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Document Title: 12
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 Special Applications
3.2.1 Aiding for Ballistic Trajectories
To allow a rapid acquisition and an optimal channel allocation in case of high vehicle dynam-
ics the Orion-HD receiver can be aided by a priori trajectory information. For sounding rock-
ets or other ballistic missions the nominal flight path is represented by a piecewise, low order
polynomial approximation stored within the receiver (Fig. 3.1, [12]). Using this information the
GPS satellites in view and the expected Doppler shift can be computed at any time after
launch.
y
x
z
w
0
,t
0
a
x
,b
x
,c
x
a
y
,b
y
,c
y
a
z
,b
z
,c
z
w
0
,t
0
a
x
,b
x
,c
x
a
y
,b
y
,c
y
a
z
,b
z
,c
z
w
0
,t
0
a
x
,b
x
,c
x
a
y
,b
y
,c
y
a
z
,b
z
,c
z
Sounding Rocket
Trajectory
Time
1st segment 2nd segment
3rd segment
Fig. 3.1 Piecewise polynomial approximation of the reference trajectory of a sounding rocket. Each time interval
is represented by its start epoch (GPS week and seconds) and three coefficients per axis.
To minimize the computational workload in each step, a simple 2
nd
-order polynomial
2
00
)()()( tt
c
c
c
tt
b
b
b
a
a
a
z
y
x
t
z
y
x
z
y
x
z
y
x
−
+−
+
=
=r (3.1)
is used to approximate the trajectory over discrete time intervals in the WGS84 reference
frame. Upon differentiation, one obtains an associated approximation of the instantaneous
Earth-fixed velocity vector
)(2)(
0
tt
c
c
c
b
b
b
z
y
x
t
z
y
x
z
y
x
−
+
=
=
&
&
&
v , (3.2)
which is linear in time. Accordingly, the individual time intervals should be chosen in such a
way as to exhibit a near constant acceleration. Up to 15 polynomials can be configured and
stored which is sufficient to provide a position accuracy of about 2 km and a velocity accu-
racy of roughly 100 m/s in representative missions.
Based on the polynomial approximation of the nominal trajectory, the reference position and
velocity of the host vehicle are computed once per second. The result is then used to obtain
the line-of-sight velocity and Doppler frequency shift for each visible satellite, which in turn
serve as initial values for the steering of the delay and frequency locked loops. The position-
velocity aiding thus assists the receiver in a fast acquisition or re-acquisition of the GPS sig-