Filtering Aircraft Surface Trajectories Using Information on the Taxiway Structure of Airports

Abstract

The analysis of aircraft surface trajectories based on open-access Automatic Dependent Surveillance-Broadcast (ADS-B) data is affected by the low quality and resolution of received data. Indeed, the quality of ground ADS-B data is subject to the coverage of the crowdsourced ADS-B receivers. Moreover, the quality of GNSS signals received and processed by aircraft while on ground, which is subject to various sources of interference and reflections of signals, affects the ADS-B data quality. In this study, we present a model to filter ground data and interpolate trajectories along runways, taxiways, aprons, and parking positions, which are also available as public information in OpenStreetMap. The proposed model functions as a Kalman smoother, which takes the distance of the trajectory to the known structure of the taxiway system as a constraint. We validate the efficacy of this model using various trajectories featuring partially missing ADS-B data. Furthermore, we discuss the limitations of the model when confronted with extensive data gaps and open the discussion regarding potential use cases enabled by improved processing of ground trajectory data.

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ICRAT 2024 Nanyang Technological University, Singapore
Filtering Aircraft Surface Trajectories Using
Information on the Taxiway Structure of Airports
Xavier Olive∗, Manuel Waltert†, Ryota Mori‡, Philippe Mouyon∗
∗ONERA – DTIS
Universit´
e de Toulouse
Toulouse, France
†Centre for Aviation,
Zurich University of Applied Sciences,
Winterthur, Switzerland
‡Kobe University
Graduate School of Maritime Sciences
Kobe, Japan
Abstract—The analysis of aircraft surface trajectories based on
open-access Automatic Dependent Surveillance–Broadcast (ADS-B)
data is affected by the low quality and resolution of received data.
Indeed, the quality of ground ADS-B data is subject to the coverage
of the crowdsourced ADS-B receivers. Moreover, the quality of
GNSS signals received and processed by aircraft while on ground,
which is subject to various sources of interference and reflections
of signals, affects the ADS-B data quality. In this study, we present
a model to filter ground data and interpolate trajectories along
runways, taxiways, aprons, and parking positions, which are also
available as public information in OpenStreetMap. The proposed
model functions as a Kalman smoother, which takes the distance
of the trajectory to the known structure of the taxiway system as
a constraint. We validate the efficacy of this model using various
trajectories featuring partially missing ADS-B data. Furthermore,
we discuss the limitations of the model when confronted with
extensive data gaps and open the discussion regarding potential
use cases enabled by improved processing of ground trajectory
data.
Keywords — ADS-B, open data, airports, Kalman smoother
I. INTRODUCTION
An increasing number of studies rely on the availability of aircraft
trajectory data, which describe the course of flights as a function
of time. In the past, such trajectory data was mainly recorded by
primary and secondary radar systems. Today, Automatic Dependent
Surveillance–Broadcast (ADS-B), an air traffic surveillance technology
that relies on aircraft to periodically broadcast their identity, position,
and other relevant information as Mode S extended squitter [1], is
finding increasing use. Networks of crowdsourced, ground-based ADS-
B receivers such as the OpenSky Network [2] collect and archive aircraft
trajectories for use by the scientific community.
As ADS-B information is transmitted on the 1090 MHz frequency,
ground-based receivers require line-of-sight to the transmitter for suc-
cessful data transmission [1]. For airborne transmitters, line-of-sight
conditions often improve with increasing altitude. On the ground,
however, transmitters can be shadowed from potential receivers by
terrain, buildings, or vegetation. In addition, the reception quality of
Global Navigation Satellite System (GNSS) receivers, which are used
by aircraft to determine their position, is often impaired on the ground.
In most cases, the quality and availability of airborne portions of ADS-B
trajectories is considerably better than the ground segment.
In terms of coverage and quality of the surface part of ADS-B tra-
jectories, airports can be divided into different categories, as illustrated
in Figure 1. At airports where numerous ADS-B receivers are installed
directly on the perimeter, as is the case at Stockholm–Arlanda (ESSA),
for example, data quality is exceptional. For aerodromes such as Zurich
Figure 1. Example of different levels of ADS-B coverage at European airports:
(i) exceptional at Stockholm–Arlanda (ESSA) with more than five receivers (green
triangles) located within the airport perimeter; (ii) very good at Zurich (LSZH),
although some areas between the two terminals display more erratic reception,
and (iii) incomplete at Munich (EDDM) and Toulouse (LFBO).
(LSZH), where many receivers are placed in proximity, the data quality is
very good. In contrast, many airports, even major ones, do not show any
ground coverage. At these aerodromes, data quality of surface ADS-
B trajectories can only be improved by installing (more) receivers at
or near the airport. Finally, there are airports where receivers installed
close to the airport may not be able to receive all the ADS-B trajectory
data from aircraft on the ground. In practice, this situation manifests
itself in the fact that trajectory data from aircraft taxiing on the ground
is received at irregular intervals, or cannot be received at all in certain
areas of the airport which are shadowed from the receivers. For instance,
