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MATHEMATICAL MODELS FOR DETERMINING THE LOCATION OF RADIO EMISSION SOURCES IN RADIO MONITORING SYSTEMS ON THE BASIS ON LOW-ORBIT SATELLITES
Aitmagambetov Altai Zufarovich,
International Information Technologies University, Almaty city, Kazakhstan, [email protected]
Butuzov Yuri Alekseevich,
Institute of space technique and technology,
Keywords: radio-electronic means, radio monitoring, small spacecraft, radio emission source, the orbital group.
Almaty city, Kazakhstan, [email protected]
Kulakayeva Аigul Еrgalievna,
International Information Technologies University, Almaty city, Kazakhstan, [email protected]
The article describes and features the methods for determining coordinates of radio emission sources while radio monitoring on the basis of low-orbit satellites. The method of choosing the initial approximation for solving the system of nonlinear equations while radio monitoring on the basis of the orbital group of satellites was justified. The angular measuring method of determining the coordinates of radio emission sources while radio monitoring on the basis of a single spacecraft is proposed.
Ground-based radio monitoring stations are mainly used for radio monitoring of radio-electronic means (REM). However, for larger countries it is appropriate to use low-orbit small-size (small) spacecrafts (SSC), which allow to control REM radio emission parameters [1]. In this case the system of radio monitoring will consist of space and ground segments, and perform complex functions, including the detection of REM [2]. One should note the relevance in using satellite radio monitoring systems for determining the location of civilian aircrafts, which are outside of the visibility zone of ground-based surveillance devices [3].
Differential distance, direction finding, and Doppler methods are the three main methods which are widely used to determine the coordinates of an object. To solve the problem of determining the coordinates of radio emission source (RES), each of the above mentioned methods should meet certain requirements.
Для цитирования:
Айтмагамбетов А.З., Бутузов Ю.А., Кулакаева А.Е. Математические модели для определения координат источников радиоизлучений в системах радиомониторинга на базе низкоорбитальных космических аппаратов // T-Comm: Телекоммуникации и транспорт. - 2016. - Том 10. - №1. - С. 73-76.
For citation:
Aitmagambetov AZ., Butuzov Yu.A., Kulakayeva А.Е. Mathematical models for determining the location of radio emission sources in radio monitoring systems on the basis on low-orbit satellites. T-Comm. 2016. Vol. 10. No.1, рр. 73-76. (in Russian).
T-Comm Vol.10. #1-2016
T
The system of equations is compiled for known values of RES coordinates:
X = 1271905 m, Y = 3785945 m and Z = 4963843 M.
The solution to this system of equations in Mathcad 15.0 for different values of initial approximations has allowed to find out that when |X0 - X| < 400 km |Y0 - Y| < 400 km and |Z0 - Z| < 400 km, the RES coordinates can be determined with high accuracy.
It is important to check that the difference between the coordinates with the specific parameters of the SSCI antenna is within the above set limits. Let the diameter of the coverage area {of half power) of the receiving antenna be 400 km (width of orientation digramma is 28°). Then the distance between the aiming point of the antenna and the point of RES location will not exceed 200 km at the time of signal receiving. Since [(X0 - X)2 + (Y0 - Y)2 + (Z0 - Z)2] 0,5 < 200 km, the choice of the initial approximation can be acceptable.
Also the system of equations was solved when using the OG on the basis of three SSC (one of the equations of the system is replaced by the equation of the sphere of the Earth). The coordinates of the initial approximation to the RES coordinates have been increased to 200 km. Analysis of the results shows that the RES coordinates for the considered cases are not significantly different (AX = 3 m; AY = 4 m; AZ = 2m).
3. THE LOCATION OF RADIO EMISSION
SOURCES ON THE BASIS OF SINGLE SMALL
SPACECRAFT
The paper also proposes for consideration a method of determining the RES coordinates using one small spacecraft, which is in a circular polar orbit {inclination i = 90°).
