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ree-point interpolation is used if the IPP i ithin the triangular region covered by the three corrections that are provided.
otection levels. The horizontal protection level (HPL) and the vertical protection level (VPL) are:
HPL
K d for precision approach (PA) and approach with vertical guidance (APV) modes
⎧⎪
= ⎨⎩⎪ ×
VPLSBAS = KV,PA × dV
here
2
,
are selected; else,
4) if any three IGPs that define a 10-degree-by-10-degree triangle that circumscribes the IPP are set to “1” in the
IGP mask, they are sele
5) an ionospheric correction is not available.
c) For an IPP between N75° a
1) if the two nearest IGPs at 75° and the two nearest IGPs at 85° (separated by 30° longitude if Band 9 or 10 is
used, separated by 90° otherw
IGPs at 75°; else,
2) an ionospheric correction is not available.
d) For an IPP north of N85°:
they are selected; else,
longitudes of W140°,
the information provided in the mask, without regard to w
IGPs are
ionospheric correction is not
th s w
3.5.5.6 Pr
H,NPA ×dmajor for en-route through non-precision approach (NPA) modes
SBAS
H,PA major
K
w
N
2 2
V vi i
i 1
d s
=
=Σ σ = variance of model distribution that overbounds the true error distribution in the vertical axis;
2 2 2 2 2
x y x y 2 d d d d
2
⎛ ⎞
dmajor dxy ;
2
+ −
= + + ⎟⎟
⎝ ⎠
⎜⎜
APP B-53 23/11/06
Annex 10 — Aeronautical Communications Volume I
23/11/06 APP B-54
where
N
2 2 2
x x,i i
i 1
d s
=
=Σ σ = variance of model distribution that overbounds the true error distribution in the x axis;
N
2 2 2
y y,i i
i 1
d s
=
=Σ σ = variance of model distribution that overbounds the true error distribution in the y axis;
N
2
xy x,i y,i i
i 1
d ss
=
=Σ σ = covariance of model distribution in the x and y axis;
where
sx,i = the partial derivative of position error in the x-direction with respect to pseudo-range error on the ith
satellite;
sy,i = the partial derivative of position error in the y-direction with respect to pseudo-range error on the ith
satellite;
sV,i = the partial derivative of position error in the vertical direction with respect to pseudo-range error on the ith
satellite; and
σ2
i = σ2
i,flt + σ2
i,UIRE + σ2
i,air + σ2
i,tropo.
The variances (σ2
i,flt and σ2
i,UIRE) are defined in 3.5.5.6.2 and 3.5.5.6.3.1. The parameters (σ2
i,air and σ2
i,tropo) are determined by
the aircraft element (3.5.8.4.2 and 3.5.8.4.3).
The x and y axes are defined to be in the local horizontal plane, and the v axis represents local vertical.
For a general least-squares position solution, the projection matrix S is:
x,1 x,2 x,N
y,1 y,2 y,N T 1 T
v,1 v,2 v,N
t,1 t,2 t,N
S S S
S S S
S (G W G) G W
S S S
S S S
−
⎡ ⎤
⎢ ⎥
≡⎢ ⎥= × × × ×
⎢ ⎥
⎢ ⎥
⎢⎣ ⎥⎦
…
…
…
…
where
Gi = [–cos Eli cos Azi –cos Eli sin Azi –sin Eli 1] = ith row of G;
1
1 2
i
w 0 0
0 w 0
W ;
0 w
−
⎡ ⎤
⎢ ⎥
=⎢ ⎥
⎢ ⎥
⎢ ⎥
⎣ ⎦
…
…
…
Eli = the elevation angle of the ith ranging source (in degrees);
Azi = the azimuth of the ith ranging source taken counter-clockwise from the x axis in degrees; and
wi = the inverse weight associated with satellite i.
Note 1.— To improve readability, the subscript i was omitted from the protection matrix’s equation.
Note 2.— For an unweighted least-squares solution, the weighting matrix is an identity matrix (wi = 1).
Appendix B Annex 10 — Aeronautical Communications
APP B-55 23/11/06
3.5.5.6.1 Definition of K values. The K values are:
KH,NPA = 6.18;
KH,PA = 6.0; and
KV,PA = 5.33.
3.5.5.6.2 Definition of fast and long-term correction error model. If fast corrections and long-term correction/GEO
ranging parameters are applied, and degradation parameters are applied:
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