Evolution of Integrity Concept – From Galileo to Multisystem - Global Navigation Satellite Systems: Signal,Theory and Applications - page 95

• Bias on SISA and SISMA.

We chose the step function because it is able to characterize a lasting failure on a satellite. In
fact, when we are looking at aeronautical applications, any failures lasting more than six
seconds (TTA) are relevant. SISA results from the predictions on a satellite clock and
ephemeris errors, and these error estimations are based on long term observations: SISA
increases mark out long term failures. SISA derives from a large data batch, so the
anomalous behaviour of just one sample is not relevant. On the other hand, pseudorange
variations point out instantaneous failures. In case of failures, the new algorithm is able to
protect users from:

• long term bias due to errors from the clock and ephemeris data (IR equation);

• long term bias and short term bias due to local errors (multipath, receiver noise) and

errors caused by the SV, the SV payload and the navigation message (i.e. ephemeris
data, clock) (RAIM algorithm).

5.3.3.1 No failure mode

In a “no failure” condition we are able to judge the behaviour of the new algorithm
compared to the single constellation case, and we can also evaluate the performances
offered by the code in term of probability of false alarm and missed detection.

Figure 6 illustrates the RAIM statistic in normal operations (Vertical case), without failure,
and the correct functioning of this part of the algorithm. In this case the RAIM algorithm has
been simulated independently from the IR algorithm, in order to estimate how it behaves
with many samples in an epoch.

We tested the IR algorithm in the same way, for the two constellations and in absence of
failures (Figure 7).

Figures 6 and 7 show that the RAIM statistic presents some samples that exceed the
threshold. In particular, these samples do not exceed the VPL (Vertical Protection Level),
therefore they are in the False Alarm zone. This tells us that the RAIM statistic presents a
low probability of triggering an alarm, whenever it is not necessary (the main reason for this
behaviour of the WRAIM could be seen in the largest sensibility to the outliers of this
integrity algorithm). Instead, the IR algorithm has a lower false alarm probability than the
previous case, consequently to the fact that the threshold is never exceeded, and the system
does not trigger any alarms when the SIS is not affected by any bias.
5.3.3.2 Error on pseudoranges

We simulated the local error by adding a bias (fixed value) to the pseudoranges. Our intent
was to emulate the contribution of some types of errors (i.e. multipath) that are not present
in the SIS transmitted (local errors) and consequently are not detectable by the ground
segment of EGNOS or Galileo, but only by a RAIM technique.

The pseudoranges are calculated by using the true distance between the satellites and the
receiver, adding a Gaussian noise that depends on the variance 2

σ (Eq. 34). In addition to
the noise, in order to simulate the malfunctioning in the biased case, by a certain epoch we
added a fixed value to the range measurement. Since the IR algorithm is not able to detect
these kinds of errors, we present the results of the WRAIM part of the proposed algorithm
for this first model of failure.