Performance of Stand-Alone GPS - Understanding GPS: Principles and Applications - page 352

Estimated horizontal
position error

Slope max

Miss rate

Horizontal
integrity
limit

T D pbias Test statistic |p|

Figure 7.23 Scatter plot with critical bias on Slope max satellite.

to the left, increasing the missed detection rate beyond the allowable limit. This criti-
cal bias value in parity space is denoted as pbias. The pbias term is completely deter-
ministic, but it is dependent on the number of visible satellites [43]:

pbias = σ λ

UERE

where λ is the noncentrality parameter of the noncentral chi-square density function,

and σ UERE is the standard deviation of the satellite pseudorange measurement error.

The HPL is determined by

HPL = Slope max × pbias

When SA was the dominant error source, other error terms that depend heavily
on the elevation angle were negligible. For this reason, pre-2000 RAIM and FDE
availability analyses typically assumed a fixed σ UERE value of 33.3m for all satellites,

regardless of the satellite elevation angles. Now that SA has been discontinued,
errors that depend on the elevation angles make

σ UERE values for each satellite signifi-

cantly different.
Accounting for elevation-dependent errors is accomplished through weighting
(or deweighting) of individual satellite range measurements [46]. The only differ-
ence between the weighted solution RAIM and the nonweighted solution RAIM is
the formula for the maximum horizontal slope, which is shown next.
The threshold and pbias values are the same as with SA on. This is because the
maximum false alarm rate is set at 0.333 10 −6 /sample, which is consistent with the ×

guidance in [14] for SA off.

()

2 2

SLOPE i = AA + σ S

1 i 2 i i ii

where: