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International Journal of Advanced Computer Science, Vol. 2, No. 9, Pp. 348-351, Sep., 2012.
Manuscript
Received:
10,Oct., 2011
Revised:
1,Apr., 2012
Accepted:
21,May,2012
Published:
15,Oct., 2012
Keywords
Azimuth,
bore sight,
Geosynchronous
satellite vehicle
(GSV),
satellite ground
control station,
Satellite look
angles,
Sub-satellite
point,
Elevation
Abstract Antenna look angles of
geostationary communications satellite
provide the information required to
ensure that control station antenna is
directed towards the satellite; more
specifically to ensure that the main lobe of
the antenna is aligned with the main lobe
of the satellite’s antenna, and to ensure
that the largest amount of energy is
captured from the satellite. To optimize
the performance of a satellite
communications system, the directions of
maximum gain of a satellite ground
control station antenna (referred to as
boresight) must be pointed directly at the
satellite. To ensure that the earth station
antenna is aligned, two angles must be
determined: the azimuth and the elevation
angle. Azimuth angle and elevation angle
are jointly referred to as the antenna look
angles.
This paper describes in detail, the
mathematical modelling of antenna look
angles of two models of satellite ground
control station. The mathematical models
developed are abstract models that use
mathematical equations to describe the
antenna look angles. The mathematical
representations presented takes into
consideration the redundancy of the
control stations. Two models are used in
order to pave way for redundancy so that
if one fails the other takes over.
Mathematical model of antenna look
angles is a mathematical representations
of the equations governing them.
1. Introduction
The orbital slot of a geostationary communications
satellite determines the look angles at which a ground
antenna needs to be positioned to see the satellite. Higher
This work was supported by the National Space Research and
Development Agency (NASRDA) organization.
Ogundele Daniel Ayansola (National Space Research and Development
Agency, NASRDA, Abuja, Nigeria, ayansolaodaniel@gmail.com) and
Adediran Yinusa A. (Electrical Department, University of Ilorin,
yinusade@yahoo.com).
look angles provide greater reliability by improving the
quality of the communication link. On the other hand, low
or shallow look angles usually face obstructions from trees,
nearby buildings, or other objects and are more subject to
interference, particularly in heavy rain. The antenna of a
satellite ground control station needs to be properly
positioned in order to be able to track geostationary satellite.
With geosynchronous satellites, the look angles of
control earth station antennas only need to be adjusted once
as the satellite will remain in a given position permanently,
except for occasional minor variations [Wayne, 2001]. To
communicate with a satellite, ground-based reflector (dish)
antennas are used. Reflector parabolic antennas can focus
the transmitted power from/to a narrow region of the sky.
This allows for establishment of communication links over
long distances, thus minimizing transmitted electromagnetic
power requirements. However, because the signal is
concentrated in a narrow region of the sky, the antenna must
be precisely pointed at the emitting/receiving source. The
problems in pointing an antenna can range from simple to
complex, depending on the motion of the satellite in its orbit
[Tomas and David, 1994].
Look angles are most commonly expressed as azimuth
(Az) and elevation (El), although other pairs exist. For
example right ascension and declination are standard for
radio astronomy antennas. Azimuth is measured eastward
(clockwise) from geographic north to the projection of the
satellite path on a (locally) horizontal plane at the earth
station. Elevation is measured upward from the local
horizontal plane at the earth station to the satellite path. In
all look angle determinations, the precise location of the
satellite is critical. A key location in many instances is the
subsatellite point [Timothy et al, 2003].
The location of a satellite is generally in terms of
latitude and longitude similar to the way the location of a
point on earth is described. However, because a satellite is
orbiting many miles above the earth’s surface, it has no
latitude or longitude. Therefore, it location is identified by a
point on the surface of earth directly below the satellite.
This point is called the sub satellite point (SSP).
Angle of elevation (sometimes called elevation angle)
is the vertical angle formed between the direction of travels
of an electromagnetic wave radiated from an earth station
antenna pointing directly toward a satellite and the
horizontal angle. The smaller the angle of elevation, the
greater the distance a propagated wave must pass through
earth’s atmosphere. As with any wave propagated through
Mathematical Model of Antenna Look Angle of
Geostationary Communications Satellite Using Two
Models of Control Stations
Ogundele Daniel Ayansola & Adediran A. Yinusa
Ogundele Daniel Ayansola et al.: Mathematical Modeling of Antenna Look Angle of Geostationary Communications Satellite Using Two Models of Control Stations.
International Journal Publishers Group (IJPG) ©
349
earth’s atmosphere, it suffers absorption and may also be
severely contaminated by noise. Azimuth angle is the
horizontal angular distance from a reference direction,
either the solution or northern most point of the horizon.
