Evolution of Integrity Concept – From Galileo to Multisystem - Global Navigation Satellite Systems: Signal,Theory and Applications - page 84

N

∑

[ ] [ ] [ ]

2

σ = Kmi Kni , ⋅ , ⋅ σ i (10)

mn , uRX ,

i = 1

where “i” indicates the ith satellite, “m” and “n” the reference axis: X, Y or Z.

The “Faulty Position Error” module computes the characteristic of the position error in
faulty mode (faulty geometry: one single failure satellite). In particular, the standard
deviation of the distribution that overbounds the vertical position error and the variance of
the distribution that overbounds the horizontal position error are computed. The principal
formulas are reported here:

2

σσ = (11)

V ZZ _ F

2

2 2 2 2

⎛ ⎞

σ + σ σ − σ

2 XXF _ YYF _ XXF _ YYF _ 4

ξ = + + σ (12)

⎜ ⎟

H XY _ F

⎜ ⎟

2 2

⎝ ⎠

where σ is the standard deviation of the model (zero-mean normal CDF) used to
overbound the vertical position error in faulty mode.
2
ξ is the variance of the model used to overbound the horizontal position error (along the
semi-mayor axis of the error ellipse) in faulty mode.

The σ components are obtained using the following general expression:

mn F ,_

N

( )

∑

[ ] [ ] [ ] [ ] [ ] [] []

2 2 2

(13)

σ = Kmi Kni , ⋅ , ⋅ σ i + Kmi , ⋅ Kni , ⋅ σ i − σ i

m n ,_ F u RX , 0 0 SISMA 0 SISA 0

i = 1

where “i” indicates the i th satellite, “m” and “n” the reference axis: X, Y or Z.

The “HMI Probability” module computes the probability of HMI. The principal formulas
are reported as follows:

P = P + p P (14)

HMI HMI Fault , − Free fail HMI Faulty ,

P = P + P (15)

HMI Fault , − Free HMI Fault , − Free V , HMI Fault , − Free H ,

P = P + P (16)

HMI Faulty , HMI Faulty V , , HMI Faulty H , ,

3. EGNOS integrity

The GPS system is neither accurate nor reliable enough to be accepted as the only
instrument of navigation for critical applications. One of the reasons is that no reliable and
quick (within seconds) information can reach the user if any problems with the system
occur. As a consequence, the GPS system cannot be used for landing approaches, for
instance. Airplanes still have to use ILS-systems (Instrument Landing Systems) in case of
poor visibility. But the installation and the maintenance of ILS-systems in every airport is
expensive. With the SBAS systems, CAT I approaches (limited visibility) will be possible