Telescope inaccuracy model based upon satellite laser ranging data
In this paper, a new approach to constructing a telescope pointing model is described. Procedures of data collection, data processing, and model construction are presented. Telescope encoder countings, obtained during satellite laser ranging, are used as input data for the construction of the model....
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| Zitieren: | Telescope inaccuracy model based upon satellite laser ranging data / V.P. Zhaborovskyy, V.O. Pap, M.M. Medvedsky, V.Ya. Choliy // Advances in Astronomy and Space Physics. — 2013. — Т. 3., вип. 1. — С. 63-65. — Бібліогр.: 5 назв. — англ. |
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irk-123456789-1196122017-06-08T03:04:15Z Telescope inaccuracy model based upon satellite laser ranging data Zhaborovskyy, V.P. Pap, V.O. Medvedsky, M.M. Choliy, V.Ya. In this paper, a new approach to constructing a telescope pointing model is described. Procedures of data collection, data processing, and model construction are presented. Telescope encoder countings, obtained during satellite laser ranging, are used as input data for the construction of the model. The model is presented as a harmonical series with frequencies obtained by the maximum entropy spectral analysis method. 2013 Article Telescope inaccuracy model based upon satellite laser ranging data / V.P. Zhaborovskyy, V.O. Pap, M.M. Medvedsky, V.Ya. Choliy // Advances in Astronomy and Space Physics. — 2013. — Т. 3., вип. 1. — С. 63-65. — Бібліогр.: 5 назв. — англ. 2227-1481 http://dspace.nbuv.gov.ua/handle/123456789/119612 en Advances in Astronomy and Space Physics Головна астрономічна обсерваторія НАН України |
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In this paper, a new approach to constructing a telescope pointing model is described. Procedures of data collection, data processing, and model construction are presented. Telescope encoder countings, obtained during satellite laser ranging, are used as input data for the construction of the model. The model is presented as a harmonical series with frequencies obtained by the maximum entropy spectral analysis method. |
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Article |
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Zhaborovskyy, V.P. Pap, V.O. Medvedsky, M.M. Choliy, V.Ya. |
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Zhaborovskyy, V.P. Pap, V.O. Medvedsky, M.M. Choliy, V.Ya. Telescope inaccuracy model based upon satellite laser ranging data Advances in Astronomy and Space Physics |
| author_facet |
Zhaborovskyy, V.P. Pap, V.O. Medvedsky, M.M. Choliy, V.Ya. |
| author_sort |
Zhaborovskyy, V.P. |
| title |
Telescope inaccuracy model based upon satellite laser ranging data |
| title_short |
Telescope inaccuracy model based upon satellite laser ranging data |
| title_full |
Telescope inaccuracy model based upon satellite laser ranging data |
| title_fullStr |
Telescope inaccuracy model based upon satellite laser ranging data |
| title_full_unstemmed |
Telescope inaccuracy model based upon satellite laser ranging data |
| title_sort |
telescope inaccuracy model based upon satellite laser ranging data |
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Головна астрономічна обсерваторія НАН України |
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2013 |
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http://dspace.nbuv.gov.ua/handle/123456789/119612 |
| citation_txt |
Telescope inaccuracy model based upon satellite laser ranging data / V.P. Zhaborovskyy, V.O. Pap, M.M. Medvedsky, V.Ya. Choliy // Advances in Astronomy and Space Physics. — 2013. — Т. 3., вип. 1. — С. 63-65. — Бібліогр.: 5 назв. — англ. |
| series |
Advances in Astronomy and Space Physics |
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AT zhaborovskyyvp telescopeinaccuracymodelbaseduponsatellitelaserrangingdata AT papvo telescopeinaccuracymodelbaseduponsatellitelaserrangingdata AT medvedskymm telescopeinaccuracymodelbaseduponsatellitelaserrangingdata AT choliyvya telescopeinaccuracymodelbaseduponsatellitelaserrangingdata |
| first_indexed |
2025-07-08T16:16:07Z |
| last_indexed |
2025-07-08T16:16:07Z |
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1837096100324966400 |
| fulltext |
Telescope inaccuracy model based upon satellite
laser ranging data
V.P. Zhaborovskyy1∗, V.O. Pap1, M.M. Medvedsky1, V.Ya. Choliy1,2
Advances in Astronomy and Space Physics, 3, 63-65 (2013)
© V.P. Zhaborovskyy, V.O. Pap, M.M. Medvedsky, V.Ya. Choliy, 2013
1Main Astronomical Observatory of NAS of Ukraine, 27 Akademika Zabolotnoho St., 03680 Kyiv, Ukraine
2Taras Shevchenko National University of Kyiv, Glushkova ave., 4, 03127, Kyiv, Ukraine
In this paper, a new approach to constructing a telescope pointing model is described. Procedures of data
collection, data processing, and model construction are presented. Telescope encoder countings, obtained during
satellite laser ranging, are used as input data for the construction of the model. The model is presented as a
harmonical series with frequencies obtained by the maximum entropy spectral analysis method.
