Analysis of the preliminary results of GPS observation series at the Poltava Gravimetrical Observatory
The first results of researches of GPS observations in Poltava are submitted. Linear trend, annual, semi-annual terms as well as a number of additional terms are marked out on each coordinate. It is shown that the annual term considerably prevails above semi-annual one. Numerical values of parameter...
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| Zitieren: | Analysis of the preliminary results of GPS observation series at the Poltava Gravimetrical Observatory / N.M. Zalivadnyi, V.V. Nekrasov, V.V. Schliahovoi // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 365-368. — Бібліогр.: 5 назв. — англ. |
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| author | Zalivadnyi, N.M. Nekrasov, V.V. Schliahovoi, V.V. |
| author_facet | Zalivadnyi, N.M. Nekrasov, V.V. Schliahovoi, V.V. |
| citation_txt | Analysis of the preliminary results of GPS observation series at the Poltava Gravimetrical Observatory / N.M. Zalivadnyi, V.V. Nekrasov, V.V. Schliahovoi // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 365-368. — Бібліогр.: 5 назв. — англ. |
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| container_title | Кинематика и физика небесных тел |
| description | The first results of researches of GPS observations in Poltava are submitted. Linear trend, annual, semi-annual terms as well as a number of additional terms are marked out on each coordinate. It is shown that the annual term considerably prevails above semi-annual one. Numerical values of parameters of these components are determined. Comparison of the obtained results with results of the similar researches at the Kyiv Station has been carried out.
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| first_indexed | 2025-12-07T18:08:30Z |
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ANALYSIS OF THE PRELIMINARY RESULTS OF GPS OBSERVATION
SERIES AT THE POLTAVA GRAVIMETRICAL OBSERVATORY
N. M. Zalivadnyi, V. V. Nekrasov, V. V. Schliahovoi
Poltava Gravimetrical Observatory, NAS of Ukraine
27/29 Myasoedova Srt., 36029 Poltava, Ukraine
e-mail: geo@poltava.ukrtel.net
The first results of researches of GPS observations in Poltava are submitted. Linear trend, annual,
semi-annual terms as well as a number of additional terms are marked out on each coordinate.
It is shown that the annual term considerably prevails above semi-annual one. Numerical values of
parameters of these components are determined. Comparison of the obtained results with results
of the similar researches at the Kyiv Station has been carried out.
INTRODUCTION
Since September 2001 regular GPS observations within the EPN (the EUREF GPS Permanent Net) have been
started at the Poltava Gravimetrical Observatory (POLV is the acronym used by the EPN). The first GPS data
have been analyzed with the goal of studying some local effects (stability of the observational place coordinates,
local Earth’s crust deformation, etc.).
The GPS data analysis was divided into two stages. Such approach to processing of observation results is
explained by the absence of a priori data on structure of the researching series at the initial investigation phase
that complicated the choice of optimum length of series for realization of the analysis. On the other hand,
the available period of supervision is not long enough for studying the structure of series based on the spectral
analysis on multiple harmonics. The high frequency band is limited to rather big interval of discretization
(averaged week values). Presence of signals in this frequency band will result in the effect of aliasing. The big
interval of discretization also reduces resolution on the periods in the low frequency band. As the results of
GPS observations are unequivocally not in statistical balance, the non-stationary part was originally filtered in
the initial series of observations. The size of linear trend on a two-year interval of observations for the POLV
Station amounted for coordinate x = −36.3 mm, y = 25.3 mm, and z = 16.3 mm.
METHOD OF ANALYSIS
At the first phase of research we applied the spectral analysis method which is widely used for researches of
latitude observations [4]. The spectrum estimation is calculated based on Fourier discrete transformation of
the unbiased correlation function. For suppression of narrow-band casual process which may be present in
the observation lines, the Tucker window was used [3].
At the first stage of calculations based on application of the spectral analysis the frequency-response chara-
cteristics of the series components were obtained. At the second stage the determination of these components
was carried out on the maximal value of spectral capacity.
