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Aircraft Trajectory Prediction for Terminal Automation
James L. sturdy*,John W. ~nd.rews**,Jerry D. ~ e l c h t
M.I.T. Lincoln Laboratory, Lexington, Massachusetts
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | | DOI: 10.2514/6.1989-3634
The FAA's Terminal Air Traffic Control Automation
(TATCA) program is developing automation aids that will
help to approach the full inherent capacity potential of
airports in all weather conditions by providing the team of
terminal area controllers with tools for precisely planning
and controlling the traffic stream. As part of the arrival
planning process, the TATCA logic will predict a fourdimensional trajectory for each aircraft to determine both
when each aircraft would reach the runway if it followed a
nominal approach route and what sequence of controller
directives could be employed to bring it to the runway at
the desired time.
Ground-referencedglidepath angle
Bank angle
turn rate
Acceleration due to Earth's gravity
True (geometric) altitude
Time rate of change of true altitude
Engine thrust
Equations and aircraft performance models are available
for predicting specific segments of an aircraft's flight, such
as descent from cruise and final approach. The work
described in this paper has integrated these equations and
that can make
performance models into a d ~ e framework
use of TATCA's detailed knowledge of winds aloft to
support automation assistance over all phases of aircraft
Rate of change of true airspeed
Tail wind magnitude
Aircraft weight
The prediction software is composed of several layers.
The lowest level calculates aircraft performance
characteristics such as thrust and drag. The next layer
contains algorithms which are tailored to efficiently predict
aircraft motion during specific modes of flight such as
descent, acceleration, and turn. A higher layer determines
the appropriate mode of flight for the aircraft at each point
in its trajectory. At the top level are software modules that
generate time-to-fly predictions and candidate trajectories
that meet planning constraints.
The layered structure of the TATCA trajectoryprediction software has proven to be flexible. Validation
against trajectories observed by radar have shown that the
algorithms used in the prediction software are accurate and
can support simulation of a complete terminal environment
without excessive computational loading.
***Technical Staff
Assistant Group Leader
t Associate Group Leader
The views expressed are those of the authors and do not
reflect the official policy or position of the U.S.
Government. This work was sponsored by the Federal
Aviation Administration.
Copyright O American Institute of Aeronautics and
Astronautics, Inc., 1989. All rights reserved.
True airspeed
Increasing congestion in the air traffic system and the
resultant delays are causing serious economic disruption and
inconvenience to air travelers and aircraft operators. Much
of the delay results from an inability to realize the full
capacity potential of key airports during adverse weather.
Since it seems likely that few new runways will be added to
the most congested airports, it is imperative to develop
methods of increasing the operational efficiency of the
existing facilities.
The Terminal Air Traffic Control Automation
VATCA) program was initiated in 1987 by the Federal
Aviation Administration in response to this growing
national need. The primary objective of this program is to
increase terminal area throughput, especially under
instrument meteorological conditions. The principal
automation functions being investigated to accomplish this
goal are: traff~planning and controller coordination aids,
speedcontrol and holding advisories, descent advisories
(topofdescent point and descent speed prof~les),and finalapproach spacing aids. The outputs of these automation
functions will be presented to individual members of the
terminal controller team in the form of coordinated
graphical displays.
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | | DOI: 10.2514/6.1989-3634
The heart of the TATCA approach is the generation
and automatic dissemination of a dynamic time-based plan
(DTP). This is a detailed strategy for the efficient handling
of each arriving and departing aircraft. It includes each
aircraft's intended route of flight, when it should cross
various control points (including the runway threshold and
other srandard fixes), and when and when speed and altitude
clearances should be issued. The plan will maximize the
runway throughput while taking into account constraints
such as the spacing needed between successive anivals to
avoid wakevartex turbulence a additional spacing needed
to allow departing aircraft to take off. The plan will be
dynamic in that it will continually adjust as required to
adapt to the unfolding of events, including the progress of
traffic as observed by radar.
The accurate 4-Daircraft trajectory predictions will be
used to ensure that the plan is readily achievable and
contains advisories that can safely be issued by the air
t&c controllers to keep the aircraft in conformance with
the plan. The 4-Dtrajectory will be calculated such that
the aircraft meet the desired fix crossing times, follow the
planned route of flight, satisfy airspace constraints, operate
within aircraft performance envelopes and according to
standard piloting practices, and conform to common air
traffic control strategies. The automation will then display
to the air tfic controllers the planned aircraft sequence, fix
arrival times, and clearance advisories.
