Estimation of Alerting Thresholds forSense-and-Avoid
Dilan Amarasinghe and Siu O’YoungFaculty of Engineering and Applied Science
Memorial University of Newfoundland
St. John’s, NL, Canada A1B 3X5
Email: {dilan.amarasinghe, oyoung}@mun.ca
Tel: +1 (709) 737-3771 and +1 (709) 737-8345
Abstract—In this paper, a method to calculate alerting thresh-olds is outlined along with the assumptions and an example.First, the definitions and recommendations of the FAA sponsoredSense-and-Avoid (SAA) workshop report has been adapted toa formal mathematical definition. These definitions are thenrealized using assumptions and other logic and are translatedinto a more concrete SAA scenarios. Alerting threshold is firstcalculated as a range-based specification and then translated intoa time-based specification using time to closest point of approach(CPA). It is shown that both, range and time based thresholdscan serve important roles in the development of a SAA systemsas well as development of the minimum performance standardsfor SAA. The range-based threshold can be used to define thebaseline sensor specification and the time-