Wiki » History » Version 10

LANVIN, Jean-baptiste, 12/13/2015 07:10 PM

1 1 LANVIN, Jean-baptiste
h1. Introduction
2 1 LANVIN, Jean-baptiste
3 1 LANVIN, Jean-baptiste
4 1 LANVIN, Jean-baptiste
Nowadays, a huge need for LEO is rising. With the spreading of the Internet of Things (IoT) we need more and more Machine To Machine (M2M) communications. However this is not conceivable with GEO satellites because the Time Round Trip is far too high. In this context, the aim of this project is to implement an orbit and link budget calculator for a ground station of a LEO satellite. The program is written with LabView as it is compatible with the antenna's processor owned by the Telecom Bretagne Lab in ISAE campus.
5 1 LANVIN, Jean-baptiste
6 1 LANVIN, Jean-baptiste
This report explain how it is possible to calculate the satellite’s position and how to perform the link budget if the satellite is in sight. Thus, the state of art of orbit propagators will be presented followed by a complete description of the Two-Lines Element (TLE) and then the calculation of the link budget will be explained.
7 2 LANVIN, Jean-baptiste
8 2 LANVIN, Jean-baptiste
9 2 LANVIN, Jean-baptiste
10 2 LANVIN, Jean-baptiste
h2. State of Art of the Orbit Propagators
11 2 LANVIN, Jean-baptiste
12 2 LANVIN, Jean-baptiste
Orbit propagators are mathematical models made to estimate the satellite’s position and velocity. These models take into account the effects which perturbate the satellite from his ideal orbit. These perturbations are mostly the result of the non-spherical earth mass distribution, the atmospheric resistance and gravitation effects from the sun or the moon.
13 3 LANVIN, Jean-baptiste
Five of these propagators exist : SGP, SGP4, SDP4, SGP8 and SDP8. SGP means Simplified General Perturbations models and SDP means Simplified Deep Space Perturbations. Here is a short description for each of these propagators : 
14 2 LANVIN, Jean-baptiste
15 2 LANVIN, Jean-baptiste
* SGP is the first orbit propagator. It has been developed by Hilton and Kuhlman in 1966 thanks to Kozai research work made in 1959. It is made for satellite orbiting near the Earth which considers satellite with an orbital period lower than 225 minutes.
16 2 LANVIN, Jean-baptiste
* SGP4 has been developed by Ken Cranford in 1970. It is a improvement of the previous propogator in order to track the growing number of satellites in orbit at this time. It is also used for near Earth satellites.
17 2 LANVIN, Jean-baptiste
* SDP4, developed by Hujsak in 1979, is the SGP4 propagator adpated for deep space objects. This consider satellites with an orbital period greater than 225 minutes.
18 2 LANVIN, Jean-baptiste
* SGP8, also used for near Earth satellites, is almost like the SGP4 propogator but the calculation methods are different. However it follows the same models for the atmospheric and gravitational effects.
19 2 LANVIN, Jean-baptiste
* SDP8 is the SGP8 propagator adpated to deep-space effects. Moreover, SGP8 and SDP8 are better to manage the orbital decay.
20 2 LANVIN, Jean-baptiste
21 2 LANVIN, Jean-baptiste
In this project, we chose to use the SGP4 orbit propagator. On one hand because we are dealing with low orbit satellites and on the other hand because this propagator is the most commonly use to develop satellite stracking software. Besides, the NORAD (North American Aerospace Defence Command) element sets are provided using SGP4 or SDP4. Thus it is more accurate to implement one of these propagator.
22 2 LANVIN, Jean-baptiste
23 2 LANVIN, Jean-baptiste
24 2 LANVIN, Jean-baptiste
h2. The Two-Lines Element
25 2 LANVIN, Jean-baptiste
26 2 LANVIN, Jean-baptiste
Once the orbit propagator is chosen, some datas are required at the input in order to calculate the satellite’s position. These datas are stored within the Two Lines Element (TLE). They can be found on the internet but it is important to check if they are up to date whereas precision will be lost in the calculation. TLE are provided by NORAD (North American Aerospace Defence Command).
