Global Positioning System Reference
In-Depth Information
⎡⎤
p
p
p
p
P
ρ
+−+
cdt
cdT
T
11 0 0
1
k
k
k
k
⎢⎥
p
⎢⎥
p
P
I
α
0
0
k
k
=
(5)
p
11
λ
0
p
⎢⎥
φ
N
N
1
k
k
1
α
0
λ
p
p
2
⎢⎥
φ
⎣⎦
k
k
Although it stands to reason that the pseudorange measurements have a beneficial
contribution to the unknowns estimation, now only the phase equations are considered. In
addition, the geometric range
p
ρ can be moved on the left-hand side of the equation.
p
p
cdt
cdT
+
T
k
k
p
p
p
φρ
11
λ
0
I
N
k
k
1
k
p
⎥ =
(6)
p
p
1
α
0
λ
φρ
⎦⎢
2
k
k
k
p
k
N
After that, in the right-hand side, it is possible to separate the tropospheric bias from the
clock errors:
p
cdt
cdT
k
p
k
T
I
N
p
p
φρ
11
1
λ
0
k
k
1
p
k
⎥ =
(7)
p
p
11
α
0
λ
φρ
2
k
k
p
k
p
k
N
Through (7), and after few mathematical processes that are not shown, it is possible to
separate the tropospheric propagation delay and the clock errors, solving the network
positioning in a non-differential way.
4. The biases interpolation
After the dispersive and not-dispersive biases estimation, three solutions can be followed:
to consider data from the reference stations of the network and to interpolate these data
on the rover position, generating a virtual reference station close to the rover (VRS
positioning);
to model with a plane the biases and to broadcast the model parameters to the rover
(FKP positioning);
to broadcast to the rover the estimated biases together with data from a master
reference station of the network (MAC positioning).
4.1 The VRS positioning
When the previous biases are estimated, the easiest and oldest way to broadcast differential
corrections is the VRS (Virtual Reference Stations).
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