Global Positioning System Reference
In-Depth Information
results for multipath phase (relative to phase of the direct path) of 0º, 90º, and 180º.
The left-hand columns show magnitude-squared correlation functions, while the
right-hand columns show the pseudorange error introduced by the multipath for
different values of early-late spacing. The phase of the multipath dictates whether
the error is positive or negative. With the narrow precorrelation bandwidth in this
case, narrower early-late spacings examined here have little effect on the error in
most cases.
Figure 6.11 shows the same results as in Figure 6.10, for a signal with
BPSK-R(1) modulation bandlimited to 24 MHz. With the wider precorrelation
bandwidth, narrower early-late spacing significantly reduces the error in most
cases.
Figure 6.12 shows the same results as in Figure 6.10, for a signal with
BPSK-R(10) modulation bandlimited to 24 MHz. Since the sharper correlation
function peak resolves this multipath better, the ranging errors tend to be smaller.
When these results are repeated for multipath excess delay of 0.4
s, the errors for
BPSK-R(1) modulation are similar to those in Figures 6.10 and 6.11, while
BPSK-R(10) modulation displays no errors, since its sharper correlation function
peak completely resolves the multipath with larger excess delay.
For a more comprehensive depiction of ranging error caused by one-path
multipath, recognize that for a given modulation and receiver design (including
precorrelation bandwidth and code tracking discriminator), multipath error is
determined by the MDR, phase, and delay of the multipath. When the MDR is con-
stant (independent of delay and phase) as in specular multipath, the error for a given
multipath delay varies with multipath phase, as seen in Figures 6.10 through 6.12.
For a given MDR, the maximum and minimum errors at each delay are taken over
all multipath phase values, producing a range of possible delay estimates for each
value of excess delay. If
µ
, ~
( ~
, ~
$
o 11 1 is the estimated delay for a specific MDR,
excess delay, and multipath phase, then denote the error in delay estimation by
εα
τα τφ
)
, ~ , ~ )
11 1
, ~
( ~
( ~
, ~
$
011 1 . The maximum and minimum errors for a spe-
cific excess delay are respectively max ( ~
τ
φ
= τ 0
τα τφ
)
, ~
, ~
, ~
11 1 and min ( ~
, ~
εα
τ
φ
)
εα
11 1 ; the enve-
τ
φ
)
~
φ
~
φ
1
lope of delay errors at a given excess delay is defined by
1
, ~
, ~
(
~
, ~
)
(
~
, ~
)
max
εατφ
,min
εατφ
(6.47)
~
~
11 1
11 1
φ
φ
1
1
The resulting envelope of ranging errors is obtained by multiplying the envelope of
delay errors by the speed of light.
Figure 6.13 shows multipath ranging error envelopes for BPSK-R(1) modula-
tion with two different precorrelation bandwidths, and BPSK-R(10), all with
early-late spacing of 50 ns. For the BPSK-R(1) modulation, the wider precorrelation
bandwidth, combined with the narrow early-late spacing, provides smaller error, as
recognized in [18]. The BPSK-R(10) modulation provides even smaller errors.
To assess multipath performance over a range of possible delay values, define
~
τ
1
,, ~
,, ~
1
[max ( ~
~
the average range error envelope as
εα
u
φ
)min
εα
u
φ
)]
du
. The
~
~
~
1
1
1
1
τ
φ
φ
1
1
1
0
average envelope can provide useful insights, particularly for modulations whose
range error envelopes oscillate with delay, such as some BOC modulations.
Search WWH ::




Custom Search