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S (G W G) G W
S S S
≡ = × × × ×
⎢ ⎥
where
Gi = [–cos Eli cos Azi –cos Eli sin in Eli 1] = ith and
22
2
N
0 0
W ;
0 0
−
Note.— The coordinate reference frame is defined such that x is along track positive forward, y is crosstrack positive left
in the local level tangent plane and v is the positive up and orthogonal to x and y.
3.6.5.5.1
x,1 x,2 x,N
y,1 y,2 y,N T 1
S S S
S S S −
⎡ ⎤
⎢ ⎥
⎢ ⎥
T
v,1 v,2 v,N
⎢St,1 St,2 St,N⎥
⎢⎣ ⎥⎦
Azi –s row of G;
2 1
⎡σ1 0 0⎤
⎢ ⎥
= ⎢⎢ σ ⎥⎥
⎢ ⎥
⎢⎣ σ ⎥⎦
where σ2
i = σ 2
pr_gnd,i + σ 2
tropo,i + σ 2
pr_air,i + σ 2
iono,i;
where
σpr_gnd,i = σ pr_gnd for the ith ranging source (3.6.4.2);
σtropo,i = the residual tropospheric uncertainty for the ith ranging source (3.6.5.3);
σiono,i = the residual ionospheric delay (due to spatial decorrelation) uncertainty for the ith ranging source
(3.6.5.4); and
σpr_air,i =
2 2
σreceiver (Eli )+σmultipath (Eli )
th
, the standard deviation of the aircraft contribution to the corrected
pseudo-range error for the i ranging source. The total aircraft contribution includes the receiver
contribution (3.6.8.2.1) and a standard allowance for airframe multipath;
where
σmultipath(Eli) = , the standard model for the contribution of airframe multipath (in metres);
Eli = the elevation angle for the ith ranging source (in degrees); and
Azi = the azimuth for the ith ranging source taken counterclockwise for the x axis (in degrees).
Note.— To improve readability, the subscript i was omitted from the projection matrix’s equation.
0.13+ 0.53e−Eli /10 deg
APP B-97 23/11/06
Annex 10 — Aeronautical Communications Volume I
3.6.5.5.1.2 Faulted measurement conditions. When the Type 101 message is broadcast without B parameter blocks, the
alues for VPLH1 and LPLH1 are defined as zero. Otherwise, the vertical protection level (VPLH1) and lateral protection level
LH1), a m ceiver, are:
LPLH1 = max [LPLj]
where VPLj and LPLj for j = 1 to 4 are
VPLj = |B_vertj| + Kmd σvert,H1 and
LPLj = |B_latj| + Kmd σlat,H1
and
B_vertj = (s_verti × Bi,j);
latj = (s_lati × Bi,j);
Bi,j = the broadcast differences between the broadcast pseudo-range corrections and the corrections obtained
excluding the jth reference receiver measurement for the ith ranging source;
Kmd = the multiplier derived from the probability of missed detection given that the ground subsystem is faulted;
σ2
vert,H1 = (s_vert2
i× σ_H12
i);
σ2
lat,H1 = (s_lat2
i× σ_H12
i);
σ_H12
i =
v(
LP ssu ing that a latent fault exists in one, and only one reference re
VPLH1 = max [VPLj]
N
i 1 =
Σ
N
i 1 =
Σ B_
N
i 1 =
Σ
N
i 1 =
Σ
i
i
M
U
⎛ ⎞
⎜ ⎟
⎝ ⎠
σ2
pr_gnd,i+ σ2
pr_air,i+ σ2
tropo,i+ σ2
iono,i;
Mi = the number of reference receivers used to compute the pseudo-range corrections for the ith ranging source
(indicated by the B values); and
Ui = the number of reference receivers used to compute the pseudo-range corrections for the ranging source,
excluding the jth reference receiver.
Note.— A latent fault includes any erroneous measurement(s) that is not immediately detected by the ground subsystem,
such that the broadcast data are affected and there is an induced position error in the aircraft subsystem.
3.6.5.5.1.3 Definition of K multipliers for Category I precision approach and APV. The multipliers are given in
Table B-67.
3.6.5.5.2 GBAS positioning service. The signal-in-space horizontal protection level is an upper confidence bound on
e horizontal error in the position relative to the GBAS reference point defined as:
ith
th
HPL = MAX{HPLH0,HPLH1}
23/11/06 APP B-98
Appendix B Annex 10 — Aeronautical Communications
Table B-67. K-multipliers for Category I precision approach and APV
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