Global Positioning System Reference
In-Depth Information
By using (15) one can derive other expression form of an
M
-order BOC signal ACF, which is
⎧
⎡
(
)
(
)
2
⎤
(
)
()
k
+
1
τ
221
2 12
Mk
−−
M kkM
− − +
kT
k T
+
1
−
1
−
,
≤ <
τ
c
c
⎢
⎥
⎪
⎣
T
M
⎦
M
M
c
=
⎨
()
R
τ
(18)
(
)
(
)(
)
(
)
(
)
()
k
+
1
⎡
τ
21
k
−
M
−
k
21
k
− −
k
⎤
k
−
M T
k
− +
M
1
T
−
1
+
,
≤ <
τ
BOC
c
c
⎣
⎦
⎩
T
M
M
M
c
0,
others
where
k
=
0, 1,
,
M
−
1
. And the CCF between an
M
-order BOC signal and a SCS signal is
(
)
(
(
)
⎧
)
kT
+
1
τ
MkT
−
kT
r
−+
r
r
,
≤<
τ
c
c
c
=
⎨
T
k
+
1
k
k
M
M
c
(
)
(
)
(
R
τ
;
d
(
)
(
)
(19)
τ
MkT MT
−+
)
kMT
−
kM
− +
1
T
r
−
r
+
r
,
≤ <
τ
c
c
c
c
B/L
L
kM
−+
1
kM
−
kM
−
T
M
M
⎩
c
0,
others
where
d
is the shape vector of SCS signal, and
1
Mk
−−
1
⎧
∑
()
i
−
1
d
,
0
≤ ≤
k
M
−
1
⎪
=
⎨
ki
+
M
i
Mk
=
−−
0
1
r
1
(20)
∑
()
ik
−
k
−
1
d
,
1
−
Mk
≤ <
0
⎪
⎪
i
M
i
=
0
0,
kM
≥
⎩
(
)
Fig. 9 shows a schematic diagram of
R
τ
d
;
. Note that within (-
T
c
,
T
c
) the correlation
B/L
L
kT
and
(
)
( )
function is piecewise linear between
k
+
1
T
, and
R T
= , for
s
s
B/L
s
k
[
]
k
∈− +
MM
1,
− and
k
∈
.
1
()
xx
R
τ
'
r
0
r
-
1
r
1
-M
r
2
r
-2
(1
-M
)
T
s
…
-2
T
s
-T
s
T
s
2
T
s
(
M
-1)
T
s
τ
…
0
r
M
-1
r
1
(
)
Fig. 9. Schematic diagram of correlation function
R
τ
d
;
.
B/L
L
4.4 SC algorithm design process under SC framework
From (15) and (17), it can be seen that the CCF of two SCS signals mostly depends on the
ACCF of their chip waveforms when these two signals have the same spreading sequences.
In SC algorithm design, since the chip waveform shape of the received signal is known, CCF
entirely depends on the shape of local signal spreading chip waveform. Note that each SCS
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