27 2 LANVIN, Jean-baptiste
.
28 2 LANVIN, Jean-baptiste
+Here is the TLE format (2 lines of 69 characters) :+ 
29 2 LANVIN, Jean-baptiste
<pre>
30 2 LANVIN, Jean-baptiste
AAAAAAAAAAAAAAA  b.b  c.c  d.d  e.e  f  RRR         KM x km
31 2 LANVIN, Jean-baptiste
1 gggggU hhiiijjj kklll.llllllll +mmmmmmmm +nnnnn-n  ooooo-o p qqqqr
32 2 LANVIN, Jean-baptiste
2 ggggg sss.ssss ttt.tttt uuuuuuu vvv.vvvv ddd.dddd xx.xxxxxxxxyyyyyz
33 2 LANVIN, Jean-baptiste
</pre>
34 2 LANVIN, Jean-baptiste
35 2 LANVIN, Jean-baptiste
+Line 0 description :+
36 2 LANVIN, Jean-baptiste
37 2 LANVIN, Jean-baptiste
AAAAAAAAAAAAAAA : name of the satellite
38 2 LANVIN, Jean-baptiste
b.b : length (meters)
39 2 LANVIN, Jean-baptiste
c.c : width (meters)
40 2 LANVIN, Jean-baptiste
d.d : height (meters)
41 2 LANVIN, Jean-baptiste
e.e : standard magnitude
42 2 LANVIN, Jean-baptiste
f : standard magnitude determination method (d = calculation ; v = observation)
43 2 LANVIN, Jean-baptiste
RRR : equivalent radar section (meter square)
44 2 LANVIN, Jean-baptiste
KM : altitude at apogee
45 2 LANVIN, Jean-baptiste
km : altitude at perigee
46 2 LANVIN, Jean-baptiste
Remark : Most of the time there is no line 0.
47 2 LANVIN, Jean-baptiste
48 2 LANVIN, Jean-baptiste
+Line 1 description :+
49 2 LANVIN, Jean-baptiste
50 2 LANVIN, Jean-baptiste
ggggg : Number within the U. S. Space Command (NORAD)
51 2 LANVIN, Jean-baptiste
U : Classification (here U means Unclassified = not secret)
52 2 LANVIN, Jean-baptiste
hh : Last two numbers of the lunching year
53 2 LANVIN, Jean-baptiste
iii : lunch number of the year
54 2 LANVIN, Jean-baptiste
jjj : one to letters pointing a piece of the lunch
55 2 LANVIN, Jean-baptiste
kk : two last numbers of the year when these elements have been estimated
56 2 LANVIN, Jean-baptiste
lll.llllllll : day and fraction of the day when these elements have been estimated
57 2 LANVIN, Jean-baptiste
+ mmmmmmmm : half of the first derivative of the mean movement (revolution per day square), this stands for the acceleration and deceleration of the satellite
58 2 LANVIN, Jean-baptiste
+ nnnnn-n : sixth of the second derivative of the mean movement (revolution per day cube)
59 2 LANVIN, Jean-baptiste
ooooo-o : pseudo balistic coefficient, used by the SGP4 orbit propagator (1/terrestrial radius)
60 2 LANVIN, Jean-baptiste
p : type of ephemeris
61 2 LANVIN, Jean-baptiste
qqqq : number of this set of elements
62 2 LANVIN, Jean-baptiste
r : cheksum (modulo 10)
63 2 LANVIN, Jean-baptiste
64 2 LANVIN, Jean-baptiste
+Line 2 description :+
65 2 LANVIN, Jean-baptiste
66 2 LANVIN, Jean-baptiste
ggggg :  Number within the U. S. Space Command (NORAD)
67 2 LANVIN, Jean-baptiste
sss.ssss : orbit inclination with respect to the terrestrial equator (degrees)
68 2 LANVIN, Jean-baptiste
ttt.tttt : right ascension of the orbit ascending node (degrees)
69 2 LANVIN, Jean-baptiste
uuuuuuu : excentricity
70 2 LANVIN, Jean-baptiste
vvv.vvvv : perigee argument (degrees)
71 2 LANVIN, Jean-baptiste
ddd.dddd : mean anomaly (degrees)
72 2 LANVIN, Jean-baptiste
xx.xxxxxxxx : mean movement (revolution per day)
