Global Positioning System Reference
In-Depth Information
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the
m
and
n
factors that generate long wavelengths according to (6.104), might also
increase the impact of multipath errors and other disturbances according to (6.102).
Combinations for which
m
and
n
have different signs are called the wide-lane
observables. Because the specific observable
(
1
,
1
)
is the most important of all the
wide-lane observables, it is usually referred to simply as the widelane (without explic-
itly mentioning the
m
and
n
); the subscript
w
is also used to identify this combination.
If the
m
and
n
have the same sign, we speak of narrow-lane observables. The partic-
ular combination (1, 1) is simply the narrowlane (without explicitly mentioning the
m
and
n
). The subscript
n
identifies the narrowlane. For example,
−
ϕ
n
=
ϕ
1
+
ϕ
2
(6.110)
ϕ
w
=
ϕ
1
−
ϕ
2
(6.111)
[22
c
f
n
=
c
f
1
+
λ
n
=
f
2
≈
0
.
11 m
(6.112)
Lin
—
5.6
——
Sho
*PgE
c
f
w
=
c
f
1
−
λ
w
=
f
2
≈
0
.
86 m
(6.113)
It is important to note that for any linear combination of the carrier phase obser-
vations, the respective variance-covariance preparation must be carried out properly.
Finding the optimal combination has at times generated considerable interest. How-
ever, that is no longer the case because of the optimal performance of LAMBDA
(Teunissen, 1999). LAMBDA automatically includes widelaning but is even more
general.
[22
6.6.7 Global Ionospheric Models
Th
e ionosphere can be estimated from (6.97) and (6.99), given dual-frequency ob-
se
rvations. Although multipath of the GPS signals is a limiting factor in all GPS
ap
plications, we neglect the multipath terms in these equations assuming that their
ef
fect averages out or has been corrected computationally using multipath models.
A
dding the subscript
k
and superscript
p
for clarity, we can write
P
k,I
=
1
− α
f
I
k,
1
,P
+
c
1
− α
f
T
p
GD
+
d
1
,P
−
d
2
,P
(6.114)
=
1
− α
f
I
k,
1
,P
+ λ
2
N
k,
2
− λ
1
N
k,
1
+
p
k,I
Φ
d
2
,
Φ
−
d
1
,
Φ
(6.115)
The first step in estimating the ionosphere is to correct all cycle slips, using, e.g., the
“phase-connected” arc method (Blewitt, 1990) or any other suitable technique. In the
second step, we assume that the receiver hardware delays
d
1
,P
−
d
2
,P
and
d
2
,
Φ
−
d
1
,
Φ
are constant over the time of the arc and compute the offset for the arc
