The International
Federation
of Congress
Automatic Control
Proceedings
of
20th
Proceedings
of the
the
20th World
World
The
International
Federation
of Congress
Automatic Control
Toulouse,
France,
July
9-14,
2017
The
International
Federation
of
Proceedings
of
the
20th
World
Congress
The International
of Automatic
Automatic Control
Control
Toulouse,
France,Federation
July 9-14, 2017
Available
online at www.sciencedirect.com
Toulouse,
France,
July
9-14,
2017
The International
of Automatic
Control
Toulouse,
France,Federation
July 9-14, 2017
Toulouse, France, July 9-14, 2017
ScienceDirect
IFAC PapersOnLine
50-1 (2017) 15627–15632
Improved
Trajectory
Prediction
and
Improved
Trajectory
Prediction
and
Improved
Trajectory
Prediction
and
Improved
Trajectory
Prediction
and
Simplification
Analysis
for
ATM
System
Improved
Trajectory
Prediction
and
Simplification
Analysis
for
ATM
System
Simplification
Analysis
for
ATM
System
Simplification
Analysis
for
ATM
System
Modernization
Simplification
Analysis for ATM
System
Modernization
Modernization
Modernization
Modernization
∗
∗
∗
Eric Conrado de Souza
∗ Caio Cesar Fattori ∗ Suely Silva ∗
Eric
Conrado de
Souza ∗∗ Caio
Cesar Fattori
∗ Suely Silva ∗
Eric
Eric Conrado
Conrado de
de Souza
Souza ∗ Caio
Caio Cesar
Cesar Fattori
Fattori ∗∗ Suely
Suely Silva
Silva ∗∗
de
Souza
Caio
Cesar
Fattori
Silva
em Tecnologias S/A, Rua do Rócio Suely
313, 4th
floor,
em
Tecnologias
S/A,
Rua
do
Rócio
313,
4th
floor,
Atech
Negócios
em
Tecnologias
S/A,
Rua
do
Rócio
313,
4th
floor,
São
Paulo/SP,
Brazil
(e-mail:
ecsouza@atech.com.br;
Atech
Negócios
em
Tecnologias
S/A,
Rua
do
Rócio
313,
4th
floor,
São
Paulo/SP,
Brazil
(e-mail:
ecsouza@atech.com.br;
∗
Atech São
Negócios
em
Tecnologias
S/A,
Rua
do
Rócio
313,
4th
floor,
Paulo/SP,
Brazil
(e-mail:
ecsouza@atech.com.br;
cfattori@atech.com.br;
ssilva@atech.com.br).
São cfattori@atech.com.br;
Paulo/SP, Brazil (e-mail:
ecsouza@atech.com.br;
ssilva@atech.com.br).
São cfattori@atech.com.br;
Paulo/SP,
Brazil
(e-mail:
ecsouza@atech.com.br;
ssilva@atech.com.br).
cfattori@atech.com.br; ssilva@atech.com.br).
cfattori@atech.com.br; ssilva@atech.com.br).
Abstract: Flight trajectory prediction is improved by additional modeling of flight dynamics,
Abstract:
Flight
trajectory
prediction
is
improved
by additional
modeling
of flight
flight dynamics,
Abstract:
trajectory
improved
by
of
allowing theFlight
aircraft
model toprediction
cope with is
input
saturation
caused bymodeling
poor flight
modeling.
Abstract:
Flight
trajectory
prediction
is
improved
by additional
additional
modeling
of intent
flight dynamics,
dynamics,
allowing
the
aircraft
model
to
cope
with
input
saturation
caused
by
poor
flight
intent
modeling.
Abstract:
Flight
trajectory
prediction
is
improved
by
additional
modeling
of
flight
dynamics,
allowing
the
aircraft
model
to cope
cope with
with
input saturation
saturation
causeddata.
by poor
poor
flight intent
intent
modeling.
Accuracythe
of aircraft
prediction
evaluation
is addressed
with flight
Trajectory
simplification
allowing
model
to
input
caused
by
flight
modeling.
Accuracy
of aircraft
prediction
evaluation
isand
addressed
with flight
flight
data.
Trajectory
simplification
allowing
the
model
to
cope
with
input
saturation
caused
by
poor
flight
intent
modeling.
Accuracy
of
prediction
evaluation
is
addressed
with
data.
Trajectory
simplification
methods
are
additionally
considered
a
novel
technique
is
proposed
and
implemented
for
Accuracy
of additionally
prediction evaluation
isand
addressed
with flightis data.
Trajectory
simplification
methods
are
considered
aa novel
technique
proposed
and
implemented
for
Accuracy
of
prediction
evaluation
is
addressed
with
flight
data.
Trajectory
simplification
methods
are
additionally
considered
and
novel
technique
is
proposed
and
implemented
numerical
investigations,
yelding
satisfactory
results.
methods
are
additionally yelding
considered
and a novel
technique is proposed and implemented for
for
numerical
investigations,
satisfactory
results.
methods
are
additionally yelding
considered
and a novel
technique is proposed and implemented for
numerical
investigations,
satisfactory
results.
numerical
investigations,
yelding
satisfactory
results.