73 2 LANVIN, Jean-baptiste
yyyyy : number of revolution when these elements have been estimated
74 2 LANVIN, Jean-baptiste
z : cheksum (modulo 10)
75 2 LANVIN, Jean-baptiste
76 2 LANVIN, Jean-baptiste
Here is an example of a TLE for the NOAA-19 : 
77 2 LANVIN, Jean-baptiste
<pre>
78 2 LANVIN, Jean-baptiste
1 33591U 09005A   15310.52866608  .00000161  00000-0  11260-3 0  9997
79 2 LANVIN, Jean-baptiste
2 33591  99.0081 260.8643 0014724 126.2184 234.0350 14.11998019347577
80 2 LANVIN, Jean-baptiste
</pre>
81 2 LANVIN, Jean-baptiste
82 2 LANVIN, Jean-baptiste
Here is some helpful remarks to interpret the TLE’s values :
83 2 LANVIN, Jean-baptiste
* concerning the day and fraction of the day, also called epoch, when these elements have been estimated at line 1, the first two numbers are the last numbers of the year (15 stands for 2015 in the example). The next three numbers designate the number of the day in the year (310 represents November the 6th). Then the last numbers are the fraction of the day. By multiplying this decimal number by 1440 (the number of minutes in one day), we obtain the time of the day when these elements have been determined. This timeStamp reprensents the epoch. It is the moment where the satellite arrives at the ascending node. 
84 2 LANVIN, Jean-baptiste
* When there is a « + » before the values it means that these values can be either positive or negative
85 2 LANVIN, Jean-baptiste
* Concerning the excentricity at line 2, the decimal is assumed (0014724 means 0.0014724 in the example)
86 2 LANVIN, Jean-baptiste
* Concerning the pseudo-balistic coefficent at line 1, the decimal is assumed and the last integer represents the minus values at the power of ten (11260-3 stands for 0.11260 x 10^-3)
87 2 LANVIN, Jean-baptiste
88 4 DE GENDRE, Raphaëlle
It is even more important to have updated TLEs for satellite with orbit lower than 350 km and if it is often subject to manover such as the ISS (International Spatial Station)
89 4 DE GENDRE, Raphaëlle
90 4 DE GENDRE, Raphaëlle
91 4 DE GENDRE, Raphaëlle
92 4 DE GENDRE, Raphaëlle
93 4 DE GENDRE, Raphaëlle
h2.  Distance elevation and azimuth calculation
94 4 DE GENDRE, Raphaëlle
95 4 DE GENDRE, Raphaëlle
96 4 DE GENDRE, Raphaëlle
97 4 DE GENDRE, Raphaëlle
98 4 DE GENDRE, Raphaëlle
h3.    ECI coordinates
99 4 DE GENDRE, Raphaëlle
100 4 DE GENDRE, Raphaëlle
101 4 DE GENDRE, Raphaëlle
102 4 DE GENDRE, Raphaëlle
103 4 DE GENDRE, Raphaëlle
104 4 DE GENDRE, Raphaëlle
The coordinates of the satellite given by the propagator are given in the Earth-Centered Inertial (ECI) coordinate system . This system is a cartesian coordinate system whose origin is located at the center of the earth (at the center of mass to be precise). The z axis is orthogonal to the equatorial plane pointing north, the x axis is pointing towards the vernal equinox, and the y axis is such that the system remains a direct orthogonal system The x and y axis are located in the equatorial plane as shown in the following figure.
105 4 DE GENDRE, Raphaëlle
106 4 DE GENDRE, Raphaëlle
107 5 DE GENDRE, Raphaëlle
!ECI.jpg!
