Harmonisation between calculated value of the ILS Reference Datum
Height and Flight Inspection results
Ivan Ferencz, Head of NAVAIDS division of the Civil Aviation Authority of the Slovak Republic,
M. R. Stefanik Airport, 82305 Bratislava, Slovak Republic
Tel: +421 2 4342 4091, fax: +421 2 4342 4503, ferencz@caa.sk
Abstract
Instrument Landing System Reference
Datum Height (RDH) is one of the most
discussed issue of these days. This Paper
describes sources of differences between
RDH calculation and measurement.
It is usually highly qualified staff, who are
involved into process of the design and
optimising of the Glide Slope Mast position.
However, sometimes flight inspection finds
unacceptable
disagreement
between
expected and measured values of RDH. In
addition to, measured values of RDH vary
too much [6], assuming that RDH is one of
the AIP-published ILS parameters. This is
almost true for modern three-dimensional
methods of computation of the RDH.
In this article it is shown, that RDH
measurement could be improved, when more
complex reference figures of the glide path
are used as an additional parameters –
forward and side slopes of the terrain - will
be accommodated directly into flight
inspection system software. It is shown, that
the uncertainty of the RDH flight inspection
results is quite normal and can be expected.
The method, how to pass over this
uncertainty is proposed.
“a point at a specified height located above
the intersection of the runway centre line and
the threshold and through which the
downward extended straight portion of the
ILS glide path passes“ exists there much
longer.
So, why has the problem come out now?
The definition mentioned above requires the
view to the glide path from the air down to
the ground. It is, of course, not possible
without position fixing equipment with
three-dimensional (x, y, z) capability.
By using of former position reference
systems, as were theodolites or infrared
trackers, it was only possible to track an
aircraft relative to the head of the theodolite
or the infrared tracker. So the view at the
aircraft was from the point fixed at the
ground to the air. Taking into account
guidance for positioning of the tracker stated
in former version of the ICAO Doc 8071 [2]
(7.4.3.1. ideally the tracker should be sited at
the theoretical point of origin of the ILS
signals) relative to the Glide Path antenna
and not relative to the RWY threshold, it is
easy to suppose, that some GP antenna
location failures remain hidden for a long
time, probably up to now.
Glide Path reference figures
Introduction
Looking backward, discussions on RDH
have begun only a few years ago. The
definition of the ILS reference datum listed
in the ICAO ANNEX 10 [1] given as
In the process of glide path analysis, the
used reference figure has significant
influence on obtained results. The GP Error
curve can be described as
(or vice versa) where
ERR = deviation of DDM=0 from the
nominal DDM=0 surface;
EXP = expected GP deviation at aircraft
position;
DEV = GP deviation reading at aircraft
position.
Obviously, while GP deviation reading is
derived from output of the navigation
receiver, expected GP deviation depends on
applied reference figures of the glide path.
Aiming Point reference
The aiming point reference means that the
origin of the reference figure lies close to the
intersection of the nominal glide path with
the concrete of the runway. Height of the
aiming point can be height of the runway
threshold or foot of the glide path antenna,
or this height can be a result of GP structure
analysis. Coordinates of this point in the
Cartesian Threshold Coordinate System are
[XGP, 0, ZGP]. Expected glide path at vertical
plane contained RWY centreline is
represented as a straight line.
Aiming point reference matches well
ANNEX 10 [1], where an ideal glide path is
considered as a plane (Plane of the nominal
ILS glide path = Plane perpendicular to the
vertical plane of the runway centre line
extended and containing the nominal ILS
glide path).
Some flight inspection systems construe
aiming point reference as a cone, in this case
0 A surface is
z 0  TAN ( )  ( x  XGP) 2  y 2  ZGP (2.)
where
 is promulgated GP angle;
or as a plane with 0A surface
z 0  tan( )  ( x  XGP)  ZGP (3.)
Expected GP deviation is deviation of the
aircraft at certain point in space from
reference 0A surface converted to intended
unit, i.e. A. For the case of conic surface is
expected deviation


z  z0
EXP  DS   ATAN
 (4.)
( x  XGP) 2  y 2 

Where
DS = displacement sensitivity in A per
degree.
Typical feature of the aiming point reference
is hyperbolically curved GP error curve.
GP Error [uA]
ERR ( x)  EXP( x, y, z )  DEV ( x, y, z ) (1.)
75
60
45
30
15
0
-15
-30
-45
-60
-75
1
2
3
4
5
6
7
8
9
10
Distance from threshold [km]
Picture 1 Aiming point reference GP Error curve no slope of the terrain
This is in accordance with expectations,
because real 0A glide path surface is the
conical surface and an intersection of this
cone and vertical plane contained runway
centreline forms such curve.