©
2017, IFAC (International yelding
Federation of Automatic
Control) Hosting by Elsevier Ltd. All rights reserved.
numerical
Keywords: investigations,
Aerospace trajectories,satisfactory
Prediction results.
problems, Data reduction, Aerospace control,
Keywords:
Aerospace
trajectories,
Prediction
problems,
Data reduction,
Aerospace
control,
Keywords:
Aerospace trajectories,
reduction, Aerospace
Aerospace control,
control,
Process Automation.
Keywords:
Aerospace
trajectories, Prediction
Prediction problems,
problems, Data
Data reduction,
Process
Automation.
Keywords:
Aerospace
trajectories,
Prediction
problems,
Data
reduction,
Aerospace
control,
Process
Automation.
Process Automation.
Process
1. Automation.
INTRODUCTION
and Management operations and represents the core asset
1. INTRODUCTION
and
Management
operations
and
represents
the
core
asset
1.
and
Management
operations
and
represents
the
asset
of
many
control and
planning
services
in these
1. INTRODUCTION
INTRODUCTION
and
Management
operations
andsystem
represents
the core
core
asset
of
many
control
and
planning
system
services
in
these
1. INTRODUCTION
and
Management
operations
represents
the core
asset
many
control
and
planning
system
services
in
these
modernization
programs.
It isand
claimed
that
advanced
DeThere is widespread
consensus, for some time now, that of
of
many
control
and
planning
system
services
in
these
modernization
programs.
It
is
claimed
that
advanced
DeThere
is widespread
widespread
consensus,
forManagement
some time
time now,
now,
that
of
many
control
and
planning
system
services
in
these
modernization
programs.
It
is
claimed
that
advanced
Decision
Support
Tools
(DST)
based
upon
TP
are
capable
There
is
consensus,
for
some
that
the
current
approach
to
Air
Traffic
(ATM)
is
modernization
programs.
It isbased
claimed
that
advanced
DeThere
is widespread
consensus,
forManagement
some time now,
that
cision
Support
Tools
(DST)
upon
TP
are
capable
the
current
approach
to
Air
Traffic
(ATM)
is
modernization
programs.
It
is
claimed
that
advanced
Decision
Support
Tools
(DST)
based
upon
TP
are
capable
of
reducing
controller
workload
and,
thus,
for
decreasThere
is
widespread
consensus,
for
some
time
now,
that
the
current
approach
to
Air
Traffic
Management
(ATM)
is
unable
to
meet
expected
capacity,
safety,
and
environmencision
Support
Tools
(DST)
based
upon
TP
are
capable
the
current
approach
to
Air
Traffic
Management
(ATM)
is
of
reducing
controller
workload
and,
thus,
for
decreasunable
to meet
meet
expected
capacity,
safety,
and
environmencision
Support
Tools
(DST)
based
upon
TP
are
capable
of
reducing
controller
workload
and,
thus,
for
decreasing
airspace
capacity
limitation,
(Schuster
and
Porretta,
the
current
approach
to
Air
Traffic
Management
(ATM)
is
unable
to
expected
capacity,
safety,
and
environmental
demands,
(Enea
and
Porretta,
2012).
Many
authors
of
reducing
controller
workload
and,
thus,
for
decreasunable
to meet(Enea
expected
safety,
and
environmening
airspace
capacity
limitation,
(Schuster
Porretta,
tal
demands,
andcapacity,
Porretta,
2012).
Many
authors
of
reducing
workload
and,
thus,
for
decreasairspace
capacity
limitation,
(Schuster
and
Porretta,
2010).
DSTs controller
have required
specific
levels
ofand
accuracy
in
unable
to
meet
expected
capacity,
safety,
and
environmental
demands,
(Enea
and
Porretta,
2012).
Many
authors
believe
that
accommodation
of future
demands
by the ing
ing
airspace
capacity
limitation,
(Schuster
and
Porretta,
tal
demands,
(Enea
and
Porretta,
2012).
Many
authors
2010).
DSTs
have
required
specific
levels
of
accuracy
in
believe
that
accommodation
of
future
demands
by
the
ing
airspace
capacity
limitation,
(Schuster
and
Porretta,
2010).
DSTs
have
required
specific
levels
of
accuracy
in
terms
of
trajectory
predictions,
(Paglione
and
Oaks,
2007),
tal
demands,
(Enea
and
Porretta,
2012).
Many
authors
believe
that
accommodation
of
future
demands
by
the
ATM
systems
is
only
possible
with
increased
automation
DSTs
have predictions,
required specific
levelsand
of Oaks,
accuracy
in
believe
that accommodation
of
future
demands
by the 2010).
terms
of
trajectory
(Paglione
2007),
ATM
systems
is
only
possible
with
increased
automation
2010).
DSTs
have
required
specific
levels
of
accuracy
in
terms
of
trajectory
predictions,
(Paglione
and
Oaks,
2007),
and
therefore
pose
stringent
accuracy
performance
requirebelieve
that
accommodation
of
future
demands
by
the
ATM
systems
is
only
possible
with
increased
automation
and
collaboration
through
interoperability
of
flight
inforterms
of
trajectory
predictions,
(Paglione
and
Oaks,
2007),
ATM
systems
is
only
possible
with
increased
automation
and
therefore
pose
stringent
accuracy
performance
requireand
collaboration
through
interoperability
of Kirk,
flight 2012).
infor- and
terms
of
trajectory
predictions,
(Paglione
and
Oaks,
2007),
therefore
pose
stringent
accuracy
performance
requirements
to
provide
prediction
services
to
meet
their
needs
ATM
systems
is
only
possible
with
increased
automation
and
collaboration
through
interoperability
of
flight
information
between
stakeholders,
(Mondoloni
and
and
therefore
pose
stringent
accuracy
performance
requireand
collaboration
through interoperability
of Kirk,
flight 2012).
infor- ments to provide prediction services to meet their needs
mation
between
stakeholders,
(Mondoloni
and
and therefore
pose prediction
stringent accuracy
performance
requireto
services
to
their
needs
accordingly.