As amplitude, period and phase were included in the determined parameters at component determining, we
came to non-linear model of the data [2]. For estimations of the parameters of the times series component,
the phased least squares adjustment was applied [1, 2]. Such approach is explained by the fact that the specific
task of studying of internal physical essence of processes inherent in GPS observation series was set, as well as
studying of the formation dynamics of these processes at the researched period.
THE RESULT OF ANALYSIS
In Fig. 1 sample spectrum changes of coordinates for GPS observations at the POLV Station are submitted.
The spectral analysis results proved that the annual and semi-annual terms are the factors that mainly contribute
to the variations of the observational place coordinates, the annual term being substantially predominant over
the semi-annual one. In all spectra the contribution of annual components forms about 50% of average power.
c© N. M. Zalivadnyi, V. V. Nekrasov, V. V. Schliahovoi, 2004
365
Estimations of harmonious component parameters for each coordinate of the GPS observations, obtained at
the second stage of calculations are given in Table 1. Comparing the results of the spectral analysis with
the results of phased least squares adjustment, we see that some additional harmonics not discovered at the first
stage were marked out. To compare the analysis results with the observations performed at the other stations
the similar research was carried out at the Main Astronomical Observatory (GLSV) in Kyiv. Comparison of
the observation analysis results at the POLV and GLSV stations shows good correlation in coefficients of linear
trends (for GLSV x = −28.6 mm, y = 31.2 mm, and z = 23.1 mm), annual and semi-annual terms, the other
harmonics being close in amplitude and period may differ in phase (Table 1).
0
25
50
0 10 20 30
S(w)
n
X
0
25
50
0 10 20 30
S(w)
n
Y
0
25
50
0 10 20 30
S(w)
n
Z
Figure 1. The sample spectrum for observations at the POLV Station
Table 1. Harmonic amplitudes (in mm), periods (in days) and phases (in degrees) coordinate variations of the POLV
and GLSV stations
POLV
Amplitude Period Phase
Coordinate X
5.35± 0.44 362.40± 8.29 167.51± 0.27
2.07± 0.34 177.46± 1.99 281.57± 0.60
1.04± 0.33 124.88± 1.24 34.35± 1.12
1.00± 0.32 87.83± 0.45 154.87± 1.12
0.97± 0.30 47.31± 0.07 280.21± 1.12
Coordinate Y
3.70± 0.32 354.75± 6.86 139.61± 0.30
1.06± 0.29 196.74± 4.14 33.95± 0.92
0.89± 0.28 112.04± 0.94 171.31± 1.14
Coordinate Z
5.91± 0.57 354.37± 8.97 142.47± 0.33
2.98± 0.45 180.01± 1.84 306.66± 0.53
1.59± 0.42 141.91± 1.56 326.10± 0.92
1.30± 0.39 114.02± 0.98 202.46± 1.12
1.25± 0.38 85.63± 0.40 107.03± 1.07
1.32± 0.36 50.14± 0.07 284.01± 1.14
GLSV
Amplitude Period Phase
Coordinate X
5.98± 0.49 362.97± 8.38 155.61± 0.28
2.86± 0.36 176.62± 1.52 257.01± 0.47
1.33± 0.35 118.47± 0.89 301.95± 0.90
1.05± 0.32 86.40± 0.43 165.27± 1.14
1.42± 0.29 47.23± 0.05 286.35± 0.74
Coordinate Y
4.20± 0.27 355.13± 6.03 138.22± 0.22
0.67± 0.22 189.26± 4.54 332.32± 0.52
0.84± 0.21 109.80± 0.70 138.11± 0.30
Coordinate Z
7.34± 0.59 365.17± 8.47 170.09± 0.29
3.17± 0.44 176.31± 1.64 272.82± 0.50
1.58± 0.44 149.33± 1.87 118.74± 0.96
1.40± 0.34 111.94± 0.82 180.37± 1.00
1.55± 0.36 87.03± 0.33 183.12± 0.85
1.06± 0.35 47.41± 0.07 303.11± 1.18
ADDITION ANALYSIS
For additional result verification of comparison of the initial series of GPS observations at the POLV and GLSV
stations the cross-correlation analysis was applied. Cross-correlation functions Kpg = (τ) for series of GPS
observations at POLV–GLSV are shown in Fig. 2. The cross-correlation maximum for all diagrams accounts
for displacement (τ = 0) and lies within the limits of 0.91 ÷ 0.93. If the average radius of correlation is
366
designated as rk (Kpg(τ) = 0 for τ > 0) then it is possible to receive the general model of cross-correlation
function Kpg(τ) as
Kpg(τ) = δpg exp(−ατ) cos(πτ/2rk). (1)
Thus, the characteristics of cross-correlation functions, as well as the results of determination of harmonious
components point out that the change of station coordinates is caused by the same physical process acting
inphasely at the POLV and GLSV stations.