When the side slope of the terrain exists,
hyperbolical nature of the GP error curve
may be accentuated or suppressed.
GP Error [uA]
75
60
45
30
15
0
-15
-30
-45
-60
-75
1
2
3
4
5
6
7
8
9
10
Distance from threshold [km]
GP Error [uA]
GP Error [uA]
1
2
3
4
5
6
7
8
9
10
Distance from threshold [km]
Picture 3 Aiming point reference GP Error curve negative side slope of the terrain (-0.5)
Disadvantages of the aiming point reference
are:
-
Due to curved GP error it is not easy to
evaluate the amplitude of GP errors
passing ILS “B” point (scaling problem).
-
Displacement sensitivity of the reference
drift away from displacement sensitivity
of the facility approaching the runway
threshold due to increasing of the
difference between aircraft-aiming point
and aircraft-GP antenna distance. This
can lead to distinctions in ARDH results
and imprecise structure results passing
ILS “B” point – details are given in table
1 and picture 4.
Flight inspection systems based on the
aiming point reference are capable of direct
measuring of the RDH, which is the main
advantage of this reference figure.
2.28 °
2.64 °
3.00 °
3.36 °
3.72 °
0.1
2.0
9.9
37.6
3.00
15.2
15.6
0.1
2.3
11.5
43.6
3.00
15.2
15.7
0.1
2.6
13.0
49.5
3.00
15.2
15.8
0.1
2.9
14.6
55.5
3.00
15.3
15.9
0.1
3.2
16.1
61.4
3.00
15.3
16.0
Table 1 Influence of the tracking angle on GP
error, Aiming point reference ( YGP=122m)
Picture 2 Aiming point reference GP Error curve positive side slope of the terrain (0.5)
75
60
45
30
15
0
-15
-30
-45
-60
-75
Tracking
angle
ILS Point
A
B
C
T
Angle
TCH
ATCH
75
60
45
30
15
0
-15
-30
-45
-60
-75
Track 3.00°
Track 2.28°
Track 3.72°
1
2
Distance from threshold [km]
Picture 4 Drift of the reference displacement
sensitivity demonstrated at three different tracks
GP origin reference
The GP origin reference means that the
origin of the reference figure lies close to the
foot of the GP antenna. Coordinates of
reference point in the Cartesian Threshold
coordinate system are [XGP, YGP, ZGP].
Nominal glide path at vertical plane
contained RWY centreline is represented as
a hyperbola.
GP origin reference does not match ANNEX
10 [1] definition of nominal glide path; on
the other hand, well conform to
characteristics greater part of the GP
facilities.
Touched flight inspection systems interpret
GP origin reference as a cone with the 0A
surface:
z 0  ZGP  tan( )  ( x  XGP) 2  ( y  YGP) 2
GP Error [uA]
(5.)
and


z  z0
EXP  DS   ATAN
 (6.)

( x  XGP) 2  ( y  YGP) 2 
GP Error [uA]
Nominal GP error curve for this reference is
a base line, which is comfort for evaluation
of the amplitude of GP errors (course
structure) over all zones.
75
60
45
30
15
0
-15
-30
-45
-60
-75
2
3
4
5
6
7
8
9
10
Distance from threshold [km]
Glidepathoid – the model of the
glide path
1
2
3
4
5
6
7
8
9
10
Distance from threshold [km]
When a side slope of the terrain exists, this
will be reflected in nominal GP error curve
form as reflected at picture 6 and 7.
GP Error [uA]
1
Picture 7 GP origin reference GP Error curve negative side slope of the terrain (-0.5)
Picture 5 GP origin reference GP Error „curve” no slope of the terrain
75
60
45
30
15
0
-15
-30
-45
-60
-75
75
60
45
30
15
0
-15
-30
-45
-60
-75
1
2
3
4
5
6
7
8
9
Therefore, implementing their methods into
flight inspection systems software can
improve flight inspection itself. It should
help to find an answer at question, whether
the GP system goes such way, as it was
designed.
10
Distance from threshold [km]
Picture 6 GP origin reference GP Error curve positive side slope of the terrain (0.5)
Flight inspection systems based on GP origin
reference are not capable of direct measuring
of the RDH.
Obviously, both of reference figures
mentioned above are not capable to cover
such installations, where terrain is not
perfectly horizontal. Often, ILS suppliers
must accept some slopes of the terrain within
the area preceding glide path antenna – as
the forward slope as well as the side slope.
People designing layout of such installations
really take these slopes into account.