This
dependence,
it is thought,
become
and
collaboration
through
interoperability
ofconcepts
flight 2012).
information
between
(Mondoloni
and
Kirk,
Hence,
the
need stakeholders,
for
modernized
ATM related
and ments
to provide
provide
prediction
services
to meet
meet will
their
needs
mation
between
stakeholders,
(Mondoloni
and
Kirk,
2012).
accordingly.
This
dependence,
it
is
thought,
will
become
Hence,
the
need
for
modernized
ATM
related
concepts
and ments
ments
to
provide
prediction
services
to
meet
their
needs
accordingly.
This
dependence,
it
is
thought,
will
become
more
outstanding
with
increased
modernization
and
intermation
between
stakeholders,
(Mondoloni
and
Kirk,
2012).
Hence,
the
need
for
modernized
ATM
related
concepts
and
systems
throughout.
ATM
modernization
is
a
global
effort,
accordingly.
This
dependence,
it
is
thought,
will
become
Hence,
the
need
for
modernized
ATM
related
concepts
and
more
outstanding
with
increased
modernization
and
intersystems
throughout.
ATM modernization
modernization
is aa concepts
global flights
effort,
accordingly.
This
dependence,
it
is
thought,
will
become
more
outstanding
with
increased
modernization
and
operability.
Hence,
the
need
for
modernized
ATM
related
and
systems
throughout.
ATM
is
global
effort,
with
worldwide
implications:
local
and
international
more outstanding with increased modernization and interintersystems
throughout.
ATM modernization
is a global flights
effort, operability.
with
worldwide
implications:
local
and
international
more
outstanding
with
increased
modernization
and
interoperability.
systems
throughout.
ATM modernization
is a global flights
effort,
with
worldwide
implications:
local
are tightly
coupled
almost
everywhere.
Additionally,
Air operability.
with
worldwide
implications:
local and
and international
international
flights
The
core
paper
objective
revolves
on
presenting
perforare
tightly
coupled
almost
everywhere.
Additionally,
Air
operability.
with
worldwide
implications:
local
and
international
flights
are
tightly
coupled
almost
everywhere.
Additionally,
Air
Traffic
in
general
is
largely
influenced
by
local
projected
core
paper
objective
on
presenting
perforare
tightly
coupledis almost
everywhere.
Additionally,
Air The
The
paper
objective
revolves
on
performance
analysis
a flightrevolves
trajectory
predictor and
its
Traffic
indemands
general
largely
influenced by
by
local projected
projected
The core
core
paper of
objective
revolves
on presenting
presenting
perforare
tightly
coupledis
almost
everywhere.
Additionally,
Air mance
Traffic
in
general
largely
influenced
local
airspace
and
by international
trends.
As such,
analysis
of
aa flight
trajectory
predictor
and
its
Traffic
in
general
is
largely
influenced
by
local
projected
The
core
paper
objective
revolves
on
presenting
performance
analysis
of
flight
trajectory
predictor
and
its
integration
to
a
post-processing
trajectory
simplification
airspace
demands
and
by
international
trends.
As
such,
mance
analysis
of
a
flight
trajectory
predictor
and
its
Traffic
in
general
is
largely
influenced
by
local
projected
airspace
demands
and
by
international
trends.
As
such,
tactical
and
strategic
system
services
are
being
revisited
integration
to
a
post-processing
trajectory
simplification
airspace
demands
and
by
international
trends.
As
such,
mance
analysis
of
a
flight
trajectory
predictor
and
its
integration
to
a
post-processing
trajectory
simplification
engine.
These
are
part
of
an
analysis
and
systems
develtactical
and
strategic
system
services
are
being
revisited
integration
to
a
post-processing
trajectory
simplification
airspace
demands
andsystem
by international
trends.
As
such, engine.
tactical
and
strategic
services
being
revisited
in current
modernization
programs,
such
as NextGen,
These
are
part
of
an
analysis
and
systems
develtactical
and
strategic
system
services are
are
being
revisited
integration
to
a
post-processing
trajectory
simplification
engine.
These
are
part
of
an
analysis
and
systems
development
framework
being
devised
in
which
accurate
flight
in
current
modernization
programs,
such
as
NextGen,
These
are part
of devised
an analysis
and systems
develtactical
and
strategic
system
services
are
revisited
in
current
programs,
such
as
NextGen,
SESAR,
andmodernization
Brazil’s SIRIUS.
These programs
based engine.
opment
framework
being
which
accurate
flight
in
current
programs,
suchbeing
as are
NextGen,
engine. These
part
of devised
an analysis
and systems
development
framework
being
devised
inprovided
which
accurate
flight
predictions
andare
time
estimates
arein
to a conflict
SESAR,
andmodernization
Brazil’s SIRIUS.
SIRIUS.
