CC BY
8Journal of Siberian Federal University. Engineering & Technologies 6 (2014 7) 655-659
УДК 621.396.663; 621.396.969; 629.78
Direction Finding in Satellite Systems
Vitaly V. Sukhotin*
Siberian Federal University, 79 Svobodny, Krasnoyarsk, 660041, Russia
Received 07.07.2014, received in revised form 14.08.2014, accepted 29.08.2014
In article the method allowing to determine coordinates of a source a radio emission located on a terrestrial surface in satellite systems with use of the geostationary satellite is stated.
Keywords: determination of coordinates, radio emission source, satellite systems, difference of phases
Пеленгация
в спутниковых системах
В.В. Сухотин
Сибирский федеральный университет Россия, 660041, Красноярск, пр. Свободный, 79
В статье описан метод, позволяющий определить координаты источника радиоизлучения, расположенного на земной поверхности, в спутниковых системах с использованием геостационарного спутника.
Ключевые слова: определение координат, источник радиоизлучения, спутниковые системы, разность фаз.
Introduction
In satellite technologies the problem determination of coordinates a source a radio emission (SRE) which can settle down both on Earth surface, and on the aero-space carrier [1] is actual.
Method determination of location SRE
For measurement of coordinates the SRE (corners a and p in topocentric system of coordinates, Fig. 1), Bg located in a point the phase radio direction finder established onboard a communication
© Siberian Federal University. All rights reserved
* Corresponding author E-mail address: VSuhotin@sfu-kras.ru
Fig. 1. Antenna arrays
artificial satellite (ASE), has to have two couples antennas 1-2! and 3-4 with mutually perpendicular bases. Shift of phases between E.D.S.,induced in anteunas 1-2 and 3-4, [2]:
2-n-d . n i/s1-2 =--sin a - cos ß,
A 2-n-d A =--cos a-cos ß
(1)
V V
Where: d - base of antennas 1-2 and 3-4; - length of a wave an accepted signal. Corners a and (3 from (1):
a = arctg
ß = arceos
2 - n-d
- VA Ai-2 + A A32-
(22)
A 3-3-4
Having placed an antenna ai^r^ys on a geostationary ASE it is possible to define this direction on SRE concerning an ASE [y ... 6]. For determination of coordinates SRE it is necessary to calculate its coordinates in geocentric system of coordinates taking into account ellipticity of Earth
Foc calculntioo of rec[uired width arrd longitude oya source signal we will addrers to Fiy. 2 [7]. Transition 2o ohe geocenteic domands modificotion of expressions (2s) thetefoec comers a and (3 pay off on formuler foonr topocentric s^st;e;n^ oF coordinates:
a = arctg
Am
ß = arcsin
2 - it • d
-./a sg + A (232_4.
(3)
aVl-f
Here a= 90 -c^p = 90 - ft.
Tine point Dg lieîs in the plane of the equator and is the projection of a point Bg. The angle 9 of the triangle BgODg is the breadth of the signal source. The longitude X of the signal source is 1 = Xsp + 1g, where 1g - angle triangle CgODg; 1sp - longitude of the satellite. If the sateilite is on the Greenwich Meridian, 1sp=0. The point Cg on the line R1 is a projection ol a point Dg on the meridional plane. Note that R1=42253,135km til].
To determine 1g refer to the section of the Earth meridional plane (Fig. 3b). In the triangle KgONg angle a is calculated according to the formula
Segment KgNg is perpendicular to the plane of the equator. Required in this triangle is the n-end. Fig. 3a shows the plane spheroid with minor radius n, at an angle a to the plane of the equator. Semi-minor axis n intersects the plane of a triangle BgAO at the same angle a to the plane of the equator. In
2
Fig. 3. Additional geometric constructions to calculate the coordinates of SRE with regard to the ellipticity of the Earth
the triangle BgAO angle p is calculated according to the formula (3). The required Fig. 3a is a Rg party in the triangle BgAO.
Calculation oflatitude cp and longitude I includes the following 7 stages.
1. Is the point of intersection (Fig. 3b) minor axis n and arc spheroid, the solution of systems of two equations
k = q ■ tga
(4)
where the first equation describes the mino r axi s , and the second is arc of a spheroid. The solution (4) has two roots
(5)
Further used only p-sitive root, since a negative value belongs to the opposite part of a spheroid. Substituted qi i is any of the equations (4), we obtg n the vaiue oU K . T he se mi minor axis n of a right triangle Kg ONg is equal to :
i = t] k2 + q2
(6)
2. Is the point of intersection (Fig. 3a) direct Rl, which i.s give n by the e quation ag = tg(Ri - fg) and arc spheroid by solving the system of two equationi:
« =tg( R2- f )
a = n■ ,(2 - f^r
g AI RR r
Solution of the (quadratic equation
(7)
Rr
tgr ß + nA-ft - 2-R2Dgß■■ fR + (2ß-R2r -n2) = 0,
are tire two roots fg1 h fg2
= 2 ■ R2 ■ ig 2ß + -225 =2 ■ R2 ■ ig 2ß--25
f g2 = 2 ' J g 2 = 2 '
2 ■ (ig 2ß + ~T)
2 ■ (ig ß +
R
where 5 = (2t ■ Rt Zg2/1)2 - 4 ■ (zg2/ + ■£+) ■ rgf ■ R12 - «2).
R
(8)
(9)
From Fig. 3a and (9) follows tliat, in furthar calculations will need eha root fgi meaning equal side OCg. Subnituting fg1 into any equation of system (7), we obtain the value of the side ag1, then from a right-angled triangle BgOCg, wis find Rg1:
Rg2 = V« gl +fg2
3. From righl-angled triangle BgCgDg (Fig. 2) we find og:
4. From right-ongled triangle BgODg we find latitucse 9 of SRE:
(10)
■ 0g
<p = arcsin ——. (12)
—i
5. From right-angled triangle BgODg we find cg:
. (13)
6. From right-angled triangle BgOCg, angle 1g:
f
À = arccosfi-. (14)
7. Longitude X of SRE:
X = 1= + V (15)
In geocentric system of coordinates (Fig. 2):
x = cgcos1, y = cgsinX, z = og. (16)
Conclu sion
Thus, the described technique relying on use onboard the spacecraft of an antenna arrays, allows to solve a problem determination of coordinates of the Source a radio emission.
Work is performed with financial support of the Ministry of Education and Science of the Russian Federation in the Siberian federal university (Contract No. 02.G25.31.0041).
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