Munich (EDDM) or Toulouse (LFBO) fall into the last category.
At airports with incomplete reception of ADS-B ground tracks, data
quality can of course be improved in the long-run by adding well-
positioned ground-stations to the receiver network. To improve data
quality in the short term, this study investigates whether appropriate
filtering algorithms can be used to estimate missing parts of surface
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ICRAT 2024 Nanyang Technological University, Singapore
aircraft trajectories. Subsequently, the objectives of this study are (i) to
provide a brief literature overview on existing surface trajectory filtering
algorithms, (ii) to develop a Kalman smoother-based surface trajectory
filtering algorithm that uses the distance of observed ADS-B messages
to the known structure of an aerodrome’s taxiway system as a constraint,
and (iii) to validate this algorithm on surface trajectories obtained from
the OpenSky Network.
The remaining sections are structured as follows: Section II provides
an overview of filtering algorithms for surface aircraft trajectories. Next,
a Kalman smoother for ADS-B trajectories is presented in Section III
and validated in Section IV. Finally, Section V introduces a number of
potential use cases showing how the presented Kalman smoother can be
applied in a practical context, while Section VI discusses and concludes
this study.
II. LITERATURE REVIEW
Due to data availability and coverage issues, most aircraft trajectory
filter algorithms presented in the literature focus on the airborne part
of flights. In the following, a brief introduction is given to the rather
limited literature focusing on filters explicitly designed for aircraft
surface trajectories. These contributions make use of Kalman filters,
which are used in practice not only for aircraft surface trajectories, but
also for trajectories of trains [3], vehicles [4], [5], or ships [6].
Pledgie, Atkins, and Brinton [7] introduced a single-mode extended
Kalman filter (EKF) and an interacting multiple model (IMM) tracking
filter for aircraft surface trajectories. The single-mode EKF describes
the state of the aircraft in terms of their position expressed in Cartesian
coordinates (x, y)in north-south and east-west direction, their taxi
speed v, their heading θ, and the derivatives of x, y, v and θwith respect
to time. The EKF considers only one mode, i.e., aircraft taxiing. In
contrast, the proposed IMM estimator considers several states, which
refer to different modes of motion. A Markov process is then used
to describe the transition between the modes, and to determine which
mode has the highest probability. Both the EFK and IMM-based filtering
approaches are applied to trajectories of aircraft taxiing at Dallas-Fort-
Worth Airport, obtained from the Airport Surface Detection Equipment
Model-X (ASDE-X)1system. The results show that in sections of the
filtered trajectories where aircraft are stationary or moving very slowly,
the root-mean-square (RMS) error is 98.9% lower than in the raw
ASDE-X trajectories.
Khadilkar and Balakrishnan [8] presented a multi-modal unscented
Kalman filter (UKF) for aircraft surface trajectories obtained from the
ADSE-X system. On the one hand, this filter allows the estimation of the
state vector ˆxof a taxiing aircraft, which includes the aircraft position
(x, y)in Cartesian coordinates, the taxiing speed v, and the heading
θ. On the other hand, the taxi mode of the aircraft is detected using
a bank of filters. As such, eleven different modes are distinguished,
which differentiate the taxiing behaviour of aircraft in terms of their
taxiing speed, acceleration, and turn rate. For validation purposes,
Khadilkar and Balakrishnan calculated the taxiing distance of a total of
20 flights using both raw ADSE-X trajectories and trajectories filtered
using the proposed method. When compared to the absolute length
of taxiways travelled by the aircraft, the results suggest that taxiing
distances calculated from filtered trajectories are both significantly more
accurate and have lower variance than taxiing distances calculated from
raw trajectories.
1Airport Surface Detection Equipment – Model X (ASDE-X) is a system
operated by the FAA at 35 major US airports. The system tracks aircraft surface
movements by fusing information from surveillance radars, multilateration
sensors, ADS-B, Mode S and flight plan data
Bloem and Churchill [9] extended the works of [7] and [8] by
introducing a two-mode interacting multi-mode unscented Kalman filter
that both considers four aircraft state variables (i.e., x, y, v, and θ)
and makes use of reverse-time Rauch-Tung-Striebel (RTS) smoothing.
One mode of this filter assumes that the aircraft are taxiing at constant
speed vand constant heading θ, while in the other mode the aircraft
are stationary. The filter is then applied to ASDE-X surface trajec-
tories of aircraft taxiing at New York John F. Kennedy Airport and
Charlotte Douglas International Airport. The results presented suggest
that filtered trajectories deviate less from the taxiway centrelines than
raw trajectories, and consecutive data points of filtered trajectories are
more evenly spaced than in the raw trajectories. Also, for parts of the
trajectories where the aircraft is not moving, the root-mean-square error
of the filtered trajectories is significantly lower than that of the unfiltered
trajectories.
The filtering methods presented in the above-mentioned studies
are applied to ASDE-X-derived trajectories with no coverage issue.
However, to the best knowledge of the authors of this study, a Kalman-
based filter for aircraft surface trajectories has never been used for open-
data ADS-B trajectories which are only partially covered. Furthermore,
the filter approaches mentioned in the literature do not explicitly
consider information about the structure and geometry of an airport’s
taxiway system.
III. METHODOLOGY
A. Open data information about airports’ taxiway structure
Official information on the structure of airport infrastructure, e.g.,
dimension and location of runways, taxiways, stands, etc., are in
most countries publicly accessible through national electronic Aero-
nautical Information Publication (eAIP) platforms, primarily in PDF
format. In addition, crowdsourced platforms such as OpenStreetMap
play a significant role in modelling airport infrastructures. As such,
OpenStreetMap uses structured data representations, employing nodes,
ways, and relations associated with metadata information. Specifically,
the ’aeroway’ tag on OpenStreetMap encompasses various elements
of airport infrastructure. While not all airports are fully modelled,
dedicated enthusiasts regularly contribute to refining these models using
satellite imagery and eAIP data.
The cartes library, which is integrated into the traffic pack-
age [10], facilitates the retrieval of OpenStreetMap data through the
Overpass API. The data is downloaded, then transformed into a
GeoDataFrame, where the geometry associated with each element is
represented as a Point,LineString, or Polygon. For this study, our
focus is particularly on essential airport elements for aircraft trajectories,
i.e., runways, taxiways, parking positions, and apron areas, as illustrated
in Figure 2 for the example of Zurich Airport.
B. Overview of ADS-B ground trajectory data
Automatic Dependent Surveillance–Broadcast (ADS-B) is a surveil-
lance system based on the concept of aircraft broadcasting important
parameters twice per second in a Mode S Extended Squitter on the 1090
MHz frequency. In certain geographical regions, ADS-B is mandated for
flights under instrumental flight rules, which is why a large proportion
of all commercial aircraft are equipped with this system.
For aircraft in flight, specific ADS-B messages contain position,
velocity, and identification information. Notably, position and velocity
details are transmitted at different timestamps, leading to a distinctive
treatment of such measurements in Kalman filters. For aircraft on the
ground, which is detected upon ground contact of the nose wheels, the
ADS-B communication protocol shifts to a different type of message.
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ICRAT 2024 Nanyang Technological University, Singapore
runway
taxiway
parking position
apron
Figure 2. OpenStreetMap federates many enthusiast contributors who continu-
ously improve the modelling of the structure of airports. This map of Zurich
Airport (LSZH) depicts a central part of the airport with buildings (black),
runways (blue), taxiways (green), parking positions (orange), and apron areas
(light blue).
Given that altitude information becomes somehow irrelevant, segments
of the 112 bits comprising an ADS-B message are allocated for ground
speed and true track angle information. Furthermore, a marker identifies
invalid values if the aircraft fails to transmit these fields.
Considering the need for proper modelling of measurement uncer-
tainty in the following section, it is to be noted that track angle values
are encoded as multiples of 360
128 = 2.8125 degrees. Ground speed
displays varying precision based on the speed interval, as shown in
Table I. from [1].
TABLE I. SURFAC E PO SIT IO N MOVE ME NT (GR OUN D SP EED )DECODING.
Encoded speed Ground speed range Quantization
0speed not available
1stopped (v <0.125 kt)
2–8 0.125 ≤v<1 kt 0.125 kt steps
9–12 1 kt ≤v<2 kt 0.25 kt steps
13–38 2 kt ≤v<15 kt 0.5 kt steps
39–93 15 kt ≤v<70 kt 1 kt steps
94–108 70 kt ≤v<100 kt 2 kt steps
109–123 100 kt ≤v<175 kt 5 kt steps
124 v ≥175 kt
125–127 reserved
In the following, trajectories consist of sequences of timestamped
information with latitude (in degrees), longitude (in degrees), as well as
potentially missing information on ground speed (in kts) and track angle
(in degrees) information. The standard message rate is approximately
one message per second; however, information gaps may arise in
situations where GNSS signals are affected my multi-path effects or
when ADS-B receiver coverage is incomplete.
C. Formulation of the filter
Kalman filters help to predict the most likely state of a system by using
noisy measurements to improve and update predictions. In this model,
we use a bidirectional Kalman filter approach, known as the two-filter
smoother, which involves computing the geometric mean between both
a forward and a backward pass on the available data.
ADS-B ground messages provide a sequence of four measurements
of the aircraft’s state at each second (with potentially invalid NaN
values): latitude, longitude, ground speed (in kts) and track angle (in
degrees). In order to simplify the model, we convert these measurements
to a four-dimensional state vector X= [x, y, ˙x, ˙y]sequence, in the
International System of Units (SI), by using a conformal projection
allowing the Euclidean distance to remain locally valid.
We consider, and will develop further in Section III-D, the function
φ(x, y)which computes the distance between the point of coordinates
(x, y)and the taxiway system of the airport.
The dynamic of the model remains simple, with no information about
the second derivatives, and with a specific constraint ensuring that the
measurement points remains on an element of the taxiway system. In
the following, we use Xto denote the state vector and Pits associated
covariance matrix. We index the state vectors in time with k, considering
that indices kand k+ 1 are separated in time by ∆t(which was set
to one second in our experiments).
The state-transition matrix Ais defined as
X+=


