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pseudo-range measurements that have not had the satellite broadcast troposphere and ionosphere corrections applied to them.
The carrier smoothing is defined by the following filter:
PCSCn = α
P(1 )PCSCn 1 (n n 1)
− 2 −
+ − α⎛⎜⎝ + λπ φ − φ ⎞⎟⎠
where
PCSCn = the smoothed pseudo-range;
PCSCn–1 = the previous smoothed pseudo-range;
P = the raw pseudo-range measurement where the raw pseudo-range measurements are obtained from a carrier
driven code loop, first order or higher and with a one-sided noise bandwidth greater than or equal to
0.125 Hz;
λ = the L1 wavelength;
= the carrier phase;
n–1 = the previous carrier phase; and
α = the filter weighting function equal to the sample interval divided by the time constant of 100 seconds.
3.6.5.2 Corrected pseudo-range. The corrected pseudo-range for a given satellite at time t is:
PRcorrected = PCSC + PRC + RRC × (t – tz-count) + TC + c × (Δtsv)L1
where
PCSC = the smoothed pseudo-range (defined in 3.6.5.1);
RRC = the pseudo-range correction rate (defined in 3.6.4.2);
nt .2);
6.5
3.6.5.3.1 The tropospheric correction for a given satellite is:
φn
φ
PRC = the pseudo-range correction (defined in 3.6.4.2);
t = the current time;
tz-cou = the time of applicability derived from the modified Z-count (defined in 3.6.4
TC = the tropospheric correction (defined in 3.6.5.3); and
c and (Δtsv)L1 are as defined in 3.1.2.2 for GPS satellites.
3. .3 TROPOSPHERIC DELAY
0
6
h / h
r 0 2
i
TC N h 10 (1 e )
0.002 sin (El )
−
= −−Δ
+
Nr = refractivity index from the Type 2 message (3.6.4.3);
Δh = height of the aircraft above the GBAS reference point;
where
APP B-95 23/11/06
Annex 10 — Aeronautical Communications Volume I
23/11/06 APP B-96
Eli = elevation angle of the ith satellite; and
h0 = troposphere scale height from the Type 2 message.
3.6.5.3.2 The residual tropospheric uncertainty is:
0
6
h /h
tropo n 0 2
i
h 10 (1 e )
0.002 sin (El )
−
σ =σ − −Δ
+
where σn = the refractivity uncertainty from the Type 2 message (3.6.4.3).
3.6.5.4 Residual ionospheric uncertainty. The residual ionospheric uncertainty for a given satellite is:
σiono = Fpp × σvert_iono_gradient × (xair + 2 × τ × vair)
where
Fpp = the vertical-to-slant obliquity factor for a given satellite (3.5.5.5.2);
σvert_iono_gradient = (as defined in 3.6.4.3);
xair = the distance (slant range) in metres between current aircraft location and the GBAS reference point
indicated in the Type 2 message;
τ = 100 seconds (time constant used in 3.6.5.1); and
vair = the aircraft horizontal approach velocity (metres per second).
3.6.5.5 PROTECTION LEVELS
3.6.5.5.1 Category I precision approach and APV. The signal-in-space vertical and lateral protection levels (VPL and
LPL) are upper confidence bounds on the error in the position relative to the GBAS reference point defined as:
VPL = MAX{VPLHO,VPLH1}
LPL = MAX{LPLHO,LPLH1}
3.6.5.5.1.1 Normal measurement conditions
3.6.5.5.1.1.1 The vertical protection level (VPLH0) and lateral protection level (LPLH0), assuming that normal
measurement conditions (i.e. no faults) exist in all reference receivers and on all ranging sources, is calculated as:
N
2 2
H0 ffmd i i
i 1
VPL K s_vert
=
= Σ × σ
N
2 2
H0 ffmd i i
i 1
LPL K s_lat
=
= Σ × σ
where
Kffmd = the multiplier derived from the probability of fault-free missed detection;
s_verti = sv,i + sx,i × tan (GPA);
s_lati = sy,i;
Appendix B Annex 10 — Aeronautical Communications
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;
GPA = the glidepath angle for the final approach path (3.6.4.5.1);
N = the number of ranging sources used in the position solution; and
i = the ranging source index for ranging sources used in the position solution.
.1.2 For a general-least-squares position solution, the projection matrix S is defined as:
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