Azimuth angle is defined as the horizontal pointing angle of
an earth station antenna. For navigation proposes, azimuth
angle is usually measured in a clockwise direction in
degrees from true north.
In the geometry of the range and elevation angle
calculation shown in Figure 1, two models of satellite
ground control stations are presented for the determination
of antenna look angles. One satellite ground control station
can be used as main station while the other can be used as
the back-up or redundant system, or vice-versa. The
redundant system will take over the control of the satellite
whenever the main control system failed or its link is being
obstructed by the rain attenuation. The models will aid
availability of the system at all time. The two ground
control stations are linked by a geostationary satellite for
continuous communications. Model 1 is for Satellite
Ground Control Station X while model 2 is for Satellite
Ground Control Station Y.
The antenna look angles of the satellite ground control
stations X and Y are modelled using Fig. 1.
re
cos Ɣ1
Center of earth
Subsatellite point
Satellite Ground Control
Station
rs
El1
Satellite
re
El2
90 – Ɣ1
θ2 =
90 – Ɣ2
90 + Ɣ2
β1 = 90 –
El1 - Ɣ1
β2 = 90 –
El2 – Ɣ2
re
cos γ
rs -
Ψ1
Z
re
re
XY
rs = distance from the center of the earth to the
satellite
re = distancer from the center of the earth to the
earth station
d = distance from the earth station to the satellite
Ɣ1 and Ɣ2 are angles between re and rs
Ψ1 and Ψ2 are angles between re and d1 and re and
d2
d1d2
Ɣ1Ɣ2
Satellite Ground Control
Station
Ψ2
θ1 =
90 + Ɣ1
D
Equator
O
V
Fig. 1 Geometry of the range and elevation angle calculation
2. Mathematical Modeling of the
Antenna Look Angle
The mathematical representations of the antenna look
angles of geostationary communications satellite are
developed for two models of satellite ground control station
designed. The look angles are separately developed for
each of the models.
A. Model 1: For Satellite Ground Control Station X
From : Using cosine formula, we have
Similarly, from
Also, from
Applying sine formula to we have
Therefore,
Figure 2 shows the position of a hypothetical
geosynchronous satellite vehicle (GSV), subsatellite point
(SSP), and an earth station (ES) all relative to Earth’s
geocenter. The SSP has 300E longitude and 00 latitude. The
earth station has a location of 300W and 200N latitude. Ls
and ls and are respectively the latitude and longitude of the
subsatellite point, while Le and le are the latitude and
longitude of the Earth station respectively.
80
70
60
50
40
30
20
10
0
-10
-20
-30
-40
010 20 30 40 50
10
20
30
40
50
N
ES geocenter
SSP
E
W
GSV
Greenwich
“prime” meridian
(00 longitude)
AB
(le, Le)
(ls, Ls)
ls - le
C
90
Fig. 2. Position of a hypothetical geosynchronous satellite vehicle (GSV),
International Journal of Advanced Computer Science, Vol. 2, No. 9, Pp. 348-351, Sep., 2012.
International Journal Publishers Group (IJPG) ©
350
its respective subsatellite point (SSP), and an arbitrary selected earth
station (ES)
Fromin Fig. 2, using Napier’s rule for a
spherical right-angled triangle which states that the sine of
an angle is equal to the product of tangents of the two
adjacent angles; then
Therefore,
Once angle A is determined, the azimuth angle can
be found. Four situations must be considered, the results for
which can be summarized as follows:
1.
2.
3.
4.
B. Model 2: Satellite Ground Control Station Y
From : Using cosine formula, we have
(
Similarly, from
Also, from
Applying sine formula to we have
Therefore,
Similarly, fromin Figure 2, using Napier ’s rule for a
spherical right triangle
Once angle A is determined, the azimuth angle can be
found in the same manner as in Model 1.
For a satellite to be visible from a satellite ground
control station, and must satisfy the inequalites
[Timothy et al, 2003]:
1) (
2)
From Figure 1, using and
the following are obtained:
a) For , we have (
i.e. (.
b) For , we have
i.e.
.
Considering the values obtained in (a) and (b),
additional assumptions to the ones in (1) and (2) of Timothy
et al (2003) for a satellite to be visible from a Satellite
Ground Control Station are that and must satisfy the
inequalities:
1) (
and
2) i.e.
.
Angles and are related to the earth station north
latitude Le and west longitude le and the subsatellite point at
north latitude Ls and west longitude ls by [Timothy et al,
2003]
For most geostationary satellites, the subsatellite point
is on the equator at longitude ls, while latitude Ls is 0.
and therefore simplify to
3. Comparison of Results
The comparison is done using the real parameters of
Abuja Satellite Ground Control Station and Nigerian
Communications Satellite (Nigcomsat-1) and the results
obtained using the mathematical models developed. The
parameters of Abuja Satellite Ground Control Station and
Nigcomsat-1, given by Chai (2005) are as follows: satellite
longitude (sub-satellite point), ; satellite
latitude, ; satellite ground control station longitude,
and satellite ground control station latitude
; Azimuth angle, Az = ; Elevation
angle, El = and Range, R = .