xk+1
yk+1
˙xk+1
˙yk+1


=


10∆t0
0 1 0 ∆t
0 0 1 0
0 0 0 1



| {z }
A



xk
yk
˙xk
˙yk



| {z }
X
+w. (1)
The process noise wcan be expressed based on random variables
axand ay(afor acceleration) as:
w=









ax
∆t2
2
ay
∆t2
2
ax∆t
ay∆t









(2)
We make two assumptions about the random variables: we consider
that axand ayare independent, and that the expectation values for both
a2
xand a2
yare equal to σ2. Then we can express Q, the process noise
covariance matrix, as follows:
Q=Ew·wt=σ2










∆t4
40∆t3
20
0∆t4
40∆t3
2
∆t3
20 ∆t20
0∆t3
20 ∆t2










(3)
Denoting b
Xthe state estimate and b
Pthe covariance of the state
estimation error at time k, the predicted state and its covariance matrix
at the next timestamp are given by:
b
X+=A·b
X(4)
b
P+=A·b
P·AT+Q(5)
In our model, the constraint stating that the distance of the position
to the taxiway system must be zero, i.e., φ(x, y) = 0, is introduced as a
fictive measurement. Then it appears in the expression of the innovation
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ICRAT 2024 Nanyang Technological University, Singapore
ν, which is the difference between the measurement values and their
predicted values:
ν=





xm−bx+
ym−by+
˙xm−b˙x+
˙ym−b˙y+
0−bφ+






with (0 = φ(x, y)
bφ+=φ(bx+,by+)(6)
The covariance matrix Rassociated to the measurements can be cali-
brated based on the known uncertainties from the ADS-B specifications,
along with a very small residual noise associated to the constraint, as
Kalman filtering machinery requests that Ris non singular:
R=










