Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2021. No. 2

in Russian (pdf)

DOI https://doi.org/10.30898/1684-1719.2021.2.1

UDC 528.629.195

Generalized algorithm for determining AES orbit parameters based on quadratic functionals

D. D. Gabriel’yan, A. N. Gorbachev, V. I. Demchenko

Rostov-on-Don Research Institute of Radio Communication, Nansena str. 130, Rostov-on-Don 344038, Russia

The paper was received on January 29, 2021

Abstract. The questions of development a generalized algorithm for determining the parameters of the low circular orbit (LCO) of an Earth satellite (ES) based on the use of quadratic functionals are in the focus of this paper. The functionals represent the square of the differences between the measured values of the ES sighting angles and the frequency of the received signal with the values of the same parameters obtained for the assumed values of the Keplerian orbital elements in accordance with the adopted model of the ES motion. Estimates of the orbit parameters are formed from the condition of the minimum of the proposed quality functionals. The proposed algorithm is aimed at the developing two equations for the relationship between the measured values of the azimuth and elevation angles, as well as the frequency of the received satellite signal and the parameters of the satellite orbit. The use of the indicated constraint equations makes it possible to pass from the six-dimensional space of the Keplerian orbital elements to the four-dimensional space of the Keplerian orbital elements when constructing the algorithm and choosing the initial approximations of the orbit parameters. Such a reduction in the dimension of space makes it possible to significantly reduce the amount of computational expenditure, which ensures the stability of the algorithm and expands the possibilities of its practical use with limited resources (computing power and restrictions on the permissible processing time). The following Keplerian orbital elements are proposed as four basic parameters: eccentricity, ascending node longitude, orbital inclination, and perigee argument. The other two elements, the semi-major axis of the orbit and the mean anomaly, are expressed as functions of four basic parameters. This choice is determined by the fact that, in the case of LCO, the pivoting of the initial values of the eccentricity and the argument of perigee is quite simple, which makes it possible to ensure convergence to the exact values of the orbit parameters in a wide value of the initial approximations. Within the Keplerian approximation of the satellite's orbital motion, mathematical relations are presented that determine the operations performed within the framework of the considered algorithm. However, a more complete consideration of the factors influencing the motion of the satellite only leads to more volumetric relations, but does not fundamentally affect the construction of the algorithm itself.

Keywords: quadratic functionals, multidimensional space of orbit parameters, iterative algorithm for estimating the parameters of the satellite orbit.

References

1.      Tsyrempilova N.S., Avdyushev V.A., Banshchikova M.A. Iterative methods for determining orbits in inverse problems of satellite dynamics. Izvestiya vysshikh uchebnykh zavedeniy. Fizika [Proceedings of Universities. Physics]. 2011. Vol.54. No.6/2. P.55-62 (In Russian).

2.     Avdyushev V.A. Chislennoye modelirovaniye orbit [Numerical modeling of orbits]. Tomsk., NTL Publ. 2010 . 282 p. (In Russian)

3.     Avdyushev V.A., Banshchikova M.A. Determination of the orbits of nearby satellites of Jupiter. Astronomicheskiy vestnik [Astronomical Bulletin]. 2008. Vol.42. No.4. P.317-340. (In Russian)

4.     Attetkov A.V., Galkin S.V., Zarubin V.S. Metody optimizatsii [Optimization methods]. Moscow, Publishing house of Bauman Moscow State Technical University. 2001 . 439 p. (In Russian)

5.     Urmaev M.S. Orbital'nyye metody kosmicheskoy geodezii [Orbital methods of space geodesy]. Moscow, Nedra Publ. 1981, 256 p. (In Russian)

6.     Sukhanov S.A., Khutorovsky Z.N. Metody i algoritmy postroyeniya trayektoriy nizkoorbital'nykh ob"yektov [Methods and algorithms for constructing trajectories of low-orbit objects]. Publishing house LAP LAMBERT Academic Publishing. 2012.160 p. (In Russian)

7.     Gabrielyan D.D., Gorbachev A.N., Demchenko V.I. Geostationary and geosynchronous satellites orbit determination by single-position passive radar systems. Radiotekhnika [Radio Engineering]. 2014. No.8. P.16-23. (In Russian)

8.     Gabrielyan D.D., Gorbachev A.N., Demchenko V.I. Quadratic functionals usage for spacecraft orbit determination by a passive radar system. Proceedings of the X All-Russian scientific and technical conference “Radiolokatsiya i radiosvyaz’“ [Radar and Radio Communication]. November 21-23, 2016, Moscow. Kotelnikov IRE RAS. 2016. (In Russian)

9.  Gabrielian D.D., Gorbachev A.N., Demchenko V.I. Assessment of the influence of the composition of measurements in a single-position passive radio engineering system on the accuracy of the satellite orbit determination. Zhurnal radioelektroniki [Journal of Radio Electronics]. 2020. No.6. (In Russian)

For citation:

Gabrielian D.D., Gorbachev A.N., Demchenko V.I. Generalized algorithm for determining AES orbit parameters based on quadratic functionals. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2021. No.2.   (In Russian)