Global Positioning System Reference
In-Depth Information
time for software receiver design. Theoretically, the BASS method at worst case
may lose about 1 dB of sensitivity with 5 MHz sampling rate due to the potential
misalignment between the input signal and the locally generated signal. Two
methods of generating fine time resolution are discussed. The outputs from the
tracking are also discussed. These outputs will be used in the next chapter to find
the user position.
APPENDIX
(
10
)
Equation (8.26) can be written as
∞
1
+
4
ζ
2
x
ω
n
2
π
ω
n
2
π
I
1
+
ω
n
2
π
4
ζ
2
I
2
B
n
=
−
1
)x
+
1
dx
=
(
8A
.
1
)
x
4
+
2
(
2
ζ
2
0
where
∞
dx
I
1
=
(8A.2)
x
4
+
2
(
2
ζ
2
−
1
)x
2
+
1
0
∞
x
2
dx
I
2
=
(8A.3)
x
4
+
2
(
2
ζ
2
−
1
)x
2
+
1
0
These integrals can be found from
(
11
)
∞
x
µ
−
1
dx
γ
µ/
2
−
1
−
β
µ/
2
−
1
π
2
csc
µπ
2
x
2
)
=
(
8A
.
4
)
(β
+
x
2
)(γ
+
β
−
γ
0
with the condition that
|
arg
β
|
<π,
|
arg
γ
|
<π
0
<
real
µ<
4
The values of
β
and
γ
in Equation (8A.4) can be found by comparing this
equation with Equation (8A.3) or (8A.2) as
βγ
=
1
2
(ζ
2
β
+
γ
=
−
1
)
(8A.5)
Solving for
β
and
γ
, the results are
ζ
2
1
)
2
β
=
(ζ
+
−
ζ
2
1
)
2
γ
=
(ζ
−
−
(8A.6)
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