Global Positioning System Reference
In-Depth Information
designed to meet the Nyquist criterion. Finally the local code rate taking into account the
Doppler effect, as presented in (27), is used.
5.3 Data wipe-off mechanism
In order to increase the coherent integration over the data bit duration (i.e.
20 ms), the
acquisition stage performs data wipe-off process.
Basically, the conventional data wipe-off
process is done as follows
MN
n
=
1
d
[
n
]
·{
r
[
n
]
c
[
n
+
τ
]
e
j
(
2
π
(
f
IF
+
f
D
))
nT
S
1
N
R
=
}
(43)
{
d
with
being the data sequence provided by the assisted data. However,
at the acquisition stage, the signal snap-shot and the assisted data are not synchronized.
Therefore, in order to determine the correct bit sequence for the signal snap-shot, the
acquisition stage needs to test all possible data sequence in a predetermined uncertainty.
Then the maximum likelihood estimator is used for decision. Hence, it can be said that the
acquisition stage in this scenario searches for the presence of a desired signal on 4-dimensions,
namely: PRN, code-phase, frequency and bit-phase (i.e. 4D search-space).
[
n
]
|
n
=
1...
MN
}
In fact, this mechanism requires an unacceptable computational effort for a single position fix,
because for each bit-phase (i.e. a data bit sequence candidate), the whole search-space must
be re-computed. As a result, the number of elementary steps (i.e. multiply&add) is
10
8
(
T
coh
·
f
S
)
×
(
N
cp
·
N
f
)
×
N
bit
−
seq
=
4.092
·
·
N
cp
·
N
f
(44)
with
N
cp
,
N
f
,
N
bit
−
seq
being the numbers of code-phase, Doppler frequency and bit-phase
bins respectively;
f
S
=
4.092 MHz and
T
coh
=
1s.
However, (43) can be rewritten as
M
m
=
1
d
m
R
m
=
R
(45)
where
R
m
is partial correlation value with representation in (5). With this approach, the
acquisition stage can compute
R
1
,
R
2
, ...,
R
M
then save these values for testing with all possible
values of bit-phase. This approach in fact utilizes the coherent combination presented in (16).
For this mechanism, the number of elementary steps is
10
6
[
M
(
f
S
·
T
coh
1
)+
M
·
N
bit
−
seq
]
·
N
cp
N
f
=
4.192
·
·
N
cp
·
N
f
(46)
with
M
being the number of partial correlations obtained after 1-ms coherent integration time
(
T
coh
1
). From (44) and (46), the computational complexity of the partial correlation approach
has a reduction of approximately 2 orders of magnitude with respect to the conventional one.
5.4 Performance analyses
This section demonstrates the application of the test-bed for indoor signal acquisition. The
required integration time for indoor signals is longer than for outdoor ones. The sky plot, see
Fig. 10, has been generated by means of an auxiliary receiver with the antenna placed out of
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