
Figure 1: Three kinds of observations (left to right): equator crossing, reference star occultation, mutual paths
crossing.
Three di�erent types of events were interesting for us. First of all if there was a visible satellite path
crossing with celestial equator (left part of Fig. 1). Such events may be easily forecasted. Processing of the
pictures consists in �xing the place on the equator where the satellite crossed it. Sometimes, the satellite
occults reference astrometric star (central part of Fig. 1). As the star is a point-like source it is very di�cult
to forecast such events. That is why they were observed mostly occasionally. The third type of events was
visible intersection of satellite paths (right part of Fig. 1). It is quite possible, as inclinations of GPS and
GLONASS orbits are di�erent. The mutual intersections are quite rare: 1− 2 observable events per night.
The last type of events needs very precise ephemeris. Good example is presented on the right part of
Fig. 1. According to ephemeris we planed to catch the intersection near the center of telescope �eld of view.
Despite of that, the real intersection point lies de�nitely not in the center of the image, which can be clearly
seen on right part of Fig. 1.
99
Advances in Astronomy and Space Physics V. Ya. Choliy, V. P. Zhaborovskyy
Satellite positions
Navigation messages in RINEX format and �nal orbits in SP3 �les were used to determine satellite
positions according to GPS [3] and GLONASS [4] interface control documents.
For GPS the keplerian elements (a, e, i0, Ω0, ω0, M0, ∆n) their time derivatives
(
dΩ
dt
,
dω
dt
,
di
dt
)
and per-
turbation model (Cic, Cis, Crc, Crs, Cuc, Cus) were extracted for the moments, closest to the observations.
Coordinates in orbital reference frame were then deduced according to the following algorithm:
n =
√
γM⊕
a3
+ ∆n,
M = M0 + n(t− te),
E − e sinE = M → E,
tan v =
√
1− e2 sinE
cosE − e
→ v,
u = ω + v,
Ω = Ω0 +
dΩ
dt
(t− te) + Ω⊕(t− t0),
i = i0 + Cic cos (2u) + Cis sin (2u) +
di
dt
(t− te),
ω = ω0 + Cuc cos (2u) + Cus sin (2u),
r = a(1− e cosE) + Crc cos (2u) + Crs sin (2u),
(1)
and the coordinates itself:
r =
(
a(1− e2)
1 + e cos v
cosu,
a(1− e2)
1 + e cos v
sinu, 0
)
, (2)
where γM⊕ is the geocentric gravitational constant, Ω⊕ is the Earth's rotation velocity, te is the moment of
ephemeris data.
The di�erence (t−te) never exceeds 2h for GPS and 30m for GLONASS. Then coordinates (2) are transformed
to equatorial reference frame (in our case it is ICRF � International Celestial Reference Frame):
rICRF = R(−Ω) · P(−i) · R(−ω)r, (3)
where P and R are rotation matrices:
P(α) =
(
1 0 0
0 cosα sinα
0 − sinα cosα
)
, R(α) =
(
cosα sinα 0
− sinα cosα 0
0 0 1
)
. (4)
SP3 �nal orbits [5] contain satellite positions for every 15 min. They should be interpolated to �nd
position on desired moment.
In contrary to GPS, determination of GLONASS position implies numerical integration of satellites equations
of motion:
dr
dt
= V,
dV
dt
= γM⊕ · r
r3
·
(
−1 +
3C20a
2⊕
r2
(
k − 5
z
r2
))
+ j( + j¯,
(5)
where k = 3 for z and k = 1 for x and y. These equations account for perturbation from second zonal
geopotential garmonics C20 and direct in�uence of the Sun (j¯) and the Moon (j(). One should select the
data from RINEX �le for the closest possible moment and integrate to the moment of interest. There are no
SP3 �les for GLONASS.
De�ection angles
Coordinates rs and r′ in two di�erent reference frames satisfy the Helmert transform [1]:
rs =
(
µ1 R −Q
−R µ2 P
Q −P µ3
)
r′ + a, (6)
100
Advances in Astronomy and Space Physics V. Ya. Choliy, V. P. Zhaborovskyy
where P , Q and R are rotation angles around x, y and z correspondingly, µi are the scale factors, a is
the center shift vector. Having coordinates of the same point in two reference frames one can solve (6) for
rotation angles, scales and shift vector.
Unfortunately, we cannot account GLONASS satellite coordinates in GPS dynamical reference frame and
vice versa. That is why the third reference frame � optical one � was used.
If we have transformation angles from optical frame to the �rst and the second ones: P1, Q1, R1 and
P2, Q2, R2, they can be presented as ephemeris values Be with small corrections ∆B as Be + ∆B. Thus
they satisfy the following relation [6]:
(
P
Q
R
)
=
(
0 cos Pe1 sinPe1 cosQe1
1 0 sinQe1
0 − sinPe1 cosPe1 cosQe1
)(
∆P1 −∆P2
∆Q1 −∆Q2
∆R1 −∆R2
)
. (7)
Ephemeris values for rotation angles may by calculated from:
tanP1 = tan i sinΩ; sinQ1 = sin i cosΩ; tan(R1 + ω) = tan Ω/ cos i. (8)
Equations (7) can be modi�ed to trivial ones:
P = ∆P2 −∆P2, Q = ∆Q1 −∆Q1, R = ∆R3 −∆R3 (9)
in the case of geostationary satellites or when a satellite crosses the equator.
Results and conclusions
We used Astrometrica software [7] with UCAC2 astrometric catalogue [2] for processing the pictures.
Three kinds of observations were used to deduce P, Q, R between GPS and GLONASS dynamical Reference
frames. Typical result is present below:
(
P
Q
R
)
=
(
2.38± 1.88
1.56± 1.32
−0.90± 1.06
)
; a =
(
0.070± 1.420
−0.703± 1.420
1.413± 1.128
)
, (10)
angles in arcsec, shifts in km.
Di�erences between two reference frames are above their errors, especially P , Q and z components of a.
They are quite large and need further analysis.
Acknowledgement
Authors kindly acknowledge M. Andreev from Terskol observatory for his help in optical observations.
References
[1] Ho�man-Wellenhof B., Lichtenegger H., Collins J. Global Positioning System � Theory and Practice, McGraw Hill, NY
(1995)
[2] Zacharias N., Urban S. E., Zacharias M. I. et al. Astron. J., V. 127, pp. 3043-3059 (2004)
[3] GPS Interface Control Document. Rev. D. ICD-GPS-200D, Navstar GPS Space Segment (2003)
[4] GLONASS Interface Control Document. Rev. 5. 1. ICD-GLONASS-5.1, RosNII SI (2008)
[5] http://www.ngs.noaa.gov/orbits/
[6] Duma D. P. Determination of mutual orientation of stellar catalogues, Naukova Dumka, Kyiv, (1968)
[7] Raab H., http://www.astrometrica.at/
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