Global Positioning System Reference
In-Depth Information
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7.7.5 Initialization on the Ground
A
kinematic survey requires an initialization. This means the double-difference am-
bi
guities are resolved first and then held fixed while other points are being surveyed,
as
suming of course that no cycle slips occurred while the rover moves or that cycle
sli
ps are repaired appropriately. A simple way for initial determination of ambiguities
is
to occupy two known stations. The procedure works best for short baselines where
th
e ionospheric and tropospheric disturbances are negligible. The double-difference
eq
uation (7.92) can be readily solved for the ambiguity,
N
pq
km
ϕ
pq
km
− λ
−
1
pq
km
=
ρ
(7.110)
when both receiver locations
x
k
and
x
m
are known. Usually simple rounding of the
computed values is sufficient to obtain the integers. Once the initial ambiguities are
known, the kinematic survey can begin. Let the subscripts
k
and
m
now denote the
fixed and the moving receiver, then
[27
− λ
ϕ
pq
km
km
Lin
—
1.0
——
Sho
*PgE
pq
k
N
pq
pq
m
ρ
= ρ
−
(7.111)
If four satellites are observed simultaneously, there are three equations like (7.111)
available to compute the coordinates of the moving receiver
x
m
. If more than four
satellites are available, the usual least-squares approach is applicable and cycle slips
can be repaired from phase observations. In principle, if five satellites are observed
we can repair one slip per epoch, if six satellites are observed, two slips can occur at
the same time, etc.
Remondi (1985) introduced the antenna swap procedure in order to initialize
the ambiguities for kinematic surveying. Assume that four or more satellites were
observed at least for one epoch while receiver
R
1
and its antenna were located at
station
k
and receiver
R
2
and its antenna were at station
m
. This is followed by the
antenna swap, meaning that antenna
R
1
moves to station
m
and antenna
R
2
moves to
station
k
, followed by at least one epoch of observations to the same satellites. The
antennas remain connected to their respective receivers. During data processing, it
is assumed that the antennas never moved. Using an expanded form of notation to
identify the receiver and the respective observation, a double difference at epoch 1
when
R
1
was at
k
and at epoch
t
when
R
1
was at
m
can be written, respectively, as
[27
= λ
−
1
m
(R
2
,
1
)
ϕ
pq
p
k
(R
1
,
1
)
q
k
(R
1
,
1
)
N
pq
km
(7.112)
p
q
k
m
(R
2
−
R
1
,
1
)
ρ
− ρ
− ρ
m
(R
2
,
1
)
+ ρ
+
= λ
−
1
ρ
k
(R
2
,t)
+
ϕ
pq
p
k
(R
2
,t)
q
N
pq
km
(7.113)
p
m
(R
1
,t)
q
m
(R
1
,t)
km
(R
2
−
R
1
,t)
− ρ
− ρ
+ ρ
Notice the sequence of subscripts on the right-hand side of (7.113). Differencing both
observations gives
