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frame and the intermediate (Earth-fixed) coordinate systems F0
E and F00
E . Notice
that the airplane in the picture is turning to the right after a missed approach; this
position corresponds with positive values of the xf and yf coordinates!
From figure 5.8 it can be seen that the deviation angle #gs can be computed from
the coordinates xf and yf and the height above the runway, Hf , using the following
expressions:
Rgs =
q
(xgs − xf )2 + (yf − ygs)2 (5.11)
#gs = ggs + arctan

Hf
Rgs

(5.12)
The distance from the aircraft to the nominal glideslope is:
dgs = (Rgs tan ggs + Hf ) cos ggs (5.13)
In these expressions #gs and dgs are positive if the aircraft flies above the glideslope
reference line. Notice that ggs is always negative!
5.1. The Instrument Landing System 63
Performance category
of the ILS system
Maximum deviation
from nominal localizer
sensitivity [%]
Maximum deviation of
localizer runway reference
plane from centerline at
runway threshold [m]
I ± 17 ± 10.5
II ± 17 ± 7.5
(± 10 where practicable) (± 4.5 for new installations)
III ± 10 ± 3
Table 5.1: Maximum permissible localizer steady-state errors
Performance category
of the ILS system
Maximum deviation
from nominal glideslope
sensitivity [%]
Maximum deviation from
nominal glideslope
elevation angle [rad]
I ± 25 ± 0.075 ggs
II ± 20 ± 0.075 ggs
III ± 10 ± 0.04 ggs
Table 5.2: Maximum permissible glideslope steady-state errors
In order to be able to verify whether the aircraft flies in the glideslope coverage area
(figure 5.5), we will also calculate the angle Ggs:
Ggs = arcsin

yf − ygs
Rgs

(5.14)
Due to the lateral position of the glideslope antenna this angle is not exactly equal to
Gloc, although the differences are small.
5.1.2 Steady-state ILS offset errors and ILS noise
ICAO has established limits for ILS steady-state offset errors introduced by ground
equipment. For obvious reasons, these limits are most stringent for category III approaches.
Tables 5.1 and 5.2 provide these limits for the localizer and glideslope transmitters,
respectively. The nominal glide path must pass over the runway threshold
at an altitude of 15 ± 3 m.
Due to interference effects caused by buildings, high voltage cables, etc., the actual
ILS signals can become distorted in the spatial and time domains. To an ap64
Chapter 5. Radio-navigation, sensors, actuators
proaching aircraft, these distortions appear as noise in the time-domain, superimposed
on the nominal ILS signals. Based on available experimental data, localizer
and glideslope noise may be approximated by stochastic signals which have rather
simple power spectral density functions.
Refs.[1] and [19] present power spectra for ILS noise, which are expressed in the
same general form as the Dryden model for longitudinal atmospheric turbulence,
see equation (4.11). The power spectral density function for localizer noise can be
approximated by: 1
Sloc(W) = 2sloc
2Lloc
1
1 + (WLloc)2
h
μA2rad−1m
i
(5.15)
where:
sloc = standard deviation of the localizer noise,
Lloc = ‘scale’ of the localizer noise, approximately 130 m
W = spatial frequency [radm−1]
The power spectral density of the glide path noise appears to be similar to the localizer
noise and may be approximated by:
Sgs(W) = 2sgs
2Lgs
1
1 + (WLgs)2
h
μA2rad−1m
i
(5.16)
where:
sgs = standard deviation of the glideslope noise,
Lgs = ‘scale’ of the glideslope noise, approximately 85 m
W = spatial frequency [radm−1]
For atmospheric turbulence it is often assumed that the turbulence velocities are functions
only of the position in the atmosphere (the frozen field concept or Taylor’s hypothesis).
This assumption can be made because aircraft usually fly at large speeds
compared to turbulence velocities.
Using Taylor’s hypothesis for the ILS noise will probably introduce errors, especially
for aircraft with very low final approach speeds such as the Beaver. Still,
this assumption makes it possible to convert the spatial power spectral density functions
to temporal expressions in w, which can be used for practical simulations. One
should remember that the power spectral density functions are in any case approximations
of the actual ILS noise, so if a really accurate representation of ILS noise is
　
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