Global Positioning System Reference
In-Depth Information
(
)
(
)
()
()
gt
,
X
t
=
gt
,
X
t
eph
l
oe
eph
l
nom
oe
(3.15)
(
)
gt
,
λ
eph
l
+
(
)
()
()
()
λ
=
X
t
X
t
X
t
∂λ
nom
oe
oe
nom
oe
and then (3.10) becomes equivalently
(
)
[
]
T
(
)
(
)
()
()
rtt
PX X
t
,
t
t
sa
l
k
l
nom
oe
oe
E
(3.16)
(
)
[
]
(
)
(
)
()
()
()
W
t
r
t
t
P
t
,
X
t
X
t
l
l
sa
l
k
l
no
m e
e
E
where
[
]
[
]
(
)
(
)
(
)
()
rtt
=
rtt
g t
, X
t
(3.17)
sa
l
k
sa
l
k
eph
l
nom
oe
E
E
(
)
gt
,
λ
(
)
()
l
eph
PX
t
,
t
=
(3.18)
l
nom
oe
∂λ
()
λ
=
X
t
nom
oe
() ()
()
X
t
=
X
t
X
t
(3.19)
oe
oe
nom
oe
Following classical least square techniques (see description in Appendix A)
applied to the performance objective in (3.16) yields
{
}
(
)
(
)
T
()
()
()
()
PX WPX X
t
,
t
t
t
,
t
t
l
nom
oe
l
l
nom
oe
oe
(3.20)
l
{
}
[
]
(
)
T
(
)
l
()
()
=
PX W
t
,
t
t
rtt
sa
l
nom
l
l
0
r
k
E
where the solution,
t oe , is referred to as the differential correction. Since g eph ()is
nonlinear, the optimal orbital elem en ts in (3.16) are obtained by successive itera-
tion: first, a n o minal orbital vector, X nom
X ()
t ( , followed by a series of the differential
oe
correction,
t oe using (3.20), until the differential correction converges to zero.
Following a similar approach, the almanac and c lock navigation parameters are
also generated. These resulting orbital elements, X ()
X ()
, are then scaled and truncated
in compliance with the NAV Data message format. Note, these orbital elements,
X ()
, are quasi-Keplerian and represent a local fit of the satellite ECEF trajectory,
and they are not acceptable for overall orbit characterization.
Representative curve fit errors, associated with the NAV Data message genera-
tion described earlier, are shown in Figure 3.19. For 4-hour utilization intervals, three
performance metrics are depicted: RMS URE, the maximum URE, and the root sum
squared (RSS) position errors. For the June-July 2000 period and across all satellites,
the constellation RMS-URE, Max-URE, and Max-RSS errors were 8.72, 14.7, and
52.9 cm (RMS), respectively, with along-track component being the dominant error.
MCS Upload Message Dissemination
Nominally, each satellite's NAV Data message is uploaded at least once per day.
Before each new upload transmission, the NAV Data message is verified to be in
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