Evolution of Integrity Concept – From Galileo to Multisystem - Global Navigation Satellite Systems: Signal,Theory and Applications - page 86

System
Unavailable
AL<PE<PL
System
Unavailable
& Misleading
Information
AL < PL < P E

System
Unavailable
PE<AL<PL

A l er t L imi t (AL )

Nominal
Operations
PE<PL<AL

Hazardously
Misleading
Information
PL<AL<PE

Misleading
Information
PL<PE<AL

Position Error (PE)

Fig. 3. EGNOS protection level

Assuming that the error in the range domain can be overbounded by a zero-mean Gaussian
probability density function, the variance of that distribution is:

2 2 2 2 2

σσ σ = + + σ σ + (17)

i i flt , UiRE i , air i , tropoi ,

2
i fl σ may be easily derived from

2

where the variance

UDRE σ . From Eq. (17) and for a given
user/satellite geometry, it is quite simple to derive the vertical (horizontal) protection level
VPL (HPL) equation by:

,

1. passing from the pseudo range variance domain to the position variance domain,

noting that the integrity definitions are all in the position domain;

2. scaling the position domain variance to the integrity requirement. VPL (HPL) is scaled

for compatibility with the probability of non integrity detection so that the VPL (HPL)
should always be larger than PE.

Compared to the first step, the variance in the position domain residual error is a linear
combination of σ 2 i and is also representative of a zero-mean normal law.

N

2

= ∑

2 2

(18)

σ s σ

Vposition V i , i

i = 1

where S V,i are geometrical parameters.
The second step is achieved by multiplying the position domain variance by a factor k that
propagates this variance to a level compatible with the integrity requirement.

N

∑

2 2

(19)

VPL = K s σ

EGNOS V V i , i

i = 0