Global Positioning System Reference
In-Depth Information
−
=+⋅
10
El
σ
abe
(35)
i
uLi
,,
where a and b are parameters that depend directly on El
i
(Luongo, 2004). This estimation
was performed for both cases, the Galileo and GPS satellites.
The IR equation has been implemented by means of a numerical code in a computer. FF and
FM, in Eq. 2, suggest the faulty and faulty free modes. In fact, the Galileo system assumes
two separate scenarios: one in which the satellites are all set as use, and the other in which
one of the satellites set as use is supposed not to be functioning. When you are in the faulty
mode, in the case of Galileo satellites, the SISMA element comes out; in an EGNOS case,
only the faulty free mode is instead expected and, because we could not find an equivalent
for the Galileo SISMA in its navigation message, we are going to consider the following
situation:
•
Faulty free: for the Integrity Risk computation we consider all satellites in view, GPS
and Galileo are set as OK.
•
Faulty mode: the involved satellites are only those belonging to the Galileo
constellation; hence the index of the sum concerns only those satellites.
5.3.2 Inputs of the implemented algorithm
The information available a priori for the new algorithm consists of two text files containing
position (X,Y and Z components) and velocity (X,Y and Z components) of the SV belonging
to the two constellations considered, and obtained through a constellation simulator.
Pseudoranges are obtained by the true satellite-user distance, adding a zero-mean Gaussian
noise with variance depending on SISA and the elevation angles of the satellites.
Regarding the SISA and SISMA evaluation, we have considered actual values, adding a
Gaussian noise:
)
(
SISA
=+
=+
0.87
N
0,
σ
σ
SISA
(36)
(
)
SISMA
0.7
N
0,
SISMA
In this case,
σ σ= = , in order to simulate a sort of degradation on the signal
received. We must also describe the behaviour of the positioning algorithm in the combined
constellation case. Generally speaking, if we define X
k
, Y
k
and Z
k
as the coordinates of the K-
th satellite and X, Y and Z as the coordinates of the user position, we are able to compute the
distance between the satellite and the user (
0.01
SISA
SISMA
k
ρ ) as follows
d
) and the pseudoranges (
(Misra & Enge, 2001):
k
k
2
k
2
k
2
d
=
(
XXYYZZ
−
)
+
(
−
)
+
(
−
)
(37)
and
()
k
()
k
()
k
=+ +
ρ
dc t
δε
(38)
c
u
ρ
where:
k
ε : residual error on k-th satellite.
b
: clock's offset.
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