Proposed reference figure fit real glide path
installations, because it is possible to adapt
the reference figure to conditions at GP
antenna site. The used word “Glidepathoid”
means the mathematical description of the
ILS glide path in space.
A formula (simplified) to describe surface
where 0A GP deviation can be expected, is:
z 0  ( x  XGP) 2  ( y  YGP) 2  tan( )
 ( x  XGP)  tan( )
 ( y  YGP)  tan(  )  ZGP
(7.)
where
 = Electric angle of the glide path relative
to the reflection plane in degrees, normally
used for GP antenna elements height
calculation
 = Forward slope of terrain in degrees,
positive when terrain climb to threshold
 = Side slope of the terrain in degrees,
positive when the terrain climb to runway
Note. Formulas use simplification
TAN (+)=TAN ()+TAN () and
allowed lateral deviations (y) are
within  YGP
Expected GP deviation are calculated as
deviation from this surface:


z  z0
EXP  DS   ATAN
 (8.)

( x  XGP) 2  ( y  YGP) 2 
The nominal GP error curve for this
reference is a 0A base line regardless of the
slope of terrain, when all parameters are
correct.
So, the error curve can be preliminary based
on GP antenna site evaluation and finally it
will be a result of post processing of GP
deviations measured along flight path at
points determined by x, y, z values, the task
of which is to adjust GP parameters , , ,
XGP, YGP, ZGP and DS to obtain the best GP
error distribution. Any deviation from 0A
remaining after this post processing is
considered as a course structure.
So the error curve can be preliminary based
on GP antenna site evaluation and finally
this curve will be a result of post processing
of GP deviations measured along flight path
at points determined with x, y, z values.
Objective if this post processing is to adjust
GP parameters , , , XGP, YGP, ZGP and DS
to obtain the best GP errors distribution. Any
remaining deviation from 0A is considered
as a course structure.
Glide Path analysis
Glide Path Parameters
Data required to glide path analysis are:
a)
Preliminary values of:
- Glide path origin position, i.e. XGP, YGP,
ZGP
- Glide path technical data, i.e. electric
angle () and displacement sensitivity
(DS)
- Terrain data, i.e. forward slope () and
side slopes () of terrain
b)
Series of flight data:
- Aircraft glide path antenna positions, i.e.
x, y, z
- Measured glide path deviation values,
i.e. DEV
For each horizontal position of the aircraft
(x, y) is calculated the height of 0A
surface, i.e. z0 (x, y) using formula (7) and
expected GP deviation (EXP) using formula
(8) respectively.
From these data are
calculated glide path errors using formula
(1).
As a next step, an iterative solution is
required to find the best distribution of glide
path errors. Although any parameter can be
iteratively solved, it is recommended to find
the glide path origin position by method of
geodesic survey first, to eliminate number of
variables during iteration process. Further, it
is recommended to obtain data from flights
below and above glide path to get correct
value of displacement sensitivity. So,
maximum of variables to be solved during
When all GP parameters, i.e. , , , XGP,
YGP, ZGP, DS and course structure are
recognized, it is known, how the glide path
looks like. What is not known is how such
glide path serves to aircraft operation.
GP Angle and Reference Datum Height
From pilot’s point of view, slopes of terrain
or GP antenna position are not parameters.
Only a GP angle and RDH are published and
operationally significant data. Pilots expect,
that an electronic glide path will guide them
to a point, from which the landing can be
safely completed.
Therefore, our interest is pointed up to glide
path along localiser (runway) centreline.
Sources of the RDH uncertainty
Position fixing error
RDH, as the result of GP analysing can be
affected by the position fixing inaccuracy.
Depending on the basis of used system, there
can be an angular or an absolute (x, y, z)
error or a combination of thereof.
An absolute inaccuracy of “z” data directly
affects RDH by degree of error of measured
“z” values. Measured GP angle remains
correct. This is possible for GNSS or INS –
based position fixing systems. Roots of such
error can be, for example, improper
correction between the onboard GP antenna
position and GNSS antenna or INS centre.
80
GP Error [uA]
iteration process should be an electric angle
of the glide path, terrain slopes, height of GP
origin and displacement sensitivity (, , ,
ZGP and DS).
z error +1m
z error +2m
z error -1m
z error -2m
50
20
-10
1
2
3
4
5
6
7
8
9
10
Distance from threshold [km]
To find the value of descent angle and
threshold crossing height, it is necessary to
make a cut of the z0 surface, which is a result
of GP analysing, by the vertical plane
contained localiser (runway) centreline.
