Global Positioning System Reference
In-Depth Information
The creation of the wide-lane carrier phase (
φ
wl
) is straightforward:
φφφ
wl
=−
1
L
L
2
Just as there exists a combination (the difference) of L1 and L2 that yields a
wide-lane metric, there exists an alternative combination (the sum) that yields a nar-
row lane. It can be shown that frequency-independent errors (e.g., clock, tropo-
sphere, and ephemeris errors) are unchanged in either the wide-lane or narrow-lane
observations from their L1 and L2 values [19]. Such is not the case with fre-
quency-dependent effects (e.g., ionospheric, multipath, and noise effects), so
wide-lane carrier phase observables must be paired with narrow-lane pseudorange
observables to realize the same frequency-dependent effects. A detailed explanation
can be found in [35]. The narrow-lane pseudorange relationship (
P
nl
) is presented
without further elaboration:
fP f P
f
⋅
+⋅
+
P
=
l
1
l
1
l
2
l
2
(8.41)
nl
f
l
1
l
2
There is no change in the formation of either the carrier-phase or the
pseudorange (code) DDs once the wide-lane carrier phase and narrow-lane
pseudorange observables are formed, and the methodology previously described in
terms of the L1 carrier and code measurements is directly applicable. The prime
advantage accrues from the fact that the search volume can be canvassed far more
efficiently since fewer wide-lane wavelengths need to be searched. As mentioned
earlier, to search the same
±
11
λ
at L1 could be done, in theory, with
±
3
λ
wl
. In terms
of
N
, the iterations would range from [-3 -3 -3 -3] to [
3]. The integers in
the ambiguity sets that result from the search represent a greater physical span, but,
other than that, the procedure for isolating the proper set of carrier-cycle integer
ambiguity values is unchanged.
Once the proper wide-lane integer ambiguity set is determined, it is most advan-
tageous to revert to single-frequency tracking: The signal strength of L1 C/A code is
6 dB greater than that of the P(Y) code on L2, and there is an almost sixfold reduc-
tion in noise when using single-frequency observables over their dual-frequency
counterparts. In essence, such a move significantly improves system robustness.
While the transformation is quite straightforward, it is not without pitfalls. A close
look at the formation of the wide-lane carrier phase DD shows the following:
+
3
+
3
+
3
+
DD
=
DD
−
DD
(8.42)
cp
cp
cp
wl
l
1
l
2
This being the case, the integer ambiguity set for L1 can be determined by expand-
ing and rearranging (8.22) as shown next:
DD
−
N
λ
=
Hb DD
=
−
N
λ
(8.43)
cp
l
11
l
cp
wl
wl
wl
l
1
Combining (8.42) and (8.43) allows the recovery of the L1 integer ambiguity
set:
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