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MODEL VALIDATION AND ANALYSIS OF ANTENNA LOOK ANGLES
OF GEOSTATIONARY SATELLITE
Ogundele, Daniel Ayansola
Engineering and Space Systems (ESS)
National Space Research and Development
Agency (NASRDA) , Abuja, Nigeria
ayansoladaniel@gmail.com
Adediran, Yinusa A.
Electrical and Computer Engineering Department
Federal University of Technology, Minna, Nigeria
yinusaade@yahoo.com
Aiyeola, Sikiru Yommy
Centre for Satellite Technology Development,
National Space Research and Development
Agency (NASRDA) , Abuja, Nigeria
aiyetomorrow@yahoo.co.uk
Oyedeji, Elijah Oyewusi
Centre for Satellite Technology Development,
National Space Research and Development
Agency (NASRDA) , Abuja, Nigeria
e.oyedeji@hotmail.co.uk
Abstract: The performance of a satellite
communications system can be optimized
by pointing the direction of maximum gain
of an earth station antenna (referred to as
boresight) directly at the satellite. To
ensure that an earth station antenna is
aligned with the satellite, two angles must
be determined: the azimuth angle and the
elevation angle. These are the co-ordinates,
look angles, to which an earth station
antenna must be pointed in order to
communicate with a satellite. This paper
describes validation and analysis of the
models of antenna look angles of
geostationary communications satellite.
Model validation was utilized in order to
determine whether the models developed
were accurate representations of the real
system.
Keywords: azimuth angle, elevation angle,
geosynchronous satellite, simulation, look
angles, boresight, model validation.
I INTRODUCTION
Although, in general, no tracking is necessary
for satellite located in geostationary orbit, with
the large earth stations used for commercial
communications, the antenna beamwidth is
very narrow and a tracking mechanism is
required to compensate for the movement of
the satellite about the nominal geostationary
position. With the types of antennas used for
home reception, the antenna beamwidth is
quite broad, and no tracking is necessary. This
allows the antenna to be fixed in position, as
evidenced by the small antennas used for
reception of satellite TV that can be seen fixed
to the sides of homes [1][2]. An unvalidated
model is just a hypothesis; as a result, the
models of Satellite Ground Control Station
developed are validated [8][9].
In this paper, the model of antenna look angles
of geostationary satellite developed has high
validity, the model assumptions were
validated and the simulated model was
compared with the real system in order to
ascertain the genuiness of the model
developed.
II MODEL DEVELOPMENT
Two models of satellite ground control
stations were.
Oseni O.F.
Electrical and Electronics Department
Ladoke Akintola University of Technology (LAUTECH),
Ogbomoso, Nigeria
Oseni12002@yahoo.co.uk
___________________________________
978-1-4673-0089-6/12/$26.00 ©2012 IEEE
For satellite ground control station 1
Model:
(a) Range of the satellite
=
1+
−2
/(1)
(b) Elevation angle
=sin (()−
)
(2)
(c) Azimuth angle of the satellite
The azimuth angle is calculated as [6]
sin()=tantan|−| (3)
Therefore,
= tan|−|
sin(L) (4)
Once angle A is determined, the azimuth angle
can be found using the four situations
below:
1. <0; <0: =
2. <0; >0: =360−
3. >0; <0: =180+
4. >0; >0: =180−
For satellite ground control station 2
(a) Range of the satellite
=
1+
−2
/(5)
(b) Elevation angle of the satellite
=sin(()−
)
(6)
(c) Azimuth angle of the satellite
The azimuth angle is given as follows [6]:
sin()=tantan|−| (7)
Therefore,
= tan|−|
sin(L) (8)
The azimuth angle can be found in the
same manner as in Model 1.
Satellite Visibility
For a satellite to be visible from a satellite
ground control station, and must satisfy
the inequalites [3]:
1) 0≤
≤81.3 .. (0≤
≤
1.4191 )
2) 278.70≤≤ 360 . . (4.8649 ≤
≤ 6.2840 )
From Figure 2, using <!"=#
=90−
and <$!"=#
=90− , the following
are obtained:
1) For 0≤
≤81.3, we have (8.70≤
#≤90) i.e. (0.1591≤ #≤
1.571 ).
2) For 278.70≤≤ 360, we have
(−270≤#
≤−188.7) i.e.
(−4.7130≤#≤ −3.2939 ).
Considering the values obtained in (a) and (b),
another 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) (8.70≤#
≤90) i. e.(0.1591 ≤
#≤ 1.571 ) and
2) (−270≤#≤−188.7) i.e.
(−4.7130≤#≤−3.2939 ).
