Global Positioning System Reference
In-Depth Information
in [17] has RMS delay spread less than 50 ns, with delay spread less than 250 ns.
The Doppler spread is often dominated by the motion of the receiver and can be
millihertz for stationary receivers or multipaths with large excess delay, and hertz
for multipaths with small excess delay and receivers being carried by a person.
While it is difficult to make any generalizations about phenomena as highly
variable as multipath and shadowing, several observations can be made. Shadowing
exacerbates any multipath effects, and severe shadowing can cause the receiver to
track a multipath rather than a direct path, causing potentially large ranging errors.
Near-in multipaths are often the most stable over time for a receiver that does not
move relative to its local environment, but the fastest varying in time for a receiver
that moves relative to its local environment. Near-in multipaths often have the
greatest MDR, but typically introduce smaller ranging errors than multipaths with
larger excess delays.
6.3.2 Effects of Multipath on Receiver Performance
Since received signals from different satellites typically encounter different
multipath channels, the resulting pseudorange errors are not common to signals
received from different satellites, and thus produce errors in position, velocity, and
time. Further, the size of the multipath errors in tracking different satellites may also
be very different, since signals received from higher-elevation satellites tend to expe-
rience less multipath in many applications. Ironically, the contributions of
lower-elevation satellites to improved dilution of precision can provide an impor-
tant incentive to use these signals, in spite of their larger multipath errors.
As discussed in Section 6.3.1, actual multipath environments are both compli-
cated and diverse, making it difficult to quantify the effects of multipath in ways that
are both generally applicable yet accurate. Computer simulations that synthesize
waveforms, and then employ high-fidelity channel models and specific receiver pro-
cessing approaches, can provide accurate and realistic assessments, yet they provide
little insight into underlying issues and characteristics. In contrast, the multipath
model (6.43) has limited realism but provides useful insights. In fact, extensive
assessments have been made using the one-path specular multipath version of (6.43).
While the numerical results obtained are often not representative of real-world
multipath conditions, they provide useful diagnostic insights. Further, it is sufficient,
although it may not be necessary, to perform well under these simple conditions.
For the one-path specular multipath model, (6.43) can be rewritten (continuing
to neglect noise and interference), as
[
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~
~
~
~
()
(
)
(
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−
j
φ
−
j
φ
rt
=
α
e
xt
−
τ
+
α
e
xt
−
τ
−
τ
(6.45)
0
1
0
0
1
0
1
When the locally generated reference
e
j
θ
x
(
t
) is correlated against this received sig-
nal, the statistical mean of the result is
[
]
~
~
~
~
(
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()
(
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(
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−
j
φθ
−
λτ
=
α
e
R
τ
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τ
+
a e
−
j
φ
R
τ
−
τ
−
τ
0
1
0
x
0
1
x
0
1
(6.46)
~
R
x
(
)
−
j
φθ
−
(
)
=
α
e
ττ
−
0
0
0
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