Result of such section will be a curve
described with the formula:
Picture 8 Influence of "z" inaccuracy on GP Error
curve
z 0( x)  ( x  XGP)  (YGP)  tan( )
An angular inaccuracy primary affects the
measured angle and consequently the RDH.
2
2
 ( x  XGP)  tan(  )
(9.)
 (YGP)  tan(  )  ZGP
Then applying of linear regression at the
resulting curve between points A and B will
result to GP angle and RDH and doing the
same between points 1800m and 300m from
the runway threshold will result to ARDH
value. One of these values can be published
as the RDH.
-40
-70
-100
Angular error -0.04 ° -0.02 ° 0.00 °
Angle
RDH
ARDH
2.96
15.0
15.6
2.98
15.1
15.7
3.00
15.2
15.8
0.02 °
0.04 °
3.02
15.3
16.0
3.04
15.4
16.1
Table 2 Influence of angular inaccuracy on GP
parameters
While the measured GP angle well
corresponds to angular error of position
fixing system, measured RDH is not so
much affected by this kind of inaccuracy.
Receiver centring error
Receiver centring error has a similar
consequence as angular error of position
fixing equipment.
Receiver centring
-4.0 µA
error
Angle
2.98
RDH
15.1
ARDH
15.8
-2.0 µA
0.0 µA
2.0 µA
4.0 µA
2.99
15.2
15.8
3.00
15.2
15.8
3.01
15.3
15.9
3.02
15.3
16.0
Table 3 Influence of receiver centring error on GP
parameters
Flight technical error
One of features of glidepathoid is, that flight
calibration flight profiles are not so
demanding on flight technical tolerances.
Prerequisite of good repetition of results is
using of the correct value of the
displacement
sensitivity
used
by
glidepathoid.
In Table 4 are tabulated GP parameters for
flight with flight technical tolerances 2/3 
[4], when displacement sensitivity of the
facility differs from displacement sensitivity
of the glidepathoid.
Displacement
sensitivity error
Min Angle
Max Angle
Min RDH
Max RDH
Min ARDH
Max ARDH
0%
1%
2%
3%
4%
3.00
3.00
15.2
15.2
15.8
15.8
3.00
3.00
15.1
15.3
15.8
15.9
2.99
3.00
15.0
15.5
15.8
16.0
2.99
3.00
14.8
15.5
15.8
16.0
2.99
3.01
14.7
15.7
15.8
16.0
Table 4 Influence of displacement sensitivity error
for flight within 2/3 standard deviations of the
FTT
Reflecting objects
Real environment, into which the glide path
antenna is installed, is the most significant
contributor of the RDH uncertainty [5].
A degree of the RDH uncertainty depends on
the location of reflecting objects relative to
the GP antenna, beam bend potential at
object location, orientation, size and
reflecting factor of objects, speed of the
aircraft, used receivers and even on antenna
pattern of onboard GP antenna.
Due to wavelength of GP signal (1m), only
a small deviation from nominal track can
move bends formed by reflecting object
along “x” axe and change or even invert
their amplitude. Threshold crossing height
(TCH) calculated from real zDEV=0 (x) curve
differs from flight to flight often up to such
degree, that TCH results look totally
distrustfully.
GP Error [uA]
It is necessary to highlight extreme
importance of precise determination of
onboard GP antenna along measured flight
path.
75
60
45
CS0Error GS
DS1ErrorGS
DS9ErrorGS
30
15
0
-15
1
2
3
4
5
6
7
8
9
10
Distance from threshold [km]
-30
-45
-60
-75
Picture 9 Simulation of GP error curve derived
from flight at, below and above nominal GP
The obstacle simulated at picture 9 generates
quite “good looking” course structure.
Nevertheless, while a change in measured
angle is within 0.02, excursion in TCH
value is 0.5m from nominal value.
Fligt profile
Angle
TCH
ATCH
Nominal
value
2.99
16.2
16.5
-75.0 µA
0.0 µA
75.0 µA
2.98
15.7
16.3
3.00
16.2
16.5
2.98
16.0
16.5
Table 5 Change in GP parameters for flight at,
below and above nominal GP – calculated from
zDEV=0 (x) curves
Application of the method described above
helps to get tighter results, as is readable
from table 6.
Angle
RDH
ARDH
-75.0 µA
0.0 µA
75.0 µA
2.99
16.3
16.6
2.98
16.3
16.6
2.99
16.2
16.5
error curves for the Glidepathoid reference
are at picture 11.
Table 6 Glidepathoid parameters calculated for
simulated flight
Example
ILS GP parameters are:  = 3.00, XGP=293.5m,
YGP=-120.0m,
ZGP=+0.51m,
DS=208.3A/,  and  are unknown.
