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2018-01-12 12:01:35

Radio interferometric network for
tracking of  geostationary 
telecommunication satellites

Experimental radiointerferometric network was created with the purpose of providing independent continuous orbital support to the future Ukrainian  geostationary telecommunication satellite (GTS) "Lybid". The network can be used to monitor the technological maneuvers of GTS, to detect the facts of its collision with space debris, to clarify a model of moving objects in geostationary orbits.

The basic principle of network operation is the use of passive radar method and correlation analysis to calculate TDOA (Time Difference Of Arrival) using signals of digital satellite television. The network synchronously receives these signals that are compliant with the standard of DVB-S (Digital Video Broadcasting-Satellite). Orbital position of satellite is determined by using measured values of the TDOA and station coordinates. To calculate the perturbed orbit of GTS, the network must consist of four or more stations. 

Today, the network consists of five stations spaced out and located in:
- Research Institute "Mykolaiv Astronomical Observatory" (Mykolaiv);

- Institute of Radio Astronomy of the National Academy of Sciences of Ukraine (Kharkiv);

- Western Center of Radio Engineering Surveillance (Mukacheve);

Rivne Minor Academy of Sciences of School Age Youth (Rivne);

- Ventspils University College (Ventspils, Latvia).

GSS network

The orbital elements of a tracked satellite are determined by diurnal arrays of measured values of TDOA using the analytical model SGP4/SDP4 and the numerical model of integrating the satellite equations, given in the left and right columns of table, respectively. The numerical model takes into account the perturbations caused by the gravitational attraction of the Moon, the Sun and the nonspherical Earth. Note that the error of the numerical model is 5.4 times less than the error of the analytical model. Elements of the orbit received for one day are contained in three lines, numbered from zero. Zero row contains the same information in the left and right columns, namely:
- epoch of orbital elements (date and time of UTC);
- number of base lines (pairs of stations) of the network;
- conditional symbols of station pairs;
- number of time readings with increment of one minute for which TDOA values were obtained by at least three different pairs of stations and used for determination of the orbital elements.

Conditional designations of the basic network lines contain two station numbers separated by a "x" sign. The network stations have the following numbers: 0 - Mykolaiv, 1 - Kharkiv, 2 - Mukacheve, 3 - Kiev, 4 – Ventspils, 5 - Rivne. Let "i" be the station number on the left of the "x" sign and "k" on the right. This pair of stations corresponds to the TDOA value Δτ
, calculated using the following formula:

Δτ = τi - τk ,

where τi and τk  - delays of the digital satellite television signal received by the stations "i" and "k", respectively.
In the left column, rows 1 and 2 contain the orbital elements in a format of two-line elements (TLE). The description of this format can be found at https://celestrak.com/columns/v04n03/
In the right column, rows 1 and 2 contain a satellite number of the NORAD classification (29270 for the Eutelsat-13B satellite) and the state vector of satellite. Row 1 contains coordinates (X, Y, Z), row 2 contains three velocities (dX/dt,dY/dt,dZ/dt) in the coordinate system of EME2000. Coordinates are given in meters and velocities in m/s.

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