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 [3]
cos()=cos()cos()cos(−)
+sin()sin() (9)
cos()=cos()cos()cos(−)+
sin()sin() (10)
For most geostationary satellites, the
subsatellite point is on the equator at longitude
ls, while latitude Ls is 0. %.(3.57)
and (3.58) therefore simplify to
cos()=cos()cos(−) (11)
cos()=cos()cos(−) (12)
The analysis and validation of antenna look
angle was carried out using the parameters of
Abuja Satellite Ground Control Station
located in Abuja, Nigeria and Nigeria
Communications Satellite (Nigcomsat-1) as
given in Chai (2005). The parameters are as
follows: Satellite longitude (sub-satellite
point), =42.5,Satellite latitude, =
0, Satellite ground control station longitude,
=7.3891 , Satellite ground control
station latitude =8.9916&.
Substituting the values above into
Eqns.(1),(2),(4) and using radius of the
Earth = 6,378.14 km, and orbital radius
= 42,164.17 km we have,
Central Angle: =36.1002=0.6301
Range: = 37,201.0110 '*
Elevation Angle: =48.1020=
0.8396
Azimuth Angle: Az = 1.3522 , =
35.1109 >0. Since >0 >0 ,
then -= 1.7898 .
III ANALYSIS AND MODEL
VALIDATION
(a) Range of the Satellite
For the range simulation and validation,
equations (1) and (5) are used. MATLAB
codes were written for the simulation. The
simulation results showed that Satellite
Ground Control Station X will be able to see
the satellite because it lies within the visible
region (unshaded region) 0≤
≤81.3 ..
(0≤
≤ 1.4191 ), which is to the left of
the sub-satellite point V shown in Figure 1.
r
e
cos
Ɣ1
Center of earth
Subsatellite point
Satellite Ground Control
Station
r
s
El1
Satellite
r
e
El2
90 – Ɣ1
θ2=
90 – Ɣ2
90 + Ɣ
2
β
1
=
90 –
El
1
-
Ɣ
1
β
2
=90–
El
2
– Ɣ
2
r
e
cos γ
r
s
-
Ψ1
Z
r
e
r
e
XY
r
s
= distance from the center of the earth to the
satellite
r
e
= distance 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 r
e
and r
s
Ψ1and Ψ2
are angles between r
e
and
d1
and r
e
and
d2
d1d2
Ɣ1Ɣ2
Satellite Ground Control
Station
Ψ2
θ1=
90 + Ɣ
1
D
Equator
O
V
Figure 1 Geometry of the range and
elevation angle calculation
Satellite Ground Control Station Y will also
be able to see the satellite because it lies
within the visible region (4.8695 ≤≤
6.2840 ), which is to the right of the
subsatellite point V shown in Figure 2. Abuja
Satellite Ground Control Station will be able
to see the satellite (Nigeria Communication
Satellite) because its central angle =
0.6301 falls within the visible region
(0≤
≤ 1.4191 ) as indicated in the
Table 1.
(a) Elevation Angle of the Satellite
For the elevation angle simulation and
validation equations (2) and (6) were used. The
simulation result showed that between the
visible region(0≤≤ 1.4191 ), Satellite
Ground Control Station X’s elevation angles
range from 1.5708 0.0052 and
they are positive, meaning that it is visible
region. Between the visible region (4.8695 ≤
≤ 6.2840 ), Satellite Ground Control
Station Y’s elevation angles range from
0.0052 1.5708 and they are
positive, meaning that they are in visible
region.
In the invisible region (1.4191 < <
4.8695 ) the elevation angles are negative,
indicating that any ground station located in
this region will not be able to see the satellite.
Since for a nominal geostationary orbit
[Timothy et al, 2003] the central angle
≤81.3 (. . ≤1.4191 ) and the
central angle of Abuja Satellite Ground Control
Station used as case study is less than
1.4191 (. . < 1.4191 ), then
Nigcomsat-1 is visible to it. Also from the
assumption made in chapter three, since
#=90−=90−36.1002=53.90=
0.9409 lies within the range of (8.70≤
#≤90) i. e.(0.1591 ≤#≤ 1.571 )
then the satellite is also visible. Therefore, the
proposition is correct and valid.
(b) Azimuth Angle
Validation of the azimuth angle of the
satellite was carried out using equation (8). By
running the azimuth angle MATLAB codes,
the program requested for the values of ls, le
and Le. The following values of Abuja
Ground Control Station and Nigeria
Communication Satellite (Nigcomsat – 1) as
given in [Chai, 2005] were used for the
simulation; = 0.7419 , =
0.1290 and = 0.1569. is the
longitude of the satellite, is the longitude of
the ground station and is the latitude of the
ground station. The azimuth angle obtained is
Az = 1.7894. Figure 2 shows the geometry of
range and elevation angles calculation
showing visible and invisible region.