-0,6
-0,2
0,2
0,6
1
-100 -50 0 50 100
Rxx
-0,6
-0,2
0,2
0,6
1
-100 -50 0 50 100
Ryy
-0,5
0
0,5
1
-100 -50 0 50 100
Rzz
Figure 2. Cross-correlation functions of the initial series of observations (solid) and the remainders (dotted) for POLV –
GLSV stations
After removal of the determined components (Table 1) from the initial observation lines, we received remain-
ders zp (t) and zg(t) for the POLV and GLSV stations. respectively. In Fig. 2 cross-correlation functions Kz
pg(τ)
of the remainders zp (t) and zg(t) in the series of GPS observations at POLV– GLSV stations are submitted.
We see that interdependence of the remainders reaches its maximum only for displacement τ = 0 and matters
for Kz
xx(0) = 0.62, Kz
yy(0) = 0.63, Kz
zz(0) = 0.42. And for other z displacements estimation Kz
pg(τ) does not
exceed |Kz
pg| < 0.25 on module practically meaning that the dependence between the lines is absent.
Hence, after determination of periodic components the remainders can be considered as correlated casual
processes z(t) and z(t′) with dispersions σ2
p and σ2
g and cross-correlation function
Kpg(τ) = σpgδ(t − t′), (2)
where δ(t − t′) is delta-function.
The method of comparison of integrated spectral functions of the remainders with spectral function of white
noise is applied for judgement about internal structure of the zp (t) and zg(t). We tested the remainder research
method at statistical analysis of latitude observations in high-frequency band [5]. In Fig. 3 the data on accident
of the remainders for zx(t) and zy(t) for the POLV Station are submitted, as well as 75% and 99% confidential
intervals for white noise, and for the remainders zz(t) the intervals at level of 75% and 95% are given.
Zx
0
0,5
1
0 π 2π
99%
75%
0
0,5
1
0
99%
75%
Zy
π 2π
0
0,5
1
0
95%
75%
Zz
π 2π
Figure 3. Integral spectral functions of the remainders and confidential intervals for white noise obtained at the POLV
Station
367
As given in Fig. 3, in the low frequency band all the three spectral functions do not leave 75% confidential
intervals of white noise. For the remainders zx(t) the increase of the dispersion role is only registered in the high
frequency band. For the remainders zy(t) the insignificant overstep of the 99% limit of white noise only takes
place in the medium frequency band. The series zz(t) is close to white noise in the best way at all the interval
of low and medium frequencies.
As a rather short interval of observations was used for the analysis, it seemed expedient to carry out some
additional researches on stability of component estimations at this interval. In Fig. 4 the diagrams of amplitude,
period and phase formation of annual and semi-annual term for x coordinate at the POLV and GLSV stations
are submitted as an example. There is a change of parameter estimations of composite series at this interval;
the phase estimation has particularly small stability. Some distinction in phase estimations for the annual wave
of coordinate x and z for the POLV and GLSV stations may be explained by this fact. The results of cross-
correlation analysis (Fig. 2) indicate the phase synchronism of the processes. Therefore, the available interval
of observations is still insufficient for determination of the exact parameter estimations of the components, and
it is necessary to consider parameter estimations (Table 1) as preliminary ones.