The SSC must be equipped with two receiving active phased antenna arrays (APAA) [5] that shall meet the following requirements:
- quick (inertialess) review of space due to the swing of antenna beams by electrical methods (electrical scan);
- narrow beams in one direction to increase the accuracy of determining the angular RES coordinates and wide beams in the orthogonal direction;
- increase in the levels of received power by placing amplifiers of high-frequency energy in the grid channels;
- it is especially important that the location of elements in APAA should provide a spatial scanning sector on the spherical surface of the Earth.
Joint processing of signals received by individual elements of the antenna arrays will provide a more complete and accurate information about RES.
Figure 2 illustrates the method of determining the latitude of the RES location.
The dotted line indicates the orbital plane of a SSC, the current position of which is point B. The narrow beam of one of its antenna scans from the BO direction to the BA direction, where the RES signal located at the point A is fixed.
/ / 1 / >1 \ B\ \ >
I ^ \ \ 0 "v. __/ 1 /
Figure 2. Determination of the RES latitude when scanning
The latitude of the SSC at the time of signal reception is determined by the angle a, and the RES latitude <p is determined by the sum of the angles (a + 7). The angle a is known, since the navigation system GLONASS allows to determine the exact coordinates of SSC. Also the angle ¡3 is known, as in the process of scanning it varies linearly in function of time and is also determined at the time of signal reception.
So, in the triangle AOB, the angle b and two sides are known: AO (radius of the Earth R3 = 6371.1 km) and OB is the distance of the SSC from the geocenter (R3 + h) = 7I7I.II km (altitude of the orbit h = 800 km).
To determine the angle k we will use the theorem of sines:
BO AO
sin k sin/f
(I)
Next, we determine the angle y = (180 - (} - k) and RES latitude cp = (a + 7).
The following is the formula for calculating basic angles and distances between RES and SSC AB: k = 180-arcsin[(l+h/R3) * sinp]; e = 90 - arcsin[( 1+I1/R3) * siii(3] is the RES angle; y = arcsin[(l+h/R3) * sinp] — (3; AB = [R32 + (R3 + h)2 - 2*Ri *{R3 + h)*cosy The results of the calculation of these parameters depending on the angle p are shown in table I.
Table I
The results of the calculation to determine the RES latitude when scanning
20 30 40 50 55 60
sinß 0342 0.5 0.643 0.766 0.819 0.866
k,° 157.36 145.75 133.64 120.44 112.78 102.9
1° 2.64 4.25 6,36 9.56 12.22 17.1
67.36 55.75 43.64 30,44 22.78 12.9
It is important to note that the accuracy of determining the latitude of the RES location according to this method will depend on how the shape of the APAA directional pattern will take into account the curvature of the cross-sections of the Earth along parallels at latitudes of the radio monitoring area (RMA). The maximum and minimum latitudes, 55.41° and 40,65" respectively, of the checkpoints on the territory of Kazakhstan are known. The calculations show that the
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Ф= 40°; а = 34,8 °;ц = 5;г) = 1;Х = 6± 1°;
<р = 56й; а = 47,4°; ц = 5;т)= 1,8°; Х = в±оП.8<>.
4. CONCLUSION
ПУБЛИКАЦИИ НА АНГЛИЙСКОМ ЯЗЫКЕ
average curvature of the cross-sections of the Earth at these latitudes equate to 2,42:f:10-4 l/km. The value of curvature must be taken into account in the design of APAA.
Let us consider the method of determining second RES location coordinates (longitude). The method is illustrated in figure 3 {the view is along the Z-axis).
SSC longitude at the moment of the signal appearance from RES is denoted by 8 (this value is also known through the coordinate binding of the GLONASS navigation system).
The second beam of APAA scans in an orthogonal direction relative to the first one, and the angle relative to the normal changes from negative values (westward) to positive ones (towards the East) according to the linear law (this angle at the moment of the signal appearance was denoted by |j).