r
e
cos Ɣ
1
Subsatellite point
Satellite Ground Control
Station
r
s
El
1
Nigeria
Communication
Satellite
El
2
90 – Ɣ
1
θ
2
=
90 – Ɣ
2
90 + Ɣ
2
β
1
=90–
El
1
-Ɣ
1
β
2
=90–
El
2
– Ɣ
2
r
e
cos γ
r
s
-
Z
r
e
XY
r
s
= distance from the center of the earth to the satellite
r
e
= distance from the center of the earth to the earth station
d= distance from the earth station to the satellite
Ɣ = 360
0
–(Ɣ
1
+Ɣ
2
)
Ɣ
1
and Ɣ
2
are angles between r
e
and r
s
Ψ
1
and Ψ
2
are angles between r
e
and d
1
and r
e
and
d
2
d
1
d
2
Satellite Ground Control
Station
θ1=
90 + Ɣ
1
Center of earth
r
e
Ψ
1
r
e
Ɣ
1
Ɣ
2
Ψ
2
V
LM
O
Visible region (0
≤
Ɣ
1
≤
1.4191 rad)
lies to the left of the subsatellite
point V and between ǀLVǀ[Any
Satellite Ground Control Station
within this region will be able to
see the satellite]
Visible region (4.8695
≤
Ɣ
2
≤
6.2840) rad) lies to the right of the
subsatellite point V and between
ǀMVǀ [Any Satellite Ground
Control Station within this region
will be able to see the satellite]
Invisible region (1.4191
<
Ɣ
<
4.8695 rad) lies between ǀLMǀ
[Any Satellite Ground Control
Station within this region will not
be able to see the satellite]
Ɣ
Geostationary orbit
Geostationaryorbit
Figure 2 Geometry of Range and Elevation
angles
The value obtained for the azimuth angle of
the ground station, - = 1.7894 , is
approximately equal to the calculated value of
- = 1.7898 . The validation showed
that, the simulation results conformed to with
the mathematical model.
IV VALIDATION OF THE
SIMULATED VALUES OF ABUJA
SATELLITE GROUND CONTROL
STATION
The real values and simulated values of Abuja
Satellite Ground Control Station (ABSGCS)
[10] are compared as shown in Table 1.
Table 1 Comparison of Real values and
Simulated values of ABSGCS
As shown in Table 1, the percentage
difference of the look angles (range, elevation
angle and azimuth angle) of real values of
Abuja Satellite Ground Control Station and
simulated values were minimal indicating that
the model developed is valid and there is
confidence in it.
V CONCLUSION
Abuja Satellite Ground Control Station and
Nigcomsat-1 were used for the case study.
The values obtained using the mathematical
equations developed were compared with the
values obtained through simulation in order to
verify the assumptions made for the models.
The values were in comformity indicating that
the modelled equations are right and valid.
Nigcomsat-1 satellite was visible from the
Abuja Satellite Ground Control Station
because the station lies within the visible
region.
ACKNOWLEDGEMENT
The authors acknowledge the contribution and
conducive environment provided by the
National Space Research and Development
Agency (NASRDA) of Nigeria for carrying
out this research.
REFERENCES
[1] E.D. Williams, “Basics of Satellite
Antenna Positioning”, RF and Communication
Engineering, Steven Water Monitoring
Systems, Inc.
[2] B.G. Evans, Satellite Communication
Systems, The Institution of Electrical
Engineers, London, 1999, pp. 68- 260.
[3] P. Timothy, B. Charles and A. Jeremy,
Satellite Communications, John Wiley &
Sons, Inc., New York, 2003, pp. 1 – 43.
[4] Dennis R., Satellite Communications, New
York, Third Edition, The McGraw – Hill
Companies, Inc., 2002.
[5] S. Tomas and W. David, “Determination
of Look Angles to Geostationary
Communication Satellites”, National Geodetic
Survey, Silver Spring, MD 20910, 1994, pp.
115-126.
[6] T. Wayne, Electronic Communications
Systems: Fundamentals Through Advanced,
4th ed., Pearson Education, Inc., 2001, pp.
790-800.
[7] D.A. Ogundele, E.C.A. Akoma and Y.A.
Adediran, “Mathematical Modelling of
Antenna Look Angles of Geostationary
Communications Satellite Using Two Models
of Control Stations”, 2010 3rd International
Conference on Advanced Computer Theory
and Engineering(ICACTE), pp. V4-236 to V4-
240.
[8] A. Maria, Introduction to Modeling and
Simulation, State University of Binghamton,
Department of Systems Science and Industrial
Engineering, Binghamton, NY 13902-6000,
USA.
[9] C. Hicks and C.F. Earl, “The Validation of
Simulation Models”, University of Newcastle
upon Tyne.
[10] J. Chai, Ground Control Station (GCS)
System Design, Beijing Institute of Telemetry,
Tracking and Telecommand (BITTT), Beijing,
2005, pp. 1- 48.
Parame
ters
Real
values
Simulated
values
Differ
ence
%
Diffe
renc
e
Range
37,201.0
1 km
37,200 km
1.011
0.27
18
Elevatio
n Angle
0.8396
rad
0.8393
0.000
3
0.03
57
Azimuth
angle
1.7898
rad
1.7894 rad
0.000
4
0.02
23
