Global Positioning System Reference
In-Depth Information
From the figures it can be seen that with any
M
, no major positive side peak exists in SCF.
Although there are some pits on the SCF, their magnitudes are all below zero, so they bring
no threat to the acquisition.
Although all examples shown above are for sin-BOC signals, it is easy to demonstrate that
GRASS technique can also be applied to cos-BOC signals by simply replacing basis function
(8) with
1
⎧
{
}
(
)
(
)
sgn sin 2
⎡
π
f
tkT
−
⎤
,
kT t k
≤ < +
1
T
⎪
⎣
⎦
s
s
s
s
()
(37)
ψ
′
t
=
⎩
T
k
c
0,
others
6. PUDLL
As another example of the application of SC design framework, in this section we show the
design process of an unambiguous code tracking technique named pseudo-correlation-
function-based unambiguous delay lock loop (PUDLL) (Yao et al., 2010b) which is
applicable to any BOC(
kn
,
n
) signals. At tracking stage, because the discriminator
characteristic curve is based on the first derivative of SCF, the requirement to the shape of
SCF is more stringent than in acquisition.
6.1 Step 1 - SCF selection
It is desired that the SCF used in code tracking has an ideal triangular main peak with no
side peak. Since the CCF between the received BOC signal and the local SCS signal is
piecewise linear, utilizing this characteristic, and using the absolute-magnitude operation to
change the direction of lines on one side of the zero crossing point, following by the linear
combination, it is possible to obtain the SCF without any side peak. Therefore, in this
example, the SCF is chosen as
( )
( )
( )
( )
( )
RR R R R
τ
=
τ
+
τ
−
τ
+
τ
(38)
1
2
1
2
R
are CCFs between BOC signal and two local SCS signals
(
)
where
R
and
gt
d
;
and
1
1
(
)
gt
d
;
, respectively, in which
d
and
d
are the shape vectors of
g
and
g
respectively.
2
2
6.2 Step 2 - CCF shape constraint
A sufficient condition for (38) being symmetric with respect to
τ= is
0
( )
( )
R
τ
=
R
− .
τ
(39)
1
2
In fact, the only difference between
( )
( )
− and
( )
( )
= −− lies in the polarity
of the local SCS chip waveform. Without loss of generality, assume
( )
R
τ
=
R
τ
R
τ
R
τ
1
2
1
2
( )
R
τ
= −−, so that
R
τ
1
2
at each endpoint of CCF segment
′
= −
r
r
(40)
i
i
(
)
(
)
′
=
where
rRiTM
=
/
and
rRiTM
/
.
i
1
c
i
2
c
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