0
1
2
3
4
5
6
7
50 60 70 80 90 100
0,5 year
1 year
Amp
n
0
50
100
150
200
250
300
350
400
50 60 70 80 90 100
0,5 year
1 year
Period
n
Phase
0
60
120
180
240
300
360
50 60 70 80 90 100
1 year
0.5 year
n
Figure 4. Verification on stability of parameter estimation of harmonics in process of increase of the observation period
for the POLV (solid) and GLSV (dotted) stations
CONCLUSION
The analysis of observation series by various methods at two stations by the same technique has allowed to
research series components and to estimate their contribution to changeability of station coordinates. The ana-
lysis results of the first years GPS observations at the POLV Station have not revealed important local effects.
The mean value of post-fit residuals σ0 for the period of research after determination of components for the POLV
Station amounts 2.1 mm – (x), 2.0 mm – (y), 2.5 mm – (z); for the GLSV Station amounts 2.1 mm – (x),
1.5 mm – (y), 2.5 mm – (z).
[1] Aggarwal A. K. Numerical methods in least-squares parameter estimations // J. Astronaut. Sci.–1982.–30, N 2.–
P. 181–192.
[2] Gubanov V. S. The generalized least squares. The theory and application in astrometry.–St.-Petersburg: Nauka,
1997.–318 p. (in Russian).
[3] Munk W. H., Snodgrass F. E., Tuker M. I. Spectra of low frequency ocean waves // Bull. Univ. of California.–
1959.–7, N 12.–P. 151–176.
[4] Yatskiv Ya. Some results of analysis of non-polar latitude variations at independent latitude stations // Latitudes
variation.–Kiev: Naukova dumka, 1965.–P.75–96. (in Russian).
[5] Zalivadnyi N. M. On possibility of presentation the results of latitude observations in a high-frequency region
within the scheme of autoregression // Kinematics and Physics of Celestial Bodies.–1997.–13, N 5.–P. 48–57.
368
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| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| language | English |
| last_indexed | 2025-12-07T18:08:30Z |
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| spelling | Zalivadnyi, N.M. Nekrasov, V.V. Schliahovoi, V.V. 2015-04-03T18:36:35Z 2015-04-03T18:36:35Z 2005 Analysis of the preliminary results of GPS observation series at the Poltava Gravimetrical Observatory / N.M. Zalivadnyi, V.V. Nekrasov, V.V. Schliahovoi // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 365-368. — Бібліогр.: 5 назв. — англ. 0233-7665 https://nasplib.isofts.kiev.ua/handle/123456789/79677 The first results of researches of GPS observations in Poltava are submitted. Linear trend, annual, semi-annual terms as well as a number of additional terms are marked out on each coordinate. It is shown that the annual term considerably prevails above semi-annual one. Numerical values of parameters of these components are determined. Comparison of the obtained results with results of the similar researches at the Kyiv Station has been carried out. en Головна астрономічна обсерваторія НАН України Кинематика и физика небесных тел MS4: Positional Astronomy and Global Geodynamics Analysis of the preliminary results of GPS observation series at the Poltava Gravimetrical Observatory Article published earlier |
| spellingShingle | Analysis of the preliminary results of GPS observation series at the Poltava Gravimetrical Observatory Zalivadnyi, N.M. Nekrasov, V.V. Schliahovoi, V.V. MS4: Positional Astronomy and Global Geodynamics |
| title | Analysis of the preliminary results of GPS observation series at the Poltava Gravimetrical Observatory |
| title_full | Analysis of the preliminary results of GPS observation series at the Poltava Gravimetrical Observatory |
| title_fullStr | Analysis of the preliminary results of GPS observation series at the Poltava Gravimetrical Observatory |
| title_full_unstemmed | Analysis of the preliminary results of GPS observation series at the Poltava Gravimetrical Observatory |
| title_short | Analysis of the preliminary results of GPS observation series at the Poltava Gravimetrical Observatory |
| title_sort | analysis of the preliminary results of gps observation series at the poltava gravimetrical observatory |
| topic | MS4: Positional Astronomy and Global Geodynamics |
| topic_facet | MS4: Positional Astronomy and Global Geodynamics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79677 |
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