108 4 DE GENDRE, Raphaëlle
109 4 DE GENDRE, Raphaëlle
This system is convenient to represent the positions and velocities of space objects rotating around the earth considering firstly that the origin of the system is the center of mass of the earth, and that the system does not rotate with the earth. Indeed, "inertial" means that the coordinate system is not accelerating, therefore not rotating: considering the way the three axis are defined, the system is fixed in space regarding the stars.
110 4 DE GENDRE, Raphaëlle
The problem here is that our ground is station is located on the surface of the earth, so its coordinates are given in the geodetic coordinate system, which is obviously a system that is rotating with the earth.
111 4 DE GENDRE, Raphaëlle
We had therefore two options: either calculate the coordinates of the ground station in the ECI coordinate system, or calculate the coordinates of the satellite in the geodetic coordinate system. We chose the first option .
112 4 DE GENDRE, Raphaëlle
113 4 DE GENDRE, Raphaëlle
2) Julian date of the day
114 4 DE GENDRE, Raphaëlle
115 7 LANVIN, Jean-baptiste
	The main problem to go from the geodetic system to the ECI system is to calculate the angle between the observer meridian (longitude) and the vernal equinox direction. This angle, also called the local sidereal time depends on the star and not on the sun and that is why it is a bit touchy to calculate. For our implementation and tests, we relied on the algorithms and example given in the magazine _Satellite Time_ ,in the column Orbital Coordinate Systems, Part II. θ(τ) is actually define as the sum between the antenna east longitude and the greenwich sidereal time GST, which is the angle between the greenwich meridian and the vernal equinox that we will note  θg(τ).
116 7 LANVIN, Jean-baptiste
θg(τ)can be calculated using the formula:
117 7 LANVIN, Jean-baptiste
118 10 LANVIN, Jean-baptiste
θg(τ) = θg(0h) + ωe·Δτ (1)
119 1 LANVIN, Jean-baptiste
120 7 LANVIN, Jean-baptiste
where Δτ is the number of seconds elapsed since 0h at the time of the calculation and ωe = 7.29211510 × 10-5 radians/second is the Earth's rotation rate. θg(0h) is the GST calculated at 0h that day and it is given as
121 8 LANVIN, Jean-baptiste
122 10 LANVIN, Jean-baptiste
θg(0h) = 24110.54841 + 864018.812866 Tu + 0.093104 Tu2 - 6.2 × 10-6 Tu3 (2)
123 8 LANVIN, Jean-baptiste
where Tu = du/36525 and du is the number of days of Universal Time elapsed since the julian date 2451545.0 (2000 January 1, 12h UT1). Therefore, to calculate θg(τ), the first thing we need is the julian date of the day, which we can deduce from the julian date of the year as follow:
124 8 LANVIN, Jean-baptiste
125 8 LANVIN, Jean-baptiste
JD = Julian_Date_of_Year() + Number of day since the first of January;
126 1 LANVIN, Jean-baptiste
127 8 LANVIN, Jean-baptiste
This calculation is done in the VI julian date.vi where the calculation of the Julian date of the year is done using the Meeus' approach.
128 8 LANVIN, Jean-baptiste
129 10 LANVIN, Jean-baptiste
Once we had the Julian date, we could calculate du and therefore Tu, and that way we calculated θg(0h) using (2). From there, we were able to calculate θg(τ) using (1) and since we know the east longitude of the antenna we obtained θ(τ). Those calculations are done in the VI tetag.vi.
130 9 LANVIN, Jean-baptiste
131 9 LANVIN, Jean-baptiste
132 6 LANVIN, Jean-baptiste
133 6 LANVIN, Jean-baptiste
134 6 LANVIN, Jean-baptiste
135 4 DE GENDRE, Raphaëlle
3) Theta calculation
136 4 DE GENDRE, Raphaëlle
4) Distance
137 4 DE GENDRE, Raphaëlle
5) Elevation and azimuth
138 4 DE GENDRE, Raphaëlle
III) Link budget