Trajectory-predictionsoftware will be used by the
TAKA logic in several specific ways. The logic will use
the software to initially calculate each aircraft's nominal
direct landing time for determining the true firstame-fmtserved sequence. The logic can then use it to calculate the
earliest and latest feasible landing times achievable without
vectoring (that is, by means of speed-control alone). Once
an aircraft has been assigned a landing time by the planning
process, the Trajectory-predictionsoftware will be used f a
determining what advisories should be issued to the air
traffic controllers, monitoring the aircraft's conformance
with the plan, and predicting and helping to resolve
conflicts with other aircraft
The trajectory-prediction software takes into account
the aircraft'sperformance, the wind field including windshear,the atmospheric pressure, and the temperature.
Because the automation logic will sometimes need to
simultaneously generate new plans for many aircraft, such
as when a change in airport configmation is planned,
trajectory prediction must be computationally efficient.
Because the TATCA automation logic will be planning for
depinaues as well as arrivals fixxn ground level to cruise
altitude, the trajectory-prediction software must be capable
of simulating all flight regimes. The software must also
be able to accurately model all types of aircraft that are apt
to be found operating into and out of congested US
airports, while avoiding reliance upon propietary aircraft
Considerableresearch effort has been given in the past
to developing acclrrate and efficient ahcraft-simulation
algorithms for use in aircraft flight management
systems.*3 The results of this research have already been
applied to the task of generating top-of-descent ad~isories.~
Our approach has been to evaluate the algorithms that have
been developed by previous researchers, select those that
yield the best balance between ~ccuracyand computational
efficiency, and combine the selected algorithms into an
integrated trajectory-prediction software package which has
d i c i e n t flexibility to satisfy all of the trajectory
prediction needs of the automation logic and support realtime and fast-time simulation testing. Where accuracy
quirements are uncertain, initial algorithm development
has intentionally erred on the side of greater accuracy. As
accuracy requirements are better understood, opportunities
f a simplifying the software and internal algorithms may
The trajectory-predictionsoftware employs a layered
modular structure to maximize its flexibility and to make it
easy to to add new flight modes or to modify existing
modes. In the lowest layer are a set of aircraft performance
models which calculate lift coeffkient (a function of wingloading, true airspeed,and air density), required flap
position (a function of lift coefficient), drag (a function of
lift coefficient, mach number, flap position, and gear
position), and thrust limits (which are functions of altitude,
mach number, static pressure, and static temperature) using
polynomial approximations and table lookup of
performance data that is specific to each class of aircraftl
The middle level contains algorithms that use an aircraft
predict how the aircraft would move if it were flying in a
specifk mode based on a point-mass model of the aircraft's
dynamics. Each possible mode of flight, such as
descending, decelerating, turning, or following a fued
glideslope, has its own algorithm. The trajectoryprediction software achieves its versatility through the
integration and generalization of the routines at this level.
The highest level contains routines that use the lower level
algorithms and models to piece together trajectories out of
the variws modes. These routines perform the calculations
required by the automation logic and move simulated
targets in accordance with clearances issued by subject
controllers during simulation tests. This lay& structure
has proven to be easily adapted to new prediction and
simulation requirements.
The middlelevel algorithms used to simulate different
modes of flight are not constrained to use the same
integration procedure. Each integration step is performed
assuming constant rates of change for the duration of the
step based on a calculation of the rates for the average state
of the aircraft during the integration step. This allows the
integration step size to be selected based on the non-linear
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | | DOI: 10.2514/6.1989-3634
properties of the selected mode of flight An integration
variable (range, altitude, airspeed,a heading) most
appropriate for the flight mode being simulated is selected
for each algorithm so that the end-point values of state
variables used in the rate calculations can be determined
exactly at the beginning of each integration step and simple
integration procedures can be used in place of iterative
procedures. For example, the algorithm for predicting
aircraft motion during descents can integrate on steps in
altitude. 'Ihisfreedomtobasethetypeandsizeof
integration step on the flight mode contribute signif~antly
to the algorithm's computational efficiency. During the
calculation of descent steps, for instance, an altitude step
size of 1000 feet retains almost all of the accuracy of
arbitrarily small steps. This step size allows the algorithm
to calculate the equivalent of an approximately 3Gsecond
time step with only one calculation of the governing
equations and the aircraft's thrust and drag. For
comparison, a timestep based integration technique has
been proposed2that can use a 60-second step size during
descent calculation, but that technique requires four
calculations of the governing equations and aircraft's thrust
and drag. thus requiring twice as many computations for the
same trajectory.
'Ihe integration variable and the carresponding
governing equation used to predict the aircraft's motion in
each mode are as follows:
Cruise steps are calculated using steps in range and
a force balance (T = D) to determine fuel flow.
