Global Positioning System Reference
In-Depth Information
in which the “_observed” described by (9.48) represents what a ground-based user
located at USER_POSITION on the Earth would observe at the instant of time
“GPS_Time.” Equations (9.48) ignore the small effects of Earth rotation rate as well
as tropospheric and ionospheric delay on the signal. But from a macro level, (9.48)
are useful in determining the most likely initial receiver state for the signal detection
function to initialize the starting code phase and bit phase. The computed code
phase uncertainty from (9.44) then defines the range of code phase to search over,
specifically
()
Code_ Phase_ Search_ range
=
Code_ Phase_ Observed
+ − σ
pos
c
os
φ
el
Equation (9.40) can be used to determine the search time for a particular sce-
nario based on signal power, number of satellites, and the required PDI and
noncoherent integration dwell time required to positively detect the signal. Section
5.13 previously showed that as signals get weak, the integration dwell time required
to positively detect the signal increases substantially. For example, if the signal is
−
130 dBm (typical clear view of the sky conditions), the signal can be positively
detected with a 1-ms PDI and a 2-ms noncoherent integration dwell time. As the sig-
nal gets weaker, the required PDI and noncoherent integration time increases sub-
stantially (e.g., if the signal is -150 dBm, then a PDI of 10-12 ms and a noncoherent
integration time of 1 or more seconds is required). Tables 9.7 through 9.9 illustrate
this effect.
Equation (9.33) describes
N
c
as the number of total Doppler/code phase search
bins for all satellites for a particular scenario. Given that the dwell time per bin is
indicated by
T
dwell
, and the number of available correlators for the search is given by
N
corr
, then the maximum total search time is approximately indicated by
Table 9.7
Maximum Search Times
Signal
dBm
PDI
(seconds)
T
dwell
per Bin
(seconds)
N
cp
per SV
(half-chips)
N
dopp
per SV
T
search
12
(seconds)
T
search
32K
(seconds)
N
c
for 8 SVs
−
130
0.001
0.002
2,046
2
32,736
5.4
0.002
−
145
0.006
0.050
2,046
12
196,416
818
0.3
0.012
1.0
2,046
25
409,200
9.4 hours
13
−
150
0.020
5.0
2,046
42
687,456
80 hours
107
−
155
Time uncertainty = 1 ms; frequency uncertainty = 0.5 ppm; 8 satellites; position uncertainty = 30 km; ignoring code-phase
and Doppler search range reductions after finding a first satellite.
Table 9.8
Maximum Search Times
Signal
dBm
PDI
(seconds)
T
dwell
per Bin
(seconds)
N
cp
First SV
(half-chips)
N
dopp
First SV
T
search
12
(seconds)
T
search
32K
(seconds)
N
c
for 8 SVs
-130
0.001
0.002
2,046
2
6,240
1
0.002
-145
0.006
0.050
2,046
12
26,700
111
0.05
-150
0.012
1.0
2,046
25
53,300
1.23 hours
1.7
-155
0.020
5.0
2,046
42
90,230
10.4 hours
14
Time uncertainty = 1 ms; frequency uncertainty = 0.5 ppm; 8 satellites; position uncertainty = 30 km; taking advantage of
reduced code-phase and Doppler search range after finding a first satellite; number of code phase delays and Doppler bins is
reduced after finding first satellite by and reflected in total
N
c
.
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