These programs
programs
are
based
opment
framework
being
in
which
accurate
flight
in
current
modernization
programs,
such
as
NextGen,
SESAR,
and
Brazil’s
These
are
based
on
full
4D
Trajectory
Based
Operations,
or
TBO.
The
predictions
and
time
estimates
are
provided
to
a
conflict
SESAR,
and
Brazil’s
SIRIUS.
These
programs
are
based
opment
framework
being
devised
in
which
accurate
flight
predictions
and
time
estimates
are
provided
to
a
conflict
detection
module
under
development
and
intended
to
be
on
full
4D
Trajectory
Based
Operations,
or
TBO.
The
predictions
and
time
estimates
are
provided
to
a
conflict
SESAR,
andTrajectory
Brazil’s SIRIUS.
TheseBased
programs
are based
on
full
4D
Operations,
or
TBO.
The
fundamental
element
ofBased
Trajectory
Operations
is detection
module
under
development
and
intended
to
be
on
full
4D
Trajectory
Based
Operations,
or
TBO.
The
predictions
and
time
estimates
are
provided
to
a
conflict
detection
module
under
development
and
intended
to
be
employed
for
tactical
operations
within
the
existing
Air
fundamental
element
of
Trajectory
Based
Operations
is detection
module
under
development
andthe
intended
toAir
be
on
4D Trajectory
Based
Operations,
or
TBO.
fundamental
element
Trajectory
Based
Operations
is
thatfull
airlines
and
the of
ATM
system
will
agree
about The
the
employed
for
tactical
operations
within
existing
fundamental
element
of
Trajectory
Based
Operations
is
detection
module
under
development
and
intended
to
be
employed
for
tactical
operations
within
the
existing
Air
Traffic
Control
(ATC)
system,
(Fattori
et
al.,
2017).
that
airlines
and
the
ATM
system
will
agree
about
the
employed
for
tactical
operations
within
the
existing
Air
fundamental
element
of
Trajectory
Based
Operations
is
that
airlines
and
the
ATM
system
will
agree
about
the
trajectory
that
will
be
followed
by
an
aircraft.
Trajectory
Traffic
(ATC)
system,
al.,
2017).
that
airlines
and
the
ATM
system
will
agree Trajectory
about the employed
for tactical
withinet
Traffic Control
Control
(ATC) operations
system, (Fattori
(Fattori
etthe
al., existing
2017). Air
trajectory
that
will
be
followed
by
an
aircraft.
Traffic
Control
(ATC)
system,
(Fattori
et
al.,
2017).
that
airlines
and
the
system
agree
about prethe The aircraft
trajectory
that
will
be
followed
by
aircraft.
Trajectory
model
in (Fattori
the TP ethas
may also
include
additional
constraints
for
improved
trajectory
that
will
be ATM
followed
by an
anwill
aircraft.
Trajectory
Controlflight
(ATC)
system,
al.,evolved
2017). and
The
aircraft
flight
model
in
the
TP
has
evolved
and
may
also include
include
additional
constraints
for improved
improved
pre- Traffic
trajectory
that
will
be
followed
by
an
aircraft.
Trajectory
The
aircraft
flight
model
in
the
TP
has
evolved
and
may
also
additional
constraints
for
prematured
to
include
extended
modeling
in
a
more
robust
dictability,
thus
aiding
in
workload
reduction
for
air
traffic
The aircraft
flight extended
model in modeling
the TP in
hasa evolved
and
may
also include
additional
constraints
for improved
pre- matured
to
include
more
robust
dictability,
thus
aiding
in
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PREDICTION
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ations,
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ability
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Trajectory
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Prediction
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vision
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the
The
ability
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central
to
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myriad
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ATM
community
vision
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ries
is
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Trajectory
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(TP)
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such
as
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ATM
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resolution,
to
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few.
ATM
Partially sponsored by CNPq Brazil under RHAE Program;
such
as
the
traffic
load
forecasting,
weather
assessment,
ATM
community
vision
for modern
Air Traffic
Control conflict
detection
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to
name
aa assessment,
few.
ATM
Partially
sponsored
by CNPq
Brazil under
RHAE Program;
such
as
the
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load
forecasting,
weather
conflict
detection
and
resolution,
to
name
few.
ATM
systems,
such
as
conflict
probe,
metering
and
spacing,
Project
Grant
n. 472504/2014-2.
Partially
sponsored
by
CNPq
Brazil
under
RHAE
Program;
conflict
detection
and resolution,
to name and
a few.
ATM
Partially
sponsored
by CNPq Brazil under RHAE Program;
systems,
such
as
conflict
probe,
metering
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Project
Grant
n. 472504/2014-2.
conflict
detection
and
resolution,
to
name
a
few.
ATM
systems,
such
as
conflict
probe,
metering
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Project
Grant
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472504/2014-2.
Partially
sponsored
by
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Brazil
under
RHAE
Program;
systems, such as conflict probe, metering and spacing,
Project Grant n. 472504/2014-2.
Project Grant
n. 472504/2014-2.
Copyright
© 2017
IFAC
16197systems, such as conflict probe, metering and spacing,
∗Eric Conrado
∗ Atech Negócios
∗ Atech Negócios
∗
Copyright © 2017 IFAC
16197
2405-8963 ©
IFAC (International Federation of Automatic Control)
Hosting by Elsevier Ltd. All rights reserved.
Copyright
2017
16197
Copyright
© 2017,
2017 IFAC
IFAC
16197
Peer
review
under
responsibility
of
International
Federation
of
Automatic
Control.
Copyright © 2017 IFAC
16197
10.1016/j.ifacol.2017.08.1900
Proceedings of the 20th IFAC World Congress
15628
Eric Conrado de Souza et al. / IFAC PapersOnLine 50-1 (2017) 15627–15632
Toulouse,
France, July 9-14, 2017
air traffic advisory DSTs, and Traffic Flow Management
systems, depend on provision of prediction estimates as a
service, (Mondoloni and Kirk, 2012).
2.1 Flight Modeling
A kinetic approach to trajectory prediction is considered:
a set of deterministic, point-mass equations of motion,
based on the flight dynamics presented below, was employed to model the arbitrary airliner. The Flight Model
implemented in the Trajectory Predictor is a six degreeof-freedom, nonlinear dynamical model of commercial aircraft in trimmed flight, see Glover and Lygeros (2004). The
resulting aircraft model is a set of continuous-time ODEs
defined by Eq. 1:
ż(t) = f (z(t), u(t), t),
z0 = z(t0 )
(1)
where f is, in general, a non-autonomous mapping between
the aircraft state z, input u, time t, and the time rate of
state ż. A minimal realization of the state vector z usually
comprises aircraft position written in the Cartesian representation of the Earth geographical coordinates, altitude,
aircraft true airspeed, heading, and aircraft mass. Aircraft
engine thrust, roll angle, and wind velocity vector are
considered model inputs and are lumped together in the
input vector u. Model parameters are obtained from Base
of Aircraft Data (BADA) 3, (Eurocontrol, 2015). Atmospheric modeling is integrated to the above aircraft flight
model. This modeling provides parameters for conversion
between aircraft calibrated and true airspeed figures, provides atmospheric states’ values for the computation of
lift & drag forces acting on the aircraft model and provides intermediate states for determining mass variation
dynamics. See also Porretta et al. (2008).
2.2 Intent Modeling
The Intent model describes how the aircraft is to be
flown. The intent model is as necessary as the aircraft
flight model for a successful prediction process. Standard
flight plan information - such as, aircraft type, onboard
navigational equipment, expected route waypoints, and
anticipated cruise altitude and airspeed - is insufficient
for satisfactory trajectory estimation because flight plans
do “not contain enough information to build from it an
unambiguous rendition of the flight path in 4D”, (Klooster
et al., 2010). Intent data complements the flight plan with
information that can impact the predicted aircraft path,
(Schuster and Porretta, 2010), including controller issued
altitude and time constraints, settings for flight guidance,
speed profile intent, thrust and drag performance factors,
aircraft weight, and aircraft maneuvering procedure over
the temporal horizon for prediction. These may vary
greatly with the application operational environment and
include pilot and controller preferences and objectives.
Flight intent modeling here is based on the analysis of
flight data, to determine aircraft rates of climb and descent, and contain estimates of Top-of-Climb and Top-ofDescent. An equally important matter concerns the speed
schedule itself. In this case, aircraft speed intent is modeled
by data mining flight data. The tangible advantage of this
approach is that typical aircraft speed, climb and descent
rates, and other figures are available to describe flight intent. These intent measures represent the best description
of flight intent, along with other prediction parameters,
and are introduced into the Trajectory Predictor in the
form of a flight intent model. This proved to be more
effective means to describe intent than the Energy Share
Factor (ESF), see Schuster et al. (2012).
Additional intent information is coded into the model in
the form of aircraft guidance laws. Feedback loops are also
in place to reject disturbances and regulate cross-track
and heading deviations to zero w.r.t. a nominal trajectory
given by the expected flight route. No aircraft flight speed
scheduling look-up table was employed directly: the flight
control system was used to regulate aircraft velocity based
on intent modeling. In the early stages of research, prediction trajectories were created by inputting a sequence of
route waypoints to the predictor engine. These waypoints
are based on flight history (tracks) analysis and contain
more than just geographical coordinates of aircraft position: altitude and speed are also provided to indicate main
aircraft motion over the flight period considered. Moreover, these waypoints were transformed into continuously
differentiable class functions to be used by the guidance
and control laws in the flight model for input tracking and
aid the trajectory reconstruction process. The prediction
results presented here, on the other hand, require only discrete waypoints as intent input, and not through specific
class functions, and are less dependent on flight history
information. Intent modeling with data from departure
and approach procedures will also be considered in future
developments to enhance the flight intention information
being input to the Predictor, as mentioned above.
Under the speed scheduling context, trajectory prediction
is, generally, posed as the following problem:
Claim 1. Predict aircraft trajectory with Look-AheadTime T considering the aircraft is expected to perform
the provided speed schedule.
Considering that an aircraft is always able to perform the
provided speed schedule is, in general, a strong prediction
problem hypothesis. Instead, the proposed TP solves the
more general problem:
Claim 2. Predict aircraft trajectory with Look-AheadTime T by attempting to fly the provided speed schedule
though limited to flight dynamics and envelope.
This second prediction problem will answer “Can the aircraft model strictly fly the provided intent?” If not, it is
likely the model input will saturate and the aircraft model
will fly differently from what the intent model required it
to. Thus, the aircraft, incidental to the modeled aircraft
performance, and given mass and atmospheric conditions,
may or may not fly the provided arbitrary speed schedule.
