Evolution of Integrity Concept – From Galileo to Multisystem - Global Navigation Satellite Systems: Signal,Theory and Applications - page 99

is not typical; in fact, in the example depicted in Figure 6, different samples of one epoch 2
are considered in order to obtain an estimate of the proper functioning of the algorithm.
Figure 8 shows this kind of analysis made for the biased case (Galileo satellite, Vertical case).
The RAIM technique clearly detects the error in the pseudorange; in fact, the ellipse of point
leaves the normal operation region exceeding the TST. The same result can be achieved also
in the GPS biased case.

We can obtain different results by adding a bias on all pseudo ranges relative to all satellite
in view. Through this kind of simulation we can reach the results shown in Figure 11.

In Figure 11, the RAIM statistic remains around zero value: the receiver assigns the 10
metres bias entirely to the two temporal unknowns, the GPS time clock's offset and the
Galileo time clock's offset.

In conclusion, we figured out that the RAIM statistic is not able to detect the failures on
more than one satellite at the same time. This is a limit for this algorithm, which leads us to
conclude that the RAIM algorithm does not work properly when used as single integrity
system.

5.3.3.3 Error on the SISA/SISMA value

We simulated the error on the signal in space by adding a bias on the standard deviation of
the noise considered in the SISA and SISMA computation of two random satellites
belonging to one of the two constellations considered. In this failure mode, SISA and SISMA
values have been implemented as in Eq. 36, assuming the following value for the respective
standard deviation:

σ
σ

= 10

7

SISA

(41)

=

SISMA

Figure 12 shows the behaviour of the implemented algorithm, in particular the IR equation,
when the bias on SISA and SISMA is considered in two Galileo satellites. In this case the
algorithm triggers alarms with a probability of 2%.

Comparing this with a single constellation case (only a Galileo satellite), Figure 13 shows the
behaviour of the Integrity Risk algorithm in the Galileo case, considering the same size of
bias for the same satellite. What is clear from this comparison is the decrease of alarms
(~10%, in the second case) triggered by the system achieved by using the combined
constellations. This means that in a dual constellation the combined system provides a safe
position for the user.

As described in the previous Section, since these disturbances are not related to a variation
in the pseudoranges ( Δρ), we are not able to detect those errors through the RAIM statistic.
The trend of the statistics is similar to that in Figure 11, in which the curve never exceeds the
Threshold; for the sake of brevity we didn't report this picture.
In conclusion, Figure 14 shows the behaviour of the described algorithm when the bias is
applied to the SISA value belonging to two GPS satellites; in this case the biased SISMA is
2 the satellite configuration remains the same during the simulation; however, the noise added to the
pseudoranges varies.