NASA Technical Reports Server (NTRS) 20050237882: Handling Trajectory Uncertainties for Airborne Conflict Management

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by  NASA Technical Reports Server (NTRS)

HANDLING TRAJECTORY UNCERTAINTIES FOR AIRBORNE CONFLICT
MANAGEMENT
Richard Barhydt, NASA Langley Research Center, Hampton, VA
Nathan A. Doble and David Karr, Titan Corporation, Hampton, VA
Michael T. Palmer, NASA Langley Research Center, Hampton, VA

Abstract
Introduction
Airborne conflict management is an enabling
capability for NASA’s Distributed Air-Ground The National Aeronautics and Space
Traffic Management (DAG-TM) concept. DAG- Administration (NASA) is studying a new concept
TM has the goal of significantly increasing capacity of operations for the National Airspace System
within the National Airspace System, while known as Distributed Air-Ground Traffic
maintaining or improving safety. Under DAG-TM, Management (DAG-TM) [1]. This concept is
“autonomous” aircraft maintain separation from designed to significantly improve capacity, while
each other and from “managed” aircraft unequipped maintaining or improving safety.
for autonomous flight.
One component of DAG-TM, En Route Free
NASA Langley Research Center has Maneuvering, represents a paradigm shift between a
developed the Autonomous Operations Planner centralized ground-based system to a distributed
(AOP), an onboard decision support system that system. Under this concept, flight crews of
provides airborne conflict management (ACM) and appropriately equipped “autonomous” aircraft fly
strategic flight planning support for autonomous under Autonomous Flight Rules (AFR). These
aircraft pilots. The AOP performs conflict aircraft are able to choose their own route and
detection, prevention, and resolution from nearby altitude, subject to maintaining separation from all
traffic aircraft and area hazards. Traffic trajectory other aircraft. Controllers continue to provide
information is assumed to be provided by separation between “managed” aircraft unequipped
Automatic Dependent Surveillance Broadcast for autonomous flight and traffic flow management
(ADS-B). services for all aircraft. Managed aircraft fly under
conventional Instrument Flight Rules (IFR). Flow
Reliable trajectory prediction is a key
management is normally applied in the form of
capability for providing effective ACM functions.
waypoint speed, altitude, and time constraints at a
Trajectory uncertainties due to environmental
terminal area meter fix. Inside the terminal area,
effects, differences in aircraft systems and
AFR flights revert to IFR.
performance, and unknown intent information lead
to prediction errors that can adversely affect AOP Airborne Conflict Management (ACM)
performance. functions including conflict detection, prevention,
and resolution are key enabling capabilities for
To accommodate these uncertainties, the AOP
DAG-TM. A conflict is defined as a predicted loss
has been enhanced to create cross-track, vertical,
of separation (LOS) between the ownship and
and along-track buffers along the predicted
another aircraft. Conflict detection alerts pilots to
trajectories of both ownship and traffic aircraft.
the presence of a conflict, prevention alerts to a
These buffers will be structured based on prediction
potential ownship maneuver that would cause a
errors noted from previous simulations such as a
conflict if initiated, and resolution gives a
recent Joint Experiment between NASA Ames and
recommended avoidance maneuver to resolve the
Langley Research Centers and from other outside
conflict.
studies. Currently defined ADS-B parameters
related to navigation capability, trajectory type, and All ACM functions compare trajectories from
path conformance will be used to support the the ownship and nearby traffic aircraft. Supporting
algorithms that generate the buffers. information including state vector and intent are
presumed to be broadcast over Automatic programmed flight plan. Tactical control is often
Dependent Surveillance Broadcast [2]. Various used for shorter term goals such as convective
uncertainties are associated with all trajectories and weather avoidance or simple maneuvers around
must be properly managed by onboard systems. traffic conflicts. During flight in a tactical mode