Climb and Descent:
Descent and climb steps are calculated using steps
in true altitude and the equation
which is an extension of the energy state
approximation equations derived by ~utowslri~
and Bryson, Desai, and off man.^
Acceleration and Deceleration:
Acceleration and deceleration steps are calculated
using steps in true airspeed using the equation
Vt = g-
W *
Fixed Glideslope (umstant indicated airspeed):
Constant airspeed descents along a fixed glideslope
Fixed Glideslope( a c c e l d g or decelerating):
Accelerating and decelerating descents along a fixed.
equation in conjunction with
Cruise, climb, descent,acceleration, and
deceleration steps calculated while the aircraft is
turning use steps in heading and the appropriate
equation from the list above in conjunction with
where $ has units of radians per unit time.
Most of the processing time required for a trajectory
prediction is used to calculate thrust and drag (T-D); thus.
the computationalefficiency of the trajectoly-prediction
software is highly dependent on the computational
efficiency of the aircraft performance models and how many
calculations of thrust and drag need to be made to calculate
a complete trajectory.
The preliminary validation of the trajectory-prediction
software has been performed against trajectories of jet
transport aircraft observed by radar while arriving at
Boston's Logan Inteanational Airport. In the validation
process, the trajectory of the observed aircraft was examined
to determine its route of flight and to estimate the positions
at which it m i v e d speed and altitude clearances. This
mute and clearance information was then used as an input
to the trajectory-prediction algorithm which generated its
own estimate of how that type of aircraft would be expected
to perform when following the routing and clearances. The
estimated trajectory was then compared to the observed
trajectory to determine how well the algorithm was able to
estimate the aircraft's time-mfly and altitude profile along
the route.
The accuracy of the trajectoly prediction depends upon
several factors other than the fidelity of the aircraft
performance models and the accuracy of the integration
algorithms. Outside sources of error include: wind
. . enors,mis-modelled piloting techniques,
vamtms in controller and pilot response limes, etc. The
accuracy of the trajectory-prediction software is acceptable if
enrws introduced by its approximations are negligible
overall accuracy requirements of the automation logic. For
the cases examined to date, algorithm-induced emxs seem
to be small relative to wind estimation and pilot technique
As an example of the validation analysis, rake the case
sxmdary meilhnce radar as it appxhed Logan
International Airpoh As seen in Figure 1, the aircraft (a
Boeing 727) -he.
the airport (which is locatedat the
origin) from the southwest, entered the Boston IRACON
flight took place on 13 May 1988 under visual
meteorological conditions.
tracks,and tend to be most accurate at altitudes where
aircraft make fresuent tums at constant airspeed, such as at
holding-stack altitudes. The wind field estimates used in
the trajectory prediction are given in Table 1.
Descend to
4,000 ft.
to-oEr;5EEDownloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | | DOI: 10.2514/6.1989-3634
11,000 ft.
#**'oescend to
0.78 / 320
-100 -80 40 40 -20 0 20 40 60 80 100
East (nm)
Figure 1 - Plan View of Radar Track.
Figure 1 also shows the estimated positions at which
the real aircraft initiated altitude and speed reductions. A
simulated trajectory has been generated based on this route
of flight and the estimated clearance delivery points. The
altitude profiles of the real and simulated trajectories are
shown in Figure 2. The groundspeed profiles are shown in
Figure 3. The simulated trajectory required approximately
0.7 seconds of CPU time to calculate on an Apollo
DN4000 Computer. It used a simple wind field which was
estimated from the radar data of all the aircraft tracks
observed during a two-hour period on the same day. The
wind field was estimated by an early version of an
algorithm developed by Hollister, Bradford, and welch5
which examines the change in an aircraft's groundspeed as
the aircraft tums. These estimates are based on beacon radar
Radar Data
- SimulatedData
Along-Track Range (nm)
Figure 2 - Altitude Profile of Real and Simulated
Along-Track Range (nm)
Figure 3 - Groundspeed Profde of Real and Simulated
Table 1 - Wind Field Used in Simulated Trajectory
Wind V(feet/=)
Wind Direction
(blowing from)
The difference in the time required by the real aircraft
and the simulated aircraft to mtch each point along the
route is shown in Figure 4. This is the time-prediction
e m for each point along the route. The corresponding
error in estimating the real aircraft's position as a function
of time is shown in Figure 5.