σ2
xm0 0 0 0
0σ2
ym0 0 0
0 0 σ2
˙xm0 0
000σ2
˙ym0
0000ε2










(7)
Finally, we extend our observation model matrix Hwith estimated
derivatives of the φfunction, whose formulation is detailed in Sec-
tion III-D:
H=





1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
∂+
xbφ ∂+
ybφ0 0






with 






∂+
xbφ=∂ φ
∂x (bx+,by+)
∂+
ybφ=∂ φ
∂y (bx+,by+)
(8)
The remaining equations of the Kalman filter unfold as follows, with
Sthe covariance of the innovation νand Kthe Kalman gain:
S=H·P·HT+R(9)
K=P·HT
·S−1(10)
b
X=b
X++K·ν(11)
b
P= (I−K·H)·b
P+
·(I−K·H)T+K·R·KT(12)
where we use the Joseph’s formula for updating the covariance to avoid
any loss of positivity.
In the following, Section III-D details the implementation of the
distance-to-taxiway function φ(x, y), while Section III-E focuses on
the implementation of the double filtering approach for smoothing.
D. Implementation of the distance-to-taxiway function
Computing the distance from an aircraft’s predicted position to the
taxiway system can be challenging as the geometries are complex,
represented as collections of LineString and Polygon. Moreover, we
need to come with an analytic definition of the distance as the first
derivatives ∂+
xbφand ∂+
ybφare expected in Equation 8 in order to provide
directional information for adjusting the trajectory. To determine the
distance as well as the first derivatives, the following process is applied:
1) First, we identify the most probable segment of the taxiway where
the aircraft should be positioned at a given time: we initially
select the closest segment relative to the measured positions (when
available) and predictions otherwise;
2) Next, we compute the projection of the predicted position onto the
selected segment, determining the closest point on the segment
to the predicted position. In our implementation, we rely on the
shortest line function provided by GeoPandas;
3) With the closest point identified, let say (x, y), we then calculate
the Euclidean distance between the predicted position and the
closest point, denoted as φ:
bφ+=φ(bx+,by+) = p∆x2+ ∆y2(13)
where ∆x=bx+
−xand ∆y=by+
−y.
4) Finally, we compute the analytical definition of the partial deriva-
tives:
∂+
xbφ=∆x
φ(bx+,by+)and ∂+
ybφ=∆y
φ(bx+,by+)(14)
which corresponds to the smallest partial derivatives satisfying the
first order Taylor approximation of φ(x, y)about (bx+,by+),
(∂+
xbφ, ∂+
ybφ) = arg min ∂+
xbφ2+∂+
ybφ2(15)
with φ=bφ++∂+
xbφ∆x+∂+
ybφ∆y(16)
and knowing that φ(x, y) = 0.
Figure 3. Measured (blue), predicted (green), and corrected (orange) states after
a forward pass of the filter. One of the distance-to-taxiway vector is particularly
salient, when the aircraft exits the runway, which is represented with a thick
grey line.
Figure 3 illustrates exemplary the benefits of a properly implemented
distance function. The aircraft is landing on runway 06 at Amsterdam–
Schiphol Airport and turning left on a runway exit. We plotted for
a simple trajectory several tuples of measurement, prediction, and
correction points. The distance vector between prediction and the
runway exit is salient at one timestamp: the prediction tends to favour
the straight line (and move the correction to the runway, making the
filter diverge). The measured ADS-B position is however closer to the
runway exit, and the constraint helps to take the corrected trajectory to
the most plausible path.
E. Formulation for the double filter smoothing
In conventional Kalman filtering, predictions and corrections of states
are made based solely on past information, resulting in estimations
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ICRAT 2024 Nanyang Technological University, Singapore
that are only informed by historical measurement data. As we focus
on post-processing of trajectories, we use smoothers that make use of
future measurements to refine estimations.
The Rauch-Trung-Striebel (RTS) smoother is a notable technique
already used in [7], [8], [9], as it incorporates both forward filtering
and backward passes. During the forward pass, the filter predicts
future states using available measurements and previous estimations.
Subsequently, in the backward pass, the filter refines the estimations by
using the result of the forward pass as measurements.
We use a more simple approach to enhance the precision of esti-
mations by running two separate Kalman filters: a forward pass and a
backward pass. The forward pass yields estimations denoted as b
X1and
b
P1, while the backward pass produces b
X2and b
P2. To combine these
estimations optimally, we compute a weighted average based on the
geometric mean of the estimated covariances.
Since information matrices (i.e., inverse covariances) add, the result-
ing covariance matrix, denoted as b
Ps, is determined by:
b
P−1
s=b
P−1
1+b
P−1
2.(17)