This requires extra flight dynamics modeling not usually
accompanying kinetic based predictors, such as the Total
Energy Model (TEM). A control strategy was devised
to cope with aircraft model input saturation, i.e., engine thrust saturation. During saturation, the available
propulsive energy is appropriately allocated to climb and
acceleration motions by some ad hoc criterion. In this case
the original flight intent model provided is broken in the
sense that the coupling between different intent states,
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REV
Files
such as required altitude and speed, will not be maintained. Current TP enables the flexibility to achieve the
intent flight states, albeit in saturation, in an independent
fashion.
15629
Aircraft
Database
Aircraft
Interpreter
Formal description of intent is not a sought for objective here; this step in modeling is bypassed and intent
numerics directly feed the TP instead. Aircraft Intent
Description Language (AIDL) can be used for this purpose, (Bronsvoort et al., 2015). Also, the sole purpose
of this study is to evaluate ground-based system prediction performance. Air-ground downlink issues, such as
ground/FMS trajectory synchronization, is outside the
scope of this investigation.
PLN
Interpreter
Procedure
Interpreter
Coordinates
Pre
Processor
AISWeb
Coordinates
Interface
Trajectory
Predictor
ATC
Changes
2.3 The Prediction Process
Fig. 1. The Trajectory Prediction Process.
The prediction process involves the fast-time solution,
or simulation, of an Initial Value Problem (IVP) with
initial values z0 , yielding the state z(t) as a function
of time. The time horizon for this estimate varies from
problem to problem. For example, gate-to-gate prediction
would involve a time horizon of many hours; while conflict
detection would require flight state estimation of 20 to 40
minutes of look-ahead-time from current aircraft position.
Prediction assumes the initial position and look-ahead
time are known, though important sources of uncertainty.
departs from SBGR towards SBRP at 11h55 with an
estimated flight time of only 0h41 and a cruising flight
level of FL240 at 342kn. Intent for prediction is given in the
form of an extended route, a sequence of points detailing
spatial, speed, and altitude rate profiles.
Prediction results are, amongst many others, used to
feed the conflict detection service in tactical operations.
For acceptable prediction accuracy, a high-order aircraft
model is used for short, long look-ahead times. Therefore,
the numerical integration routines used for solving the
IVP are based on a 4th order Runge-Kutta integration
method with an adaptive timestep size control for integration performance accuracy and runtime efficiency. Similar
methods for numerical integration in trajectory prediction
have been documented in the literature, (Hadjaz et al.,
2012). Figure 1 provides a schematic diagram of the subcomponents of the Trajectory Predictor. Predicting the
aircraft future position is regarded as a difficult endeavor.
This difficulty is related specially to the estimation of perturbations influencing its motion. Aircraft flight is affected
by uncertainty in wind, for the most part, and also by
errors in navigation, guidance and control. Ground speed
data is used to feed the TP directly and the prediction
analyses with wind data, though an important source of
uncertainty, is not presented at this moment. Navigation
error is outside paper scope, guidance and control are
addressed with intent modeling.
3. PREDICTION EVALUATION RESULTS
The prediction performance analysis considered a selection
of three regular commercial flights over the Brazilian
territory. The first flight, callsign XXX1111, departs from
SBGO towards São Paulo (SBSP) at 11h50 (EOBT)
with an estimated time of flight of 1h15 (EET) and a
cruising flight level of FL390 at 450kn. The second flight,
YYY2222, departs from SBCF towards SBEG also at
11h50 with an estimated flight time of 3h32 and a cruising
flight level of FL340 at 462kn. This flight involves two
Area Control Centers (ACC) and analysis here will cover
only the ACC Brasilia branch. The third flight, ZZZ3333,
3.1 Accuracy Analyses
The performance analyses employs selected spatial and
temporal metrics for the comparison of TP trajectory
evaluations against flight track (measured) data. The motivating objective behind this comparison is to show some
level of accuracy performance the kinetic flight model is
able to deliver by reproducing real flight trajectory with
a small number of input waypoints as the main representation of intent, i.e., input to TP. Ryan et al. (2004) and
Paglione and Oaks (2007) have presented useful definitions
of metrics and related criteria, for metrics application,
to the problem of trajectory accuracy evaluation. Metrics
for quantifying the error of the predicted trajectory to a
reference trajectory, flight tracks typically, are categorized
in two groups: Spatial Errors, Horizontal (HE), AlongTrack (AE), Cross-Track (CE), Vertical Errors (VE), and
Temporal Errors (TE). Two general criteria are used to
employ metrics for spatial and temporal metrics; results
below use the closest segment for spatial metrics and the
closest point for the temporal metric.
The trajectories for flights XXX1111 and ZZZ3333 posses
a descent phase; flight YYY2222 does not have its descent
phase analysed. Flight intent modeling captured major low
frequency motions for every flight phase available. Table 1
yield RMS results for the computed spatial and temporal
errors. Notice that RMS errors should be evaluated in
light of flight duration times, since, due to its accumulative
nature, these increase with the flight duration considered
in the analysis. Hence, RMS figures for each flight instance
should not be contrasted to each other directly. Similarly,
in the TP context, a temporal metric would indicate
flight performance for distinct aircrafts flights reaching
intermediate waypoints or a final destination as a function
of their adopted trajectories. The error values disclosed
in Table 1 are normalized with the number of trajectory
points; and are of qualitative nature only: The amount of
flight intent information supplied to the predictor model
is of great significance when interpreting these numbers,
since they are relative to the quality of intent information
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Fig. 2. Prediction horizontal (CE, AE, HE) & vertical (VE)
errors.
used in each prediction. Hence, a relative importance
should be given to the analysis of absolute error values,
for this presentation, commensurate to the intent models
provided to each flight.