Key words: telescopes, methods: data analysis, site testing
introduction
Accurate pointing of the satellite laser ranging
telescope is necessary, particularly if the satellite is
not visible. A telescope model is constructed to solve
this issue. Two-axial telescopes are used for laser
ranging, and one such telescope is located at the laser
ranging station �Golosiiv-Kyiv� (ILRS # 1824). The
telescope is equipped with azimuth (A) and height
(h) encoders.
The functions f(hc, Ac, ei) and g(hc, A, ei), of
kind:
Ao = f(Ac, hc, ei),
ho = g(Ac, hc, ei),
(1)
need to be constructed, where Ac, hc are calculated
from ephemeris coordinates, Ao, ho are angular en-
coders countings, and ei are various parameters, e. g.
temperature and, possibly, time. These variables
are referred to as functions the telescope inaccuracy
model.
The model is considered �good� if |∆A| = |Aobs−
Aeph| <= ε and |∆h| = |hobs−heph| <= ε, where ε is
the half-width of laser beam. For the �Golosiiv-Kyiv�
station, ε = 10− 15 arcsec.
input data
for model construction
Several models were created at station 1824 in the
past ten years, using star and satellite observations
[1, 2]. Satellite observations are preferable for the
model construction, as they are conducted during
the main observation program.
The database from [4] was used in this work. In
Fig. 1 through Fig. 4 the Lageos-1 and Lageos-2 ob-
servations are shown in black, while all other satel-
lite observations are in grey. The total number of
the observations is 95253 and 6817 for Lageos-1 and
Lageos-2, respectively.
There were two reasons for creating our model us-
ing solely Lageos satellite observations. Firstly, they
are high priority targets for observation. Secondly,
their observations can be considered representative.
model construction
From the analysis of Fig. 1 through Fig. 2 it is
evident that ∆A and ∆h depend periodically upon
A. From Fig. 4 � ∆h depends linearly on h, and
from Fig. 3 � ∆A does not depend on h, and here
is why:
f(A) =
N∑
n=1
(Bn sin (Aϕn)+
+Cn cos (Aϕn)) +D, (2)
g(A, h) =
N∑
n=1
(En sin (Aψn)+
+Fn cos (Aψn)) +Gh+H, (3)
where selected as f(A, h) and g(A, h) (see (1)), where
Bn, Cn, En, Fn, D,G,H are linear parameters, and
ϕn and ψn are non-linear parameters of the model.
The model is to be used for h > 20◦.
The telescope errors were decomposed into the
set of the periodical functions. The D,H explain
constant discrepancy between the zeros of the en-
coders and the ephemeris, G describes the linear de-
pendence of the discrepancies from h, ϕn and ψn are
data series frequencies.