Then, the smoothed estimation of the position b
Xsis computed using
b
Psalong with the weighted sum of the inverse covariances of b
X1and
b
X2via the optimal mixing formula:
b
Xs=b
Ps·b
P−1
1b
X1+b
P−1
2b
X2.(18)
IV. VALIDATION AND LIMITATIONS
In this section, we applied the filter to specific ground trajectories of
flights observed in the year 2023. Our focus was on airports displaying
diverse levels of ground coverage quality within the OpenSky Network
database. Unlike other ADS-B data providers, OpenSky Network allows
research to access raw, unfiltered data.
We anticipate that in regions with near-optimal ground coverage, our
filter implementation will preserve data quality without degradation.
Conversely, in scenarios where data is lacking, we expect the filter to
improve trajectory accuracy compared to simplistic linear interpolation
or spline-based techniques.
Rather than presenting quantitative performance metrics comparing
the filter’s outcomes with ground truth data (that we don’t have) and
linear interpolation results, we opted for a qualitative analysis approach.
We selected situations representing three distinct categories for
evaluation:
1) The filter exhibited expected behaviour, effectively snapping tra-
jectories to an existing taxiway system.
2) While meeting implemented requirements, the filter showed limi-
tations in dealing with relevant anomalies, revealing areas where
further refinement could be necessary.
3) When dealing with sparse or incomplete data, we observed
instances where the filter’s corrective capabilities were limited.
A. Expected behaviour of the filter
Figure 4 presents two trajectories where the filter yields satisfying
results at a resolution of one sample per second. At Zurich Airport (up),
the area of interest is situated between the two terminals, where aircraft,
after landing on runway 14, cross runway 28/10 and head towards the
main terminal. Despite lacking samples in turns, the filter successfully
aligns the trajectory with the existing taxiway. Similar features are
observed at Amsterdam–Schiphol Airport (bottom).
The filter demonstrates particularly favourable results when an ad-
equate number of samples are available to determine the proper next
Figure 4. When data coverage is considered to be good, the filter produces
trajectories matching perfectly the taxiway system of the airport, as is illustrated
for two example trajectories in Zurich Airport (up) and Amsterdam–Schiphol
Airport (bottom).
taxiway segment after each intersection or turn. In the absence of such
samples, the filter defaults to moving in a straight line, as determined
by the prediction step of the filter.
B. Limitations in handling anomalies
Figure 5 brings the focus on the vicinity of apron areas, typically stands
designated for aircraft parking. Thin lines represent lead-in lines for
parking positions as modelled in OpenStreetMap, while shaded areas
are tagged with the apron marker. The filter is configured to minimise
distances to taxiways or to the inner side polygons.
On the upper-hand plot, the trajectory samples suggest that the
position transmitted in the ADS-B messages corresponds to the front
of the aircraft, most likely indicating the trajectory of the front wheel
on the ground. It is possible for pilots to overshoot the parking position
line on the ground to execute a left turn and align with the lead-in
line and/or instructions from the marshaller. However, these detailed
manoeuvres are not apparent in the filtered trajectory.
On the lower-hand side, the turn after the runway exit is smoothed,
but it appears that the pilot is making a short turn into the parking area
that is filtered out, as the filter is designed to match taxiway segments.
However, the final turn appears to be properly filtered.
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ICRAT 2024 Nanyang Technological University, Singapore
Figure 5. In some cases, the structure modelled in OpenStreetMap is not
sufficient to cover the possibilities of aircraft movement, as depicted for a
trajectory observed at Zurich Airport (up) and Amsterdam–Schiphol Airport
(bottom).
C. Challenges with sparse or incomplete data
Figure 6 illustrates scenarios where the filter struggles to reconstruct
a proper trajectory, either laterally (up) or in the speed profile (middle
and speed profile below). Initially, the filter proceeds with a prediction
step based on the previous speed vector value, followed by a correction
step taking measurements into account (when available) and aligning
the trajectory with the most plausible taxiway segment. The covariance-
based average computed during the backward pass of the filter seeks to
select the most plausible alternative.
When an aircraft crosses a taxiway intersection, the filter tends to
favour the option most aligned with the latest corrected value of the
