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Document Title: 15
User’s Manual for the GPS Orion-S/-HD Receiver
Document No. Issue 1.0
GTN-MAN-0110 June 22, 2003
DLR/GSOCNo part of this document shall be reproduced in any form or disclosed to third parties without prior authorization.
3.2.4 Aiding for LEO Satellites
The Orion-S receiver provides a dedicated aiding mode to support the GPS signal acquisition
onboard a low Earth orbiting (LEO) satellite. Similar to the HD receiver, it uses a coarse ap-
proximations of the nominal trajectory to forecast the visible GPS satellites and the expected
line-of-sight Doppler shift. This information is the used to allocate and initialize new tracking
channels. In accord with its primary application area, the Orion-S receiver employs the
SGP4 orbit model for LEO satellites [14] to predict the user spacecraft trajectory from
NORAD twoline element data sets.
Twoline elements comprise 2 lines of 69 characters each (cf. Table 3.1) to specify the epoch
and the orbital elements of a satellite, as well as information on the secular change in the
mean motion and on the ballistic coefficient (or the second derivative of the mean motion).
They also give the international satellite ID, an element number and a revolution number.
Each line contains a checksum at the end to guard against transmission errors.
Table 3.1 Description of the contents of NASA/NORAD 2-line element records
Column Description Line 1
01-01
03-07
10-11
12-14
15-17
19-20
21-32
34-43
45-52
54-61
63-63
65-68
69-69
Line number of element data
Satellite number
International Designator (last two digits of launch year)
International designator (launch number of year)
International designator (piece of launch)
Year of epoch (last two digits)
t
0
; day of epoch (day of year and fractional day)
1/2·dn
0
/dt; the time rate of change in the „mean“ mean motion (in units of [rev/d
2
]),
or the ballistic coefficient B (depending on ephemeris type)
1/6·d
2
n
0
/dt
2
; the second time rate of change in the „mean“ mean motion (in units of [rev/d
3
]). A deci-
mal point is assumed between columns 45 and 46. Will be left blank if not applicable (see above)
B*=1/2· Bρ
0
, where B=1/2· C
D
· A/m is the drag term (in units of [1/R
⊕
]; a decimal point is assumed
between columns 54 and 55
Ephemeris type
Element number
Check sum for line 1 (modulo 10); numbers count face value, letters and blanks as 0, periods and
plus signs as 0, minus signs as 1
Column Description Line 2
01-01
03-07
09-16
18-25
27-33
35-42
44-51
53-63
64-68
69-69
Line number of element data
Satellite number
i
0
; the mean inclination (in [°])
Ω
0
; the mean right ascension of the ascending node (in [°])
e
0
; the mean eccentricity. A decimal point is assumed between columns 26 and 27
ω
0
; the mean argument of perigee (in [°])
M
0
; the „mean“ mean anomaly (in [°])
n
0
; the „mean“ mean motion (in [rev/d]) dependent on SGP type
Revolution number
Check sum for line 2 (modulo 10)
The orbital elements are mean Keplerian elements (with the number of revolutions per day
substituting the semi-major axis), which best represent the actual trajectory when used in
combination with the SGP4 (or SDP4) orbit propagators. The SGP4 orbit model was devel-
oped in 1970 based on the analytical perturbation theory of Brouwer and accounts for the
Earth gravity field through zonal parameters J
2
, J
3
and J
4
and the atmospheric drag through a
power density function assuming a non-rotating, spherical atmosphere. It is recommended
for satellites in near-circular orbits with typical periods of less than 225 min.