GP Error [uA]
Nominal
value
2.99
16.2
16.5
Fligt profile
75
CS0Error GS
DS1Error GS
CS tolerances
60
45
DS9Error GS
CS tolerances
30
15
0
-15
1
2
3
4
5
6
7
8
9
10
-30
-45
Distance from threshold [km]
-60
-75
75
CS0Error AP
DS9Error AP
DS1Error AP
60
45
Picture 12 Real results - After data processing
GP Error [uA]
30
15
0
-15
1
2
3
4
-30
5
6
7
8
9
10
Distance from threshold [km]
-45
-60
-75
GP Error [uA]
Picture 10 Real results - Aiming point reference
75
CS0Error GS
DS1Error GS
CS tolerances
60
45
DS9Error GS
CS tolerances
30
15
0
-15
1
2
3
4
5
6
7
8
9
10
-30
-45
Distance from threshold [km]
-60
-75
Picture 11 Real results - Glidepathoid reference
before data processing
GP error curves as measured with aiming
point reference are at picture 10. Initial GP
Parameters of the Glidepathoid after data
processing are: =2.93, +0.08, =-0.43,
ZGP remains 0.51m. Resulting GP angle  is
3.00, RDH=15.2m and ARDH=15.5m.
Obviously, course structure data are more
suitable for obstacle situation analysis.
Regulatory aspects
a) Course structure
The application of the course structure
tolerances is explained in the ANNEX 10/I,
3.1.5.4: “…bends in the glide path shall not
have amplitudes which exceed the
following…”. It means, that course structure
is determined exclusively by bends only.
The course structure is calculated
symmetrically from zero GP error line after
post processing and tolerance lines have no
steps. It is not fully in accordance with the
Note 1 as given in ANNEX 10/I 3.1.5.4
because bend amplitudes are not realised on
the mean ILS glide path, but it is in harmony
with basic idea of the Standard, i.e. to
consider a course structure to be a bend.
b) Glide path angle
Calculated glide path angle complies fully
with the ANNEX 10/I from straight line
which represents mean ILS glide path. This
straight line is calculated direct from the
model of the ILS glide path ignoring
influence of the course structure.
specified by ground engineers is the result of
analysis of the terrain and height difference
between the runway threshold and the foot
of the GP antenna. Hence, ILS GP
installation is well described by the same
parameters, which were used in proposed
model of the glide path.
c) Reference Datum Height
The reference datum height is another
parameter of the straight line above. The
achieved reference datum is calculated
similar. Deviations accounted into course
structure are again not taken into RDH and
ARDH calculation. These deviations can be
accounted into TCH and ATCH calculation,
which ones then represent threshold crossing
height of each individual flight profile.
Applying of the glidepathoid on board or in
post flight GP evaluation, it is possible to
verify, whether ground engineer has done
good job or not.
It is the only way to improve uncertainty of
results. Assuming, the RDH is AIP –
published parameter, it is mandatory to
achieve better uncertainty as is allowed by
current ICAO Doc 8071 (0.6m). Otherwise,
our flight inspection results look to be not
reliable.
The other question is, how serious parameter
the RDH is. When RDH is less than 15m,
there is a risk, that an aircraft hits the ground
in front of the runway concrete. (It looks
serious.) When RDH is higher than 18m, it
represents a risk, that an aircraft can lose the
visual contact with aeronautical lights during
an approach. (It is not so demonstrable.) It
means that lower of RDH and ARDH should
be published as RDH in AIP.
On the other hand, the RDH was more less
results
of
calculation
rather
than
measurement for many years.
Conclusion
The reference datum height depends on GP
antenna position. GP antenna position
References
[1] ICAO ANNEX 10 - Aeronautical
Telecommunications, Volume I - Radio
Navigation Aids, Fifth edition, 1996
[2] ICAO Doc 8071 - Manual on testing of
Radio Navigation Aids, Volume II - ILS,
Third edition, 1972
[3] ICAO Doc 8071 - Manual on testing of
Radio Navigation Aids, Volume I – Testing
of Ground Based Radio Navigation Systems,
Fourth edition, 2000
[4] ICAO Doc 9274 – Manual on the Use of
the Collision Risk Model (CRM) for ILS
Operations, First edition, 1980
[5] Gerhard GREVING, L.Nelson
SPOHNHEIMER - Problems and Solutions
for ILS Category III Airborne and Ground
Measurement, 11th IFIS, Santiago, Chile,
2000
[6] Uwe BUCHHEIM – Methods of
Computing Glidepath Characteristics in
Modern Flight Inspection Systems, 11th IFIS,
Santiago, Chile, 2000