speed vector, rather than necessarily selecting the most probable taxiway
based on the entire set of future measurements. This results in a complex
ground trajectory that attempts to match the most plausible path after
the runway exit when measurements are sparse, but with unsatisfactory
results.
D. Directions for future improvements
We developed a filter aimed at enhancing the quality of ground data
and accurately aligning trajectories with infrastructure information. The
objective of this paper is to demonstrate the relevance of a constraint-
based approach applied to a Kalman smoother. The results indicate
reasonable improvements in trajectory quality, particularly when data
Figure 6. Coverage at Munich Airport is considered more problematic, and the
filter yields unsatisfactory results laterally (up) or on the speed profile (middle
and bottom).
quality is not consistent in all areas of an airport. The filter exhibited
limitations at airports with sparse data or partially obfuscated apron ar-
eas. Nonetheless, we believe that the implemented constraint represents
a promising addition for future enhancements of the filter. Specifically,
our aims for future research include:
•performing a sensitivity analyses on the parameters of the filter,
esp. the covariances of the process and measurement noises;
•creating a graph structure associated with the taxiway system to
reconstruct the most plausible sequence of segments between two
position measurements on the ground, and thereby improve the
definition of φ(x, y);
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ICRAT 2024 Nanyang Technological University, Singapore
Figure 7. The same filter is applied with a different distance function on a
trajectory with partial measurements at Toulouse airport. On the bottom, only
highlighted segments of the taxiway are considered.
•developing an EKF model in (v, θ)in order to better model
the noise on both components. First attempts showed limitations
during push-back phases of the trajectory;
•including the acceleration in the model rather than considering it
as noise, and containing values within a reasonable interval, in
order to address issues illustrate in the speed profile of Figure 6;
•incorporating information about possible speed vectors on each
segment (e.g. allow higher speeds on runways than taxiways);
•integrating historical data information about ground hotspots,
where aircraft frequently stop or line up before crossing a runway,
taking off, or obtaining a free parking position.
This would be particularly beneficial in areas of the airport where
coverage varies across different days;
•assess the impact of the proposed distance-based constraint on a
single-pass version of the filter applied on real-time data.
Figure 7 investigates potential enhancements achievable through a
refined distance-to-taxiway function. We apply the same filter (only the
forward pass) to partial trajectory measurements at Toulouse Airport.
In an effort to assess improvements in the graph-based approach, we
narrow the focus of the distance function to a manually selected subset
of potential taxiway segments.
On the upper-hand side, where all taxiways are considered, the filter
propagates the predicted speed vector near the airport terminal and
continues straight in the absence of relevant measurements. This leads
to a deviation from the intended path, as the aircraft fails to make a
left turn towards the runway threshold.
Conversely, on the lower-hand side, the faulty taxiway segment is
excluded as a potential alternative. Although it requires one iteration
to align the trajectory with the correct taxiway, as the aircraft initially
makes a 90° turn to the left instead of selecting the designated turning
area, ultimately the trajectory matches the intended taxiway path.
V. POTE NT IA L US E CA SE S
The filter introduced in this study aims to address a quality gap in
ground trajectories as they are available in crowdsourced databases,
such as the OpenSky Network, during data preprocessing for more
advanced studies. The filter successfully smoothens ADS-B ground
tracks at well-covered airports, and to a certain extent, fills gaps in
ground trajectories at less optimally covered airports. We demonstrated
that this constraint-based filter has the potential for further improvement
before integration into more in-depth analyses across various domains.
Below is a non-exhaustive overview of potential future use cases around
airport operations, airport capacity, and airport planning.
To facilitate more informed decision-making, trajectories processed
with such a filter can be used to investigate operational aspects of an
airport. For example, we can analyse how arriving and departing aircraft
use of the taxiway system and how efficiently aircraft are routed on
