Global Positioning System Reference
In-Depth Information
The baseband E1 OS signal has the form
. Due to the bi-polar nature
of the data and secondary codes, the digital received baseband signal in each code period is
always in one of the two representations
[
d
(
t
)
b
(
t
)
−
c
2
nd
(
t
)
c
(
t
)]
|
b
[
n
]
−
c
[
n
]
|
or
|
b
[
n
]+
c
[
n
]
|
(52)
This
fact
paves
the
way
for
a
new
strategy
using
one
of
the
two
equivalent
codes
b
b
(
as the local code with the decision depending on the signal
representation. Consequently, the two new equivalent channels (B-C) and (B+C) are defined.
At a time instance, without the availability of an external-aiding source, because of the
unknown navigation data bit, the acquisition stage cannot know the correct representation
of the received signal, i.e. (B-C) or (B+C). In addition, the two new equivalent codes are
orthogonal and still preserve the properties of the PRN codes (Ta et al., 2010). Therefore, if
the chosen equivalent local code is incorrect, the correlation value in the equivalent channel
might be null although the tentative parameters (i.e. PRN number, Doppler and code delay)
are correct, because of the unknown data bit sign. Hence, the availability of an external-aiding
source is crucial.
[
n
]
−
c
[
n
])
or
(
[
n
]+
c
[
n
])
Without loss of generality, let us assume that the external-aiding source assures the signal
structure is
, therefore, the (B-C) strategy is applied, see Fig. 12(c). The decision
variable of the assisted (B-C) is
(
b
[
n
]
−
c
[
n
])
m
=
1
R
(
B
−
C
)
,
m
2
M
M
2
S
R
=
(53)
(
B
−
C
)
M
(
B
−
C
)
Note that: for this external-aiding scenario, the coherent combination is used.
However, in one full primary code period, the signal can be only in one of the two
representations in (52), it is worth to test both the strategies [i.e. (B-C) and (B+C)] and
combine their results. This leads to two new strategies so-called Summing Combination and
Comparing Combination.
•
Summing Combination (SuC):
In this strategy (see Fig. 12(d)), the (B-C) and (B+C) strategies are simultaneously performed.
The square envelope outputs are summed up to form the new decision variable
2
2
2
2
S
SuC
=
S
)
+
S
)
=
|
R
)
|
+
|
R
)
|
=
2
(
|
R
B
|
+
|
R
C
|
)
(54)
(
−
(
+
(
−
(
−
B
C
B
C
B
C
B
C
In this way, the overall decision variable is no longer affected by the unknown polarity of the
data and secondary codes of the received signal. However, multiplying the decision variable
by any coefficient does not affect the ultimate performance of a strategy because the signal
and the noise powers are increased by the same rate. Therefore, the SuC strategy shares the
performance with the DC strategy.
For this reason, in the following sections, only the DC
strategy is considered.
•
Comparing Combination (CC):
This strategy (see Fig. 12(e)) uses a comparator instead of the adder as in the SuC strategy
to combine the square envelope outputs of the two equivalent channels. The larger value is
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