The ACM system should accurately predict the such as “Heading Select” or “Altitude Hold”, the
trajectories within the limits of the information AOP conflict management functions consider only
provided and properly cope with regions of the position and velocity of the ownship. They
uncertainty. consider the four dimensional intent-based
trajectories of nearby traffic, if available [4].
Because trajectory errors cannot be eliminated,
an ACM system must be aware of their potential In addition to the current flight mode, the time
impact on any alerts or guidance provided to the to predicted separation loss also affects AOP choice
pilot. NASA Langley Research Center has of a tactical or strategic resolution. Tactical conflict
developed the Autonomous Operations Planner resolutions in the form of heading, vertical speed,
(AOP) as a prototype avionics system for AFR and altitude commands are offered when this time is
pilots [3]. The AOP interacts with the Flight less than approximately three minutes. Inside this
Management System (FMS) and other aircraft point, there is little time for the pilot to consider and
systems to provide necessary conflict management execute a flight plan amendment.
and strategic flight planning capabilities. As part of
Trajectory uncertainties for tactical control can
these functions, a new AOP capability assesses
include position and velocity vector inaccuracies
features of both the ownship and traffic trajectories
[2]. Due to the shorter time horizon of tactical
that influence the magnitude of along-path, lateral,
operations, however (currently defined to be within
and vertical uncertainties. It applies an appropriate
5 minutes), the AOP emphasizes trajectory
safety buffer that varies along each trajectory and is
uncertainty handling for its strategic system.
based on the local three-dimensional uncertainty.
All ACM functions then work with this modified
trajectory. Strategic Conflict Management
A major anticipated benefit of DAG-TM En
Route Free Maneuvering is the pilot’s ability to
AOP Conflict Management
optimize his route and altitude without coordinating
To accommodate different types of flight
with air traffic control. Outside the terminal area
operations and a range of conflict scenarios, the
(where these operations occur), pilots are likely to
AOP provides both tactical and strategic conflict
use the FMS flight plan to control the aircraft. If an
management capabilities. The tactical system
airspace or traffic conflict occurs in this case, the
works with the own aircraft’s state vector and any
AOP proposes a flight plan change that resolves all
available traffic aircraft intent sent over ADS-B.
conflicts, continues to meet flow management
The strategic system considers the ownship’s active
constraints assigned by ATC, and considers pilot
four-dimensional trajectory and also uses available
efficiency preferences.
traffic intent. These paths usually consist of the
FMS flight plan and include multiple target states. For all strategic conflict management
Activation of the tactical or strategic systems are functions, the AOP compares the four-dimensional
dependent upon the time to predicted separation command trajectory of both the ownship and traffic
loss and the ownship’s current operating flight aircraft [4]. The command trajectory refers to the
mode [3]. path the aircraft will fly if the pilot doesn’t change
any automation modes or settings actively
supporting aircraft guidance. This path may include
Tactical Conflict Management
multiple flight mode transitions. For example, an
The tactical system is geared toward flight aircraft may be flying an FMS descent with a flight
involving inner loop heading, speed, vertical speed, control panel altitude between the aircraft’s current
and altitude commands given by the pilot. When altitude and the end of descent. Its descent will be
flying in these modes, pilots have normally left the limited by the selected altitude [5]. In this case, the
vertical command trajectory consists of the FMS from command trajectory elements broadcast over
descent until the aircraft reaches the flight control ADS-B) with the actual trajectory.
panel altitude and then level flight at that altitude