the ground. This is also known in the literature as the airport taxiway
scheduling problem [11], [12]. In this context, well-filtered trajectories
can improve systematic analyses of ground movements at airports in
order to (i) estimate the frequency and types of aircraft using taxiways,
which might contribute to the topic of preventive maintenance [13],
(ii) detect potential interaction and conflicts between aircraft, and (iii)
evaluate how aircraft are managed by ground air traffic control. Such
analyses can be performed for periods at which aerodromes are operated
both normally and irregularly, e.g., when certain taxiway segments
are unavailable due to maintenance reasons. Besides, by clustering
and characterising filtered ground trajectories [14], [15], [16], the
operational performance of an aerodrome or parts of an airport can be
evaluated and benchmarked. To this end, researchers determine average
ground times of aircraft operating at an aerodrome, measure the time
it takes departing aircraft from push-back to lift-off or arriving aircraft
from touch-down to in-block, or detect whether queues of departing
aircraft have been formed at runway holding points.
Another important field of application for smoothed ground trajec-
tories is the analysis of the capacity of an airport’s runway system
and/or taxiway system. The runway capacity of an airport depends on
a variety of factors, such as arrival and departure times, aircraft types,
runway occupancy times, separation requirements, potential conflicts
with other aircraft or ground vehicles, runway occupancy times, runway
departure speeds, or the utilisation of rapid exit taxiways. Data on
these factors can be obtained more efficiently on the basis of more
precise surface trajectories, e.g., in connection with trajectory prediction
models [17] which also account for uncertainty. Subsequently, models
used to determine capacity envelopes for airports on the basis of ADS-
B data [18] might benefit from the filter presented in this study. To
determine the capacity of the taxiway system, one must identify its
weakest element, i.e., the component of the system with the lowest
throughput. Consequently, on the basis of higher quality ground tra-
jectories of aircraft, one could identify such bottlenecks or determine
how disturbances, e.g., construction or winter operations, affect taxiway
capacity.
Finally, filtered ground trajectories of aircraft might also be of good
use in the domain of airport planning. For instance, the optimal design
of taxiway systems for aircraft, known as the airport taxiway planning
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ICRAT 2024 Nanyang Technological University, Singapore
problem [19], could benefit from more accurate surface trajectories.
Furthermore, smoothed surface trajectories could also be used for the
evaluation and planning of new airport equipment, as is the case with
the electrification of taxi operations [20].
VI. CONCLUSION
This study introduced a Kalman smoother specifically tailored for
surface ADS-B trajectories of aircraft, incorporating a constraint based
on the distance to the runway and taxiway structure. Given the
limited coverage of ADS-B receivers at most airports, resulting in
constrained quality and availability of aircraft surface trajectory data,
this filter holds significant utility and enables the estimation of aircraft
taxiing movements based on incomplete ADS-B surface trajectories.
Our findings suggest that the constraint integrated into the presented
filter effectively reconstructs missing surface trajectory data in many
scenarios. However, we observed instances where the generated sur-
face trajectories exhibited lower quality under certain conditions: (i)
inaccuracies or incompleteness in the information regarding taxiway
and runway structure obtained from OpenStreetMap, (ii) intentional
deviations from taxiway centrelines by pilots, such as when taxiing
into a stand, and (iii) situations where substantial unknown behaviour
persists; the filter excels in smoothing trajectories rather than making
decisions between options (e.g., selecting a taxiway or a holding
position to stop). We anticipate that integrating this constraint into
more sophisticated models capable of addressing these challenges will
significantly enhance their efficacy.
ACK NOW LE DG EM EN T
The authors are grateful to the EC for supporting the present work,
performed within the NEEDED project, funded by the European
Union’s Horizon Europe research and innovation programme under
grant agreement no. 101095754 (NEEDED). This publication solely
reflects the authors’ view and neither the European Union, nor the
funding Agency can be held responsible for the information it contains.
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