As can be seen in Figure 4, the time-to fly predictions
are more accurate for the first half of the flight, which
includes the descent from cruise altitude, Flight Level (FL)
330, to R,240. At an along-track range of about 90 nm, a
slow buildup of prediction error begins. As can be seen
from the plot of the difference between the groundspeed of
the real and simulated aircraft in Figure 6, this error buildup
is the result of an approximately 15 kt groundspeed
discrepancy. Thediscrepancyingroundspeedincreases
during the descent to 11,000 feet and reaches a maximum of
about 35 kts at an along-track range of 130 nm. The
subsequent rapid swings in the groundspeed error correspond
to the major heading changes and the two stages of speed
reduction. The final 35-second estimation emx results
froman approximately 15 kt groundspeed error during the
final approach phase of flight Though this groundspeed
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | | DOI: 10.2514/6.1989-3634
error is smaller than earlier ones, it results in a larger time
prediction error because it is a larger percent of the total
groundspeed. The two primary somes of time prediction
error seem to be misestimating the points at which the real
aircraft performed its speed reductions and misestimating
the magnitude and/or direction of the wind below FL240.
In general, the rate of time-prediction-emr accumulation,
which is shown in Figure 7, is lower during the high
altitude portion of the flight when both groundspeed and
true airspeed are relatively high. Wind estimation and
airspeed prediction become more critical at lower altitudes
where the speeds are lower.
and the difference between their descent rates is shown in
Figure 10. At the mid-point of each descent segment, the
descent rates of the real and simulated aimaftmatch fairly
closely. Much of the altitude error seems to result from the
fact that the pilot of the real aircraft transitioned slowly
into and out of his descents, while the simulation assumed
abrupt transitions.
Along-Track Range (nm)
Figure 6 - Groundspeed Prediction E m .
. . . . . . . .loo. . . . . . . . . .200. . . . .
Along-Track Range (run)
Figure 4- Time-To-Fly Prediction E m .
Figure 7 - Rate of TimeTo-Fly Prediction Error
Time (sec)
Figure 5 - Along-Track Range Prediction E m .
Figure 8 indicates the error between the real and
simulated altitude profiles which were shown in Figure 2.
During all three descent segments, the simulated aircraft is
descending ahead of the real aircraft. Ihe rate of descent for
the real and the simulated aircraft are shown in Figure 9,
The trajectory-prediction software described in this
paper satisfies the basic needs of terminal automation logic.
In order to support actual implementation of such
automation, further work must be done in several areas.
First, the accuracy achieved by the software must be
evaluated over a wider range of aircraft types and operational
conditions, and software performance must be repeatedly
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | | DOI: 10.2514/6.1989-3634
validated with respect to the evolving automation
requirements. Secondly, the aircraft performance models
that are used by the trajectory prediction logic must be
standardized and extended to cover all aircraft that are apt to
be found operating into and out of major US airports.
Only a limited number of performance groups should be
required, since aircraftof similar performance can be
accommodated with a common performance model.
Nevertheless, additional performance models must be
collected and the proper grouping of the hundreds of aircraft
types will q u i r e considerable effort
1O(lOl Simulation
Along-Track Range (nm)
Figure 10 - Rate-of-Descent Prediction Error.
An integrated set of mode-based aircraft trajectoryprediction algorithms has been shown to deliver the
accuracy required to support automated terminal planning
while simultaneously achieving computational efficiency
required to allow implementation on workstation or mini
computers. Eight differentmales of flight were required for
a complete modeling of arriving and departing trajectories.
Grouping of aircraft types is proceeding to allow the
hundmls of aircraft types operating into major airports to
be modeled with a manageable number of performance
Along-Track Range (nm)
Figure 8 - Altitude Prediction Error.
lWO1 + Radar Data
1. Collins. B. P., Bell, N. J., and Ford, D. W., "Concepts
for Aviation Fuel Efficiency," Aviation Fuel
Conservation Symposium, FAA. Washington,
D.C., Sept 1984, pp. 617-651.
2. Erzberger, H. and Tobias, L., "A Time-Based Concept
for Terminal-Area Traffic Management," AGARD
42nd Symposium of the Guidance and Control
Panel, Brussels Belgium, June 10-13,1986.
3. Rutowski, E. S., "Energy Approach to the General
Aircraft Perfotmance Problem."
Vol. 21, No.3. March 1954,
p~ 187-195.
Along-Track Range (nm)
Figure 9 - Rateof-Descent for Real and Simulated
4. Bryson, A. E., Desai, M. N., and Hoffman, W. C.,
"Energy-State Approximation in Performance
Optimization of Supersonic Aircraft,"
Aircraft. Vol. 6, No.6, Nov-Dec 1%9, pp. 481-488.
5. Hollister, W. M., Bradford, E. R.,and Welch, J. D.,
Winds Aloft Estimation from Aircraft Tracks," to
be published in
Vol. 3, No. 1, Spring 1990.
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