Table 1. Relative RMS error analysis.
Callsign
XXX1111
Climb
Cruise
Descent
YYY2222
Climb
Cruise
ZZZ3333
Climb
Cruise
Descent
HE(nm)
1.2946
1.4951
1.5305
0.9553
0.7810
0.5264
0.8469
1.4450
1.6090
1.6188
1.1092
AE(nm)
1.2793
1.4939
1.5145
0.9270
0.1487
0.1769
0.1383
1.4370
1.5995
1.6173
1.0943
CE(nm)
0.1824
0.0602
0.2210
0.1988
0.1068
0.1553
0.0855
0.1169
0.1360
0.0699
0.1321
VE(ft)
593.54
991.17
547.52
196.35
92.59
183.02
24.10
181.25
233.75
62.83
202.55
TE(s)
10.64
11.64
11.48
9.39
6.92
5.54
7.31
12.60
15.26
12.37
10.26
Spatial prediction errors are illustrated in Fig. 2, as histograms for the cross-track (CE), along-track (AE) and
vertical (VE) errors. The horizontal error as a function
of flight normalized time of flight is also depicted there.
Figure 3 shows the temporal error as a function of the
normalized time of flight. These results compare well with
the literature. Errors tend to be greater during climb and
descent, as expected: close to terminal areas where procedures are followed; en-route (cruise) prediction is easier
(YYY2222). XXX1111 intent for climb can be improved.
Observe, moreover, that horizontal errors peak when time
errors correspondingly also reach maximums. The closest
segment was the adopted criteria for these analyses, (Ryan
et al., 2004). In a conceptual exercise, flight intent were
also deliberately under-modeled, i.e., poor modeling was
considered for their prediction. In these cases, prediction showed poor prediction performance during all flight
phases, as expected, demonstrating the need for fine-tuned
intent modeling for improved performance with respect to
a specific metric employed for error computation.
4. GENERAL COMMENTS
It is easily observed that the quality of input data directly
affects trajectory prediction accuracy, this claim agrees
Fig. 3. Prediction Time errors and normalized flight time.
with reports elsewhere, (Mondoloni et al., 2005). Despite
results with wind are not exploited here, the uncertainty
related to the wind-field estimation greatly impacts alongtrack and time-of-arrival errors; this has also been observed previously, (Mondoloni et al., 2005). In contrast,
the wind influence on cross-track and altitude errors are
less apparent. Therefore, in order to mitigate differences
between true, or observed, aircraft behavior from theoretical prediction one must provide a satisfactory uncertainty
model. Intent seems to impact long term predictions more
prominently than flight dynamics. The kinetic approach to
TP, although flexible in terms of parametrization of a wide
range of different flight conditions and intent scenarios,
demands more knowledge about these same conditions
and scenarios and how to best employ this knowledge to
correctly parametrize the flight model. In many cases, the
underlying predictor flight model is significantly sensitive
to this parametrization. It is recognized, nevertheless, that
through a collaborative environment for the flow of information, this demand for flight related knowledge will be
supplied and that modernization of ATM systems will be
ready to fulfill new operational expectations.
Trajectory prediction in the context of medium-term conflict detection should consider typical look-ahead-times
of 20, up to 40, minutes; see Fattori et al. (2017) for
TP integration with conflict probe. However, in order to
validate prediction accuracy, prediction performance are
evaluated with longer flight periods.
The flight model considered currently is able to cope with
input saturation. A heuristic for replanning, even, of flight
intent with the objective of reducing undesirable effects
of saturation is being designed and tested. This is only
relevant if it mimics aircraft FMS behavior.
5. TRAJECTORY SIMPLIFICATION
The predictor provides trajectory estimates to the conflict
probe, amongst other ATM subsystems, (Fattori et al.,
2017). The trajectories are simplified before being fed into
the conflict detection process, instead of a direct input, in
order to remove excessive number of points which defines
the trajectories themselves. This simplification decreases
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Toulouse, France, July 9-14, 2017
p1
net computation, subsequently to prediction, required for
conflict probing.
p3
5.1 The Douglas-Peucker (DP) Algorithm
p2
The Douglas-Peucker (DP) algorithm (Katsikouli et al.,
2014) is applied to map reduction problems by removing
data, or contour points, while keeping deviations from
the original small. This reduction takes into account the
relevancy of a single point to the map as a whole. The
relevancy factor is given by the distance of one point to the
set of previous relevant points. The method goes as follows:
the initial and final map points are connected (these are
compulsorily relevant points). The distance between each
point and the lines connecting relevant points is computed.