( с а\ в
иу > у
fx
Figure 3. Determination of the longitude of the RES location
The RES longitude correction angle acan be determined as follows:
= arcsin|( 1 + h/R3)*cosa*sinji/cos<p] - ¿l. Then the longitude of the RES location will be determined
by:
\ = Q±{ arcsin|{l + h/Ri)*cosa*sin|j/cos<p| - n}. Below are the results of calculations of the RES longitude for the boundaries of the radio monitoring area {angle pi = 5° is used as an example):
The method of choosing the initial approximation for solving the system of nonlinear equations while radio monitoring on the basis of the orbital group of satellites was justified. The method greatly simplifies this task, as it is solved on the basis of known coordinates of the satellite, obtained with the help of the GLONASS system.
Modeling in Mathcad 15.0 has shown the applicability of this method for specific parameters of the receiving antennas of the satellites.
The angular measuring method of determining the coordinates of radio emission sources while radio monitoring on the basis of a single spacecraft is proposed. Unlike the Doppler method, the angular measuring method does not require exact knowledge of the radiation frequency. Additional research should be conducted to assess the accuracy in determining coordinates of radio emission sources according to this method.
1. Aitmagambetov A.Z., Inchin A.I., Losbin A.Yu. The possibility of radio monitoring of ground transmitters by satellites for scientific purposes. Bulletin of KazATC. Almaty, 201 I. No. 4. Pp. 25-29.
2. Spectrum Monitoring handbook. Geneva, ITU. 2011.
3. Reception of automatic dependent surveillance broadcast via satellite and compatibility studies with incumbent systems In the frequency band I 087.7-1 092.3 MHz. Working Document towards a Preliminary Draft New Report ITU-R M,[ADS-B],-Geneva.-ITU. 2015.
4. Voznyuk V.V., Zaitsev SA. Space radio monitoring system based on the grouping of low-orbit small spacecrafts. - Izvestiya vuzov. Priborostroyeniye, 2005, vol. 48, No. 6.
5. Active phased antenna arrays / ed. by D. I. Voskresensky. -M.: Radio engineering, 2004, p. 488.
References
МАТЕМАТИЧЕСКИЕ МОДЕЛИ ДЛЯ ОПРЕДЕЛЕНИЯ КООРДИНАТ ИСТОЧНИКОВ РАДИОИЗЛУЧЕНИЙ В СИСТЕМАХ РАДИОМОНИТОРИНГА НА БАЗЕ НИЗКООРБИТАЛЬНЫХ КОСМИЧЕСКИХ АППАРАТОВ
Айтмагамбетов Алтай Зуфарович, к.т.н., профессор, Международный университет информационных технологий, [email protected] Бутузов Юрий Алексеевич, к.т.н., доцент, Институт космической техники и технологий, [email protected] Кулакаева Айгуль Ергалиевна, магистр, сениор-лектор, Международный университет информационных технологий, [email protected]
Аннотация. Рассмотрены и предложены методы определения координат источников радиоизлучений при осуществлении радиомониторинга на базе низкоорбитальных малых космических аппаратов. Обоснован способ выбора начального приближения для решения системы нелинейных уравнений при радиомониторинге на базе орбитальной группировки спутников. Предлагается угломерный метод определения координат источников радиоизлучений при осуществлении радиомониторинга на основе одного космического аппарата.
Ключевые слова: радиоэлектронное средство, радиомониторинг, малый космический аппарат, источник радиоизлучения, орбитальная группировка. Литература
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4. Вознюк В.В., Зайцев С.А. Космическая система радиотехнического мониторинга на основе группировки низкоорбитальных малогабаритных космических аппаратов // Изв. Вузов Приборостроение, 2005, том. 48, №6.
5. Активные фазированные антенные решетки / Под.ред. Д.И.Воскресенского. - М.: Радиотехника, 2004. - 488 с.