∗zhskyy@gmail.com
63
Advances in Astronomy and Space Physics V. P. Zhaborovskyy, V.O. Pap, M.M. Medvedsky, V.Ya. Choliy
An iterative approach to the construction of the
model was used. For example, let's take g(A, h). For
every step n there are data series τ
(n)
i , and the fre-
quency ψn at maximum amplitude is searched for by
maximum entropy spectral analysis method [5], ac-
cording to the procedure from [3], with autoregres-
sive sequences on the order of 4
√
L, where L is the
data series length. Then, coe�cients En and Fn of
the harmonical functions are determined by the least
squares method:
τ
(n+1)
i = τ
(n)
i − (En sin (Aψn) + Fn cos (Aψn)) . (4)
Here, ∆h = hobs−heph with mean removed was used
as τ
(0)
i .
Fig. 1: Dependence of ∆A = Aobs−Aeph from azimuth.
Fig. 2: Dependence of ∆h = hobs − heph from azimuth.
At each step the standard deviation σ is used as
a criteria. The iterations run until σ >= ε, where
ε = 10−15 arcsec is half-width of the laser beam for
�Golosiiv-Kyiv� station.
The same approach was used for azimuthal
model.
results and conclusions
Numerical values of parameters from equations
(2�3) are presented in Table 1 and Table 2. Ad-
ditionally, D = 111◦.2 ± 0◦.5, G = 0.06 ± 0.02,
H = 5◦.9± 0◦.5.
Table 1: Numerical values of the azimuth model's coef-
�cients.
n Bn Cn ϕn
arcsec arcsec deg
1 19.5± 0.8 18.0± 0.4 112
2 −86.5± 0.5 114.± 4.0 71
3 16.8± 0.6 −149.± 3.9 62
4 53.7± 0.8 −1.53± 0.2 46
5 −17.0± 1.0 17.0± 0.7 41
6 0.84± 0.04 −0.84± 0.09 22
7 3.5± 0.8 1.0± 0.1 19
8 −3.2± 0.7 2.2± 0.2 18
9 −0.33± 0.02 −1.2± 0.1 16
10 0.09± 0.01 −0.09± 0.01 15
Table 2: Numerical values of the height model's coe�-
cients.
n En Fn ψn
arcsec arcsec deg
1 2573± 36 −3874± 34 292
2 343± 6 591± 5 137
3 8.30± 0.9 69.6± 1.8 59
4 −29.4± 2.3 −21.1± 0.3 51
5 −2.3± 0.3 −2.8± 0.3 33
6 1.8± 0.2 0.4± 0.2 31
The input (gray) and modelled (black) data are
presented in the Fig. 5 (for azimuth) and Fig. 6 (for
height). The residuals of the model are presented in
the Fig. 7 and Fig. 8.
The model was implemented in �Golosiiv-Kyiv�
station, and now is used during the observations.
references
[1] MedvedskyM. & PapV. 2008, in 16th International Work-
shop on Laser Ranging, Proceedings of the conference held
12-17 October, 2008 in Poznan, Poland, 84
[2] MedvedskyM. & SuberlakV. 2002, Arti�cial Satellites �
Journal of Planetary Geodesy, 37, 3
[3] MorganK. & Somerville C.R. 1976, Canadian Studies in
Population, 3, 1
[4] PapV.O. 2011, Bulletin of The Ukrainian Centre of de-
termination of the Earth Orientation Parameters, 6, 22
[5] UlrychT. J. 1972, J. Geophys. Res., 77, 1396
64
Advances in Astronomy and Space Physics V. P. Zhaborovskyy, V.O. Pap, M.M. Medvedsky, V.Ya. Choliy
Fig. 3: Dependence of ∆A = Aobs −Aeph from height. Fig. 4: Dependence of ∆h = hobs − heph from height.
Fig. 5: Azimuth model. Fig. 6: Height model.
Fig. 7: Azimuth's model residuals. Fig. 8: Height's model residuals.
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