Substituting the values above into
and using radius of the Earth
, and orbital radius
then,
A. t is
B. range is
C. elevation angle is
Ogundele Daniel Ayansola et al.: Mathematical Modeling of Antenna Look Angle of Geostationary Communications Satellite Using Two Models of Control Stations.
International Journal Publishers Group (IJPG) ©
351
D. Azimuth angle is
Since , then
The real values of Abuja Satellite Ground Control
Station and Nigcomsat-1 given by Chai (2005) are
compared with the using Table 1.
TABLE 1
COMPARISON OF THE REAL VALUES AND VALUES OBTAINED
THROUGH MODELLING FONT
S/N
Parameters
Real
Values
Values from
the model
Percentage
Difference
1
Range (km)
37,168.00
37,201.011
-0.089
2
Elevation
angle
(degree)
48.6210
48.6210
(0.8396 rad)
1.067
3
Azimuth
angle
(degree)
101.5810
102.5320
(1.7898 rad)
-0.936
As seen in the table, the values of range, elevation
angle and azimuth angle obtained through modelling are
very close to the real values given by Chai (2005) indicating
that the results obtained using the mathematical models
developed for the antenna look angles of geostationary
communications satellite are in comformity with the real
values provided by Chai (2005).
The mathematical modelling presented in this paper is
a good tool that can be used to determine look angles for
pointing satellite ground control station antenna to true
geostationary satellites. The real values of Abuja Satellite
Ground Control Station and Nigeria Communication
Satellite (Nigcomsat-1) provided by Chai (2005) were
compared with the values obtained through modelling. The
real values and those obtained through modelling are very
close, indicating that, the modelling can be used to
determine look angles of satellites moving in orbits.
Acknowledgment
The authors acknowledge financial support from the
National Space Research and Development Agency
(NASRDA), Nigeria and the assistance rendered by the
Federal University of Technology Minna, Nigeria in the
course of writing this paper.
References
[1] S. Tomas, & W. David, “Determination of Look Angles to
Geostationary Communication Satellites” (1994), National
Geodetic Survey, Silver Spring, MD 20910, pp. 115-126.
[2] Chai J., Ground Control Station (GCS) System Design,
Beijing Institute of Telemetry, Tracking and Telecommand
(BITTT), Beijing: 2005, pp. 1-48.
[3] Evans B. G., Satellite Communication Systems, The
Institution of Electrical Engineers, London: 1999, pp. 68-
260.
[4] Evans B. G., Satellite Communication Systems, The
Institution of Electrical Engineers, London: 1999, pp. 68-
260.
[5] Timothy P., Charles B., & Jeremy A., Satellite
Communications, John Wiley & Sons, Inc., New York, 2003,
pp. 1-43.
[6] Wayne T., Electronic Communications Systems:
Fundamentals Through Advanced, Fourth Edition: Pearson
Education, Inc., 2001; pp. 790-800.
[7] Ippolito L. J., Satellite Communications Systems
Engineering, ITT Advanced Engineering & Sciences, USA,
and The George Washington University, Washington, DC,
USA, John Wiley and Sons, Ltd, pp. 30-36.
Ogundele Daniel Ayansola
received B.TECH in Electronics
and Electrical Engineerig from
Ladoke Akintola University of
Technology, Nigeria in 2000.
Presently, he is undertaking his
Masters Degree of
Communication Engineering at
Federal University of
Technology, Minna, Nigeria and it is near completion. He is one
of the Nigerian Engineers sent to China Academy of Space
Technology, China and Beijing Institute of Tracking and
Telecommunication Technology (BITTT), Beijing, China for the
Know How Technology Transfer on the design, control and
operation of Nigeria Communication Satellite (Nigcomsat-1), and
design, control and installation of Abuja and Kashi Satellite
Ground Control Station. His research interests include spacecraft
dynamics and control, Telemetry, Tracking and Command (TT &
C), design of Satellite Ground Control Station and orbital
mechanics and astrodynamics.
Yinusa A. Adediran attended
Budapest Technical University,
Hungary where he obtained an
M.Sc degree in
Telecommunications in 1980. He
also obtained an M.Sc degree in
Industrial Engineering from the
University of Ibadan in 1987 and
Ph.D in Industrial and Production
Engineering in 1999 from Federal
University of Technology, Minna.
He has contributed to knowledge
through various articles in journals and proceedings. He is
currently an Associate Professor of Electrical and Computer
Engineering at Federal University of Technology, Minna.