The most relevant point are defined as those with the
greatest computed distance. If the point distance is above
a given threshold, this point is considered relevant and
belongs to the simplified map. Point distances and lines are
re-calculated and the process iterates. Figure 4 illustrates
the Douglas-Peucker algorithm.
p1
p3
p2
1 - Calculating Distances
p1
d2
p3
d3
p2
p5
A2
p3
p2
A3
A4
p2
p2
p5
A3
Fig. 5. Visvalingam-Whyatt algorithm demonstration.
a measure of relevancy. This Euclidean distance quantifies
the range between one point and a virtual point located
on the line segment considered at a position proportional
to the times of the initial and final points. Figure 6 shows
the computation of the Euclidean distance.
p2',t2
p3,t3
d2
Fig. 6. The Euclidean distance definition.
p5
d3
p3
p4
p2,t2
p3
A2
p1
p5
p1,t1
2 - Adding p2 and
recalculating distances
2 - Removing p4 and
recalculating Areas
3 - Repeting steps
p4
d4
p4
p1
p5
p4
1 - Calculating Areas
p5
p1
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d4
p4
3 - Repeting steps
Fig. 4. Douglas-Peucker algorithm demonstration.
5.2 The Visvalingam-Whyatt (VW) Algorithm
The Visvalingam-Whyatt (VW) algorithm (Visvalingam
and Williamson, 1995) is also applied to the map reduction by removing data without losing geometric features.
Differently to the DP case, which employs distances between points and lines as the criterion for relevant points
determination, this second algorithm uses the computed
area one point defines with its adjacent neighboring points
as a measure of lesser relevancy. If the computed area
attributed to a point is smaller than the corresponding
areas of its neighbors and, similarly, if the computed area
is inferior to a given threshold, this point is removed from
the solution and the areas for the remaining points are
recalculated. Figure 5 illustrates the VW algorithm.
The dynamical modification for the VW algorithm, intended for trajectory simplification, has not been discussed
in the literature. The proposition of the dynamic term is
addressed here as the composition of the area defined by
one point and its neighbors and the area defined by a pair
of points with a specific external point. For trajectories
given by geodesics, the center of the Earth was chosen as
the common external point. Figure 7 depicts the areas considered in the computation of the dynamical term for the
VW algorithm. In Fig. 7, the difference of areas A1O2 and
t3−t2
A2O3, which are averaged by the factors t2−t1
t3−t1 and t3−t1 ,
respectively, provides the definition for the dynamical term
in trajectory simplification based on the VW algorithm.
p1,t1
p2,t2
p3,t3
A2O3
A1O2
O
Fig. 7. Dynamic term used adopted in VisvalingamWhyatt algorithm for trajectory simplification.
5.4 Performance Comparison
5.3 The Dynamical Term
The map reduction algorithm cannot be employed for
trajectory simplification directly, this requires the introduction of a dynamic term to the map method, (Long
et al., 2013). Map data are given by location coordinates.
Alternatively, trajectories are defined by coordinates and
time measures. The Douglas-Peucker algorithm is modified to incorporate this term by applying the Euclidean
distance in the place of the standard point-line distance as
Trajectory simplification performance evaluations were
carried out by fixing a number points for the simplified
trajectory and varying the thresholds parameters (distance
and area). Runtime figures were logged and the (simplified) output trajectories were plotted over the original.
Measuring execution time reveals agility performance during trajectory simplification. This is an important matter since the simplification process output can be used
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Proceedings of the 20th IFAC World Congress
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Eric Conrado de Souza et al. / IFAC PapersOnLine 50-1 (2017) 15627–15632
Toulouse,
France, July 9-14, 2017
to improve performance for subsequent processes. Both
algorithms were coded in C language and processed the
same predicted trajectory. Runtime measures were obtained with the OS built-in time routines. The VW based
solution underperformed for simplified trajectories with
up to 7 points, though performed better with a greater
number of points. For 18-point trajectories, the solution
based on VW’s performed up to 5% faster than DP’s. This
mixed-performance behavior, parametrized by the number
of trajectory points for simplification, is due to the nature
of both algorithms: area calculations are more complex
than distance ones and, for each iteration with the DP
algorithm, when a new point is added to the output a recomputation of distances for all points follows. In contrast,
when a trajectory point is removed with VW’s based
solution, area calculations occur for only its two neighboring points in each iteration. Hence, for a small number
of points (≤7), DP’s solution has good performance; for
trajectories with >7 points, VW performs better.
Trajectory accuracy performance evaluations considered
qualitative graphical analysis. The original trajectory is
contrasted to the simplified trajectories obtained from the
two algorithms discussed. The simplified trajectories are
defined by the interpolation of the output points from the
simplification process. Simplification results for 18 points,
along with the original, are considered in Fig. 8.
(m)
(km)
5 000
640
Original
VW
DP
500
0
400
500
800 (km)
500
700 (km)
Fig. 8. Accuracy test for methods based on VW and DP
approaches: the vertical (left) & horizontal planes.
Observations indicate that the VW based algorithm outperformed the other for a benchmark number of points. A
second test seeking to obtain the same level of accuracy
with the DP based algorithm indicated the need for over
50 additional points to match accuracy obtained with the
VW based simplification.
6. CONCLUSION
This note on trajectory prediction and simplification represents a continued and systematic effort on devising effective methods to address prediction accuracy requirements
for future ATM demands. Future research and project
development include implementation code optimization
and tuning refinements for improved ATM system performance. Additional methods for flight state estimation and
wind data treatment are also being considered and will be
included in a forthcoming presentation.
ACKNOWLEDGEMENTS
Thanks to the Product Eng. and Innovations group at Atech. This research is partially funded by the CNPq/MCTI,
Brazil under RHAE Program, grant 472504/2014-2.
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