until the end of the prediction.
Environmental
Changes to the command trajectory normally
result from a pilot input. However, a non- ATOS allows entry of a horizontal wind field
programmed mode transition may also occur that at three dimensional grid points. This grid can also
affects the command trajectory, such as reversion to vary with time during the simulation.
speed priority on descent if the intended vertical
When an aircraft is flying on an FMS flight
path results in an over-speed condition. These
plan, open loop trajectory change points (TCPs)
intent changes can affect conflict predictability. In
such as top of climb and end of descent are affected
the former case, the intent may change as the pilot
by the wind field. If the pilot fails to enter the wind
resets the flight control panel altitude during an
conditions into the FMS prior to a climb or descent
FMS climb or descent. In the latter, a change to
or if the wind is different from that entered, the
speed priority will take the aircraft off the planned
along track position or arrival time of these points
descent profile. Despite these potential
will change from the original prediction. Since
uncertainties, use of the command trajectory to
pilots fly at constant Mach or calibrated airspeed
represent aircraft intent was proposed by the FAA
(CAS) during cruise, a change in wind will affect
and Eurocontrol in a 2000 Technical Interchange
the arrival time at subsequent waypoints.
Meeting [6] and is also supported by RTCA [2].
In addition to pilot control actions or autoflight
Aircraft Performance
mode reversions that may affect the intent-based
The AOP uses a single aircraft performance
trajectory, several factors can lead to differences
model to re-construct the trajectories of traffic
between an aircraft’s predicted trajectory and that
aircraft. During experiments conducted with the
actually flown. In order to study the DAG-TM
ATOS, there are typically several different aircraft
concept, as well as the performance of contributing
models flying within the simulation. The Langley
prototype avionics systems, NASA Langley has
subject pilot and pseudo pilot aircraft models (the
developed the Airspace and Traffic Operations
latter being developed by the National Aerospace
Simulation (ATOS) hosted by the Air Traffic
Laboratory of the Netherlands [9]) have different
Operations Lab [7]. This simulation consists of 12
characteristics. A recent Joint Experiment with
medium fidelity pilot workstations that incorporate
NASA Ames resulted in a third aircraft model when
the AOP. Information is shared over a High Level
Ames aircraft were added to the simulation [10].
Architecture between subject pilot, pseudo-pilot,
and ground stations (the latter located outside the Significant variability in path construction and
ATOL). Within this architecture, AOP guidance features between aircraft types [11] can
performance can be evaluated in the presence of lead to trajectory prediction errors. These
several forms of trajectory uncertainty. differences can include turn anticipation at a
waypoint, descent initiation near top of descent, and
path construction between two waypoints
Sources of Trajectory Uncertainty
containing speed and altitude constraints.
A recent study by Mondoloni and Bayraktutar
identified several types of trajectory uncertainty [8].
Incomplete Intent Information
Categories include environmental effects, variations
in aircraft performance, and incomplete intent Aircraft flying FMS descents within the ATOS
information. Those uncertainty types that are typically broadcast one vertical TCP at the top of
modeled within ATOS and therefore impact AOP descent and another at the end of descent. Lacking
conflict management performance are discussed any information about the middle of descent (such
below. Performance is evaluated based on the as the planned descent speed or deceleration
comparison of the predicted trajectory (as derived points), AOP makes a straight line assumption.
This path assumes constant groundspeed and Joint Experiment
constant flight path angle between the two points.
Figure 1 shows a nominal FMS descent profile Design
with a speed and altitude restriction at the end of
The Joint Experiment between NASA Langley
descent (assumed to occur above the mandatory 250
and Ames Research Centers evaluated air/ground
knot speed restriction below 10,000 ft). A two
coordination issues during DAG-TM en route and
point prediction is superimposed. Assuming the
arrival operations. It also served as a test platform
descent and cruise Mach are the same, the aircraft
for the AOP conflict management and flight
begins its descent at the top of descent. When the
planning functions. Corresponding to the DAG-TM
descent Mach equals the descent CAS, the aircraft
goal of substantially increasing traffic levels in a
tracks a constant CAS until reaching a deceleration
mixed equipage environment (autonomous and
point where the descent shallows prior to the end of
managed aircraft flying in the same airspace), the
descent.
experiment included two primary factors:

• Mixed Operations (comparison of mixture
Top of Descent
of autonomous and managed aircraft in
same airspace vs. managed aircraft alone,

at the same traffic level).
Mach/CAS Transition

• Scalability (addition of increasing levels of
Altitu de autonomous aircraft to level of managed
aircraft occurring under current

operations).
End of
Traffic scenarios were run at three different
Actual Path Descent
traffic levels (“L1,” “L2,” and “L3”), with the L1
Predicted Path level repeated for the “all managed” and “mixed”

autonomous/managed traffic conditions. This
design led to a total of four experimental
Deceleration conditions. The L2 and L3 levels included the same
D istance
number of managed aircraft as the L1 mixed
condition, while adding autonomous aircraft. The
Figure 1. Nominal FMS Descent Profile
L1 level was set to a challenging level based on all-
Compared with Two Point Prediction
managed operations. En route autonomous aircraft
Path features such as a difference between were added at L2 and L3, with L3 representing
cruise and descent Mach or a speed reduction to about twice current day capacity in the sectors
meet the 250 knot restriction may cause additional modeled. The number of aircraft descending to the
variation. These differences can be on the order of terminal area remained the same for all conditions.
hundreds of feet.
The Langley ATOL and Ames Airspace
AOP conflict prediction performance was Operations Lab were connected for the experiment
analyzed for distinct cases that occurred during the and operations at both labs were conducted
Joint Experiment between Ames and Langley simultaneously as part of an overall traffic
Research Centers. The experiment provided a good environment. Twelve subject pilots participated at
platform for comparing differences between Langley (each flying a pilot workstation equipped
predicted and actual trajectories and the operational with AOP). Five subject controllers and nine
impact of those differences for aircraft operating in subject pilots participated at Ames. Pseudo pilots
a DAG-TM environment. monitored pre-programmed background aircraft
added to achieve the desired traffic level. Subject
pilots flew four different traffic scenarios for each
of the four conditions, using a within-subjects
design.
The experimental airspace modeled the Dallas in a way that would cause a near-term conflict for
Ft. Worth area and is shown in Figure 2. Subject another aircraft (defined to be within 4 minutes to
controllers staffed the Amarillo, Ardmore, and predicted LOS). To meet these responsibilities,
Wichita Falls High Sectors and the Bowie Low pilots used the AOP conflict detection and
sector. A pseudo controller handled each “ghost” prevention functions to recognize and prevent
sector and performed handoff duties to the subject conflicts, respectively. For the descent scenarios,
controllers. Aircraft flew in the ghost sectors, but the AOP integrated with the FMS to provide
no data were collected there. Each subject pilot conflict resolutions that met the BAMBE meter fix
flew two overflights and two arrivals for each constraints. During en route scenarios, the AOP
experimental condition. Overflights crossed either looked for minimum path changes to the flight plan.
the Amarillo or Ardmore High sectors. For arriving
Because AFR pilots were solely responsible
aircraft, two streams began in level flight in
for resolving all traffic conflicts, reliable AOP
Amarillo or Ardmore and both included a descent to
conflict management performance was required to
cross the BAMBE meter fix at 250 knots and
ensure separation. A missed conflict detection
11,000 ft. The subject controller used a scheduler
would likely result in a separation violation because
to assign required times of arrival at BAMBE to
controllers were not notified of AFR/AFR conflicts.
each arriving aircraft. The scenario ended for each
As a safety buffer, they were alerted to a near-term
subject pilot when he or she crossed the high
AFR/IFR conflict, but were not required to take
altitude sector for overflights or the BAMBE fix for
action to resolve it.
arrivals. Controllers continued to work traffic until
all subject pilots from Ames and Langley had At the time the experiment took place, conflict
finished. prediction was based solely on a comparison
between the predicted trajectories of the ownship

and traffic aircraft. Pilots were only notified of a
Kansas City
conflict if the two aircraft were predicted to be
Center
within the minimum required separation between

Ghost North the current position and the look-ahead horizon (10
min). No capabilities existed to make a more
Ardmore
Wichita High conservative conflict assessment in regions of high
Falls uncertainty.
Ghost South High
Bowie G Performance Metrics
Fort Worth Low DFW
Cen ter BAMBE TRACON The primary overall experimental performance
metrics were the occurrence of separation violations
Figure 2. Joint Experiment Airspace (subject pilot aircraft within 1000 ft and 5 NM of
traffic) and the pilot’s ability to meet the required
speed, altitude, and time restrictions at the terminal
Pilot Responsibilities and Use of AOP
area meter fix. The latter were only applicable to
When flying as a managed aircraft (25% of all descending aircraft. These results as well as other
runs), pilots followed trajectory instructions from metrics related to DAG-TM concept feasibility are
controllers using conventional IFR procedures. As annotated separately [12].
in today’s operations, the controller was responsible
Relative to AOP conflict management
for separation assurance and traffic flow
performance, comparisons were made between the
management under those conditions.
predicted and actual trajectories. In a few cases
Consistent with AFR, autonomous aircraft where a separation violation was attributed to a
pilots were required to maintain separation from all conflict prediction error, a detailed analysis was
other aircraft and meet the assigned speed, altitude, performed to determine the error category and
and time constraints at the BAMBE meter fix. In likely cause. Two such cases are described below.
addition, AFR pilots were not allowed to maneuver
AOP Conflict Prediction Case Studies
10
m)
In both cases described below, the ownship n
and intruder aircraft were predicted to maintain S (
O
L
adequate separation. Therefore, the pilot was not of 0
alerted to an impending conflict. The actual h
ort
trajectories differed from the predictions N
e
sufficiently to cause an LOS. nc
a
st -10
Di
Case 1
-10 0 10 20 30
In the first case, the ownship (a Langley Distance East of LOS (nm)
subject pilot) was flying straight and level at Flight
Level (FL) 330 after having previously initiated a
lateral strategic resolution maneuver. It was 330
approaching its top of descent point. Traffic (an
Ames pseudo-pilot) was flying straight and level at 325
FL 320, and would cross underneath slightly before el
v
e
ownship’s top of descent. Figure 3 superimposes L 320
ht
tohwe naschtiupa la nandd t rparfefidci catierdc rtarfatj.e cTtowroie ms finour tbeo ttihc kth e Flig 315 OOwwnnsshhiipp APcretudaicl tPeda tPhath
Traffic Actual Path
marks allow direct comparison between the two
Traffic Predicted Path
aircraft and between the lateral and vertical 310 LOS Region
trajectories (top and bottom pane of Figure 3,
-240 -180 -120 -60 0 60
respectively).
Time Relative to LOS (sec)
As shown in Figure 3, the ownship “rounded
the corner” at the top of descent even more than Figure 3. Case 1: Comparison of Actual and
AOP anticipated and initiated its descent slightly Predicted Trajectories
before AOP predicted it would. This difference
Figure 4 shows the actual and predicted lateral
resulted in an LOS (highlighted) with ownship
and vertical separations between the two aircraft. If
descending to within 1000 ft of the traffic before
the ownship had followed the AOP trajectory as
the required 5 nm of lateral separation was
predicted, the two aircraft would have had over 5
regained.
nm of lateral separation before ownship initiated its
descent and no LOS would have occurred.
In this case, the trajectory prediction error can
be traced to a discrepancy in the assumed behavior
near the ownship’s top of descent. After further
study, it was determined that the AOP assumed the
descent would commence precisely at the top of
descent. The ownship guidance algorithm
smoothed this transition and called for the aircraft
to start its descent prior to the top of descent point
provided to the AOP. This top of descent ‘round-
off’ in the guidance algorithm had previously been
designed to be consistent with a particular FMS
type. Even if the AOP trajectory predictor were
tweaked to accommodate this nuance, it would
likely not capture the transition behavior of another
FMS aboard a different aircraft.
12
m) 10 nm)
n (n 8 OS (20
aratio 6 h of L
ep ort Ownship Actual Path
eral S 4 nce N 0 OTrwafnfisch Aipc tPuraeld Picatethd Path
Lat 2 Dista TLOraSffi cR Pegreiodnicted Path
0
-90 -60 -30 0 30 60
-60 -40 -20 0
Time Relative to LOS (sec)
Distance East of LOS (nm)
1200
n (ft) 1000 380
paratio 680000 vel360
e e
S Actual Separation L
ertical 240000 PLOreSd icTtherde sSheopldaration Flight 340
V LOS Start/End Time 320
0
-90 -60 -30 0 30 60
Time Relative to LOS (sec) 300
30 20 10 0
Distance to LOS (nm)
Figure 4. Case 1: Comparison of Actual and
Predicted Separation Figure 5. Case 2: Comparison of Actual and
Predicted Trajectories
Case 2
In the second case, the ownship (a Langley
Concerning the top of descent, it was later
subject pilot) had previously initiated a lateral
determined that the guidance algorithm for the
strategic resolution maneuver for a different
traffic aircraft called for it to fly slightly over the
conflict. At the time of the separation loss, it was
top of descent, then gradually intercept the profile
flying straight and level at FL 330. Traffic (an
from above. This behavior is different, but no less
Ames pseudo pilot) descended out of FL 380 and
correct, than that of the descending aircraft in Case
was predicted to cross ownship’s altitude with
1. In the former case, the top of descent resembled
greater than the required lateral separation.
a fly-by waypoint, whereas it was similar to a fly-
However, the traffic flight path was closer to
over waypoint in the latter. Two different FMS
ownship than predicted. These effects resulted in an
systems and guidance algorithms yielded these
LOS, with traffic passing within 5 nm of ownship
consequential trajectory prediction errors.
while descending through its altitude. Figure 5
superimposes the actual and predicted trajectories Figure 6 shows the actual and predicted lateral
for both aircraft. and vertical separations between the two aircraft. If
the aircraft speed discrepancy had not occurred, the
In this case, the LOS was attributed to a speed
difference in top of descent behavior would only
discrepancy and a difference in the way the top of
have resulted in a higher descent relative to the
descent was defined by the two aircraft. The source
prediction. If this had been the only prediction
of the speed discrepancy is still under investigation.
error, an LOS would not have occurred, because the
lateral separation would never have gone below the
minimum required distance. Because the traffic
aircraft was faster than expected, it was closer to
ownship when the former passed behind and
underneath the latter.
12 both ownship and traffic aircraft. These buffers
m) 10 account for the varying uncertainty that occurs in
n three-dimensional space along a predicted path.
n ( 8
o The buffers allow AOP to represent predicted
ati
ar 6 trajectories as three-dimensional regions of airspace
p
e
eral S 4 ioncsctuearrde do fi ns ipmrpevlei oluinse vs earnsido cnus.r ved segments as
at 2
L
Buffers along a predicted path can be assigned
0
-90 -60 -30 0 30 60 locally using a trajectory-relative coordinate
Time Relative to LOS (sec) system. The axes include cross-track (normal to the
path in the horizontal plane), vertical, and along-
4000
Actual Separation path (used to represent time uncertainty).
n (ft) 3000 PLOreSd icTtherde sSheopldaration Buffers are assigned at progressive points
o
ati LOS Start/End Time along a trajectory, with linear growth or shrink rates
par 2000 describing the rates of change between points.
e
S
al When assembling the traffic aircraft trajectory,
ertic 1000 AOP may generate intermediate points in between
V the received TCPs. These points often capture
0 details of a trajectory change such as the start and
-90 -60 -30 0 30 60
Time Relative to LOS (sec) end of turn or the transition region near top of
descent. For the ownship, AOP uses internal
Figure 6. Case 2: Comparison of Actual and performance models and communications with its
Predicted Separation FMS. It then uses the same criteria for assigning
buffers as those used for traffic aircraft.
Although the LOS in this case can be
attributed to the along-path prediction error, the After adding the buffers, each trajectory can be
vertical prediction is worth noting because such represented as a three-dimensional tube through
differences can lead to LOS events, as occurred in space, the center of which is the aircraft’s predicted
Case 1. In addition, the Mondoloni and Bayraktutar path. The trajectories have an associated time range
study determined that top of descent placement has at each position along the path. AOP’s conflict
a significant impact on the accuracy of the predicted detection routines compare the buffer-enhanced
vertical trajectory [8]. trajectories as four-dimensional objects to
determine regions of potential conflict. When
These two cases represent only a small subset
making this comparison, the entire trajectory region
of potential variation between predicted and actual
is given equal weight. This approach differs from
trajectories. It would be impractical to model the
other conflict probes that determine conflict
precise flight path techniques of all flight
probability [14].
management systems currently in operation [11].
Even for a given aircraft, the tracking performance AOP first compares the two trajectories to see
is not guaranteed to be consistent [13]. whether their vertical separation is ever less than
the minimum required. If so, these regions are
Although some improvements to the fidelity of
evaluated to determine if there is a time overlap.
the AOP trajectory generator will be made as a
Any regions of time overlap are further compared to
result of this experiment, the development of
see whether they lie within the minimum required
trajectory uncertainty-based buffers are seen as the
lateral separation. Remaining segments are marked
primary factor towards mitigating prediction error.
as potential conflicts and the pilots are notified
accordingly.
Trajectory Buffers
The buffers have been designed as a way to
AOP capability has recently been expanded to represent the types of discrepancies observed in
add dynamic buffers to the predicted trajectories of simulation between the actual and predicted
trajectories. They focus on accounting for Vertical Buffers
differences due to environmental conditions and
Vertical buffers are used to represent altitude
aircraft dynamics, performance, and guidance
uncertainty along a path. They are particularly
techniques. Trajectory errors associated with
helpful in addressing the complex and variable
potential intent changes after the predictions are
trajectories associated with FMS climbs and
made are not currently accommodated.
descents. For instance, they can be used to provide
vertical tolerance for the multiple inflection points
Cross-track Buffers shown in Figure 1. If an unexpected tailwind is
encountered during a descent and the pilot does not
While on an FMS-path, cross-track buffers can
add sufficient drag, the aircraft may leave the path
be used to accommodate uncertainty near a
in order to avoid an overspeed condition.
waypoint involving a course change. Potential
errors can include turn anticipation differences or Figure 8 shows how the altitude buffer might
modeling the radius of turn. The latter varies for account for errors in modeling the vertical profile of
fly-by and fly-over turns. These buffers can also an FMS descent without intermediate altitude
represent tracking error between waypoints. constraints. The vertical buffer is relatively small
during level flight. Approaching the top of descent,
Figure 7 shows an example of how these
the buffer below the path grows in order to protect
buffers can be applied, in this case to account for
against an early descent or the “rounding off” effect
errors in modeling the radius of a turn at a
prior to the top of descent. As the aircraft descends,
waypoint. The predicted path is shown as a heavy
the buffer above the path gradually grows until they
line, with a thinner line outlining the region swept
are large both above and below. At the end of
by the cross-track buffer along each segment. In
descent, the buffer below the path shrinks to reflect
this example, the straight-flight segments before
the assumption that the aircraft will level off at the
and after the turn have relatively narrow cross-track
target altitude.
buffers; the buffer grows during the first segment of
the turn, remains wide during the segment in the
middle of the turn, and shrinks again in the last
segment of the turn.
altitude

distance

Figure 8. Vertical Buffers during an FMS
Descent without Intermediate Altitude
Constraints

If the descent has an intermediate waypoint

altitude constraint, the buffers can be locally
reduced to reflect higher vertical path certainty
Figure 7. Cross-track Buffers at a Waypoint
when crossing the waypoint. A comparable process
Turn
can be applied for subsequent descent segments.
When extended to cover non-FMS paths,
cross-track buffers will be able to account for lateral
Along-Path Buffers
uncertainty while an airplane is flying in an air-
referenced mode (such as Heading Hold). In this Along-path buffers are used to represent time
situation, the aircraft’s ground track is subject to uncertainty along the path. This component
changing wind fields. assumes the aircraft follows its predicted path
exactly but arrives at each point earlier or later than algorithms will be designed to use trajectory
expected. elements available for broadcast over ADS-B [2].
This buffer need not grow uniformly on all The RTCA Minimum Aviation System
segments. For example, the error may grow much Performance Standards (MASPS) for ADS-B
faster during a descent segment than while in level provides industry standards for intent broadcast [2].
flight. The along-path buffer may shrink as the The latest version of this document (RTCA/DO-
aircraft approaches a meter fix with a required time 242A) has defined several additional parameters in
of arrival on the assumption that the aircraft will the mode status, state vector, target state, and
comply with the restriction. trajectory change reports that can be used to assess
trajectory uncertainty.
Application to Previous Cases
Mode Status and State Vector Reports
The differences between the actual and
predicted trajectories in the two cases described The mode status and state vector reports
previously can be related to this coordinate system. provide information on an aircraft’s operational
In Case 1 (Figures 3-4), there is good lateral and capabilities and dynamic state, respectively.
along-track agreement. The top of descent “round- Parameters describing the transmitting aircraft’s
off” can be classified as a pure vertical error. navigation accuracy and integrity are contained
within these reports. These parameters indicate the
In Case 2, there is generally good cross-track
capability of an aircraft’s navigation sensors to
agreement with the predicted trajectory. One
accurately determine its position and velocity
exception is the area near the traffic aircraft turn
(accuracy) and to know when its position exceeds a
that wasn’t modeled by the existing version of
containment radius (integrity).
AOP. (Turn modeling has since been added).
There are both vertical and along-path errors for AOP could use this information to apply cross-
this trajectory. The aircraft was faster than track and vertical buffers to the current flight
expected (along-path error), but also began its segment. A sudden drop in integrity may require
descent later than expected (vertical error). In the buffers to expand significantly. Buffer
addition, some inflection points followed by this adjustments due to accuracy changes would likely
aircraft were not modeled by AOP. When be smaller.
converted back to a common time reference, the
along-path error impacts both the aircraft’s lateral
Target State Report
and vertical predicted position. The differences
The target state report contains the target
between the predicted and actual separation are the
altitude and target heading or target track angle of
cumulative effect of the cross-track and vertical
the transmitting aircraft. During straight and level
components of the along-path error (at a given time)
flight, these elements represent the current
with the independent cross-track and vertical errors.
commanded states. For a climb, descent, or turn,
The lateral separation error results from the aircraft
they are the level-off altitude or roll-out heading or
being further along the path (and therefore closer to
track angle commanded by the guidance system.
ownship) than expected. The top of descent occurs
later than expected, but the aircraft also traveled Horizontal and vertical target source indicators
faster than expected. These two effects negate each state whether the respective targets come from the
other and the resulting vertical error is minimal flight control panel, FMS, or are the current state
during the LOS region. values commanded by the autopilot. This
information could be used by AOP to assess the
potential for future intent changes. In general,
Application of Trajectory Uncertainty
flight control panel settings represent tactical
Elements Available over ADS-B
operations that may be more subject to change than
Although the architecture to generate buffers the programmed flight plan.
has been implemented within AOP, the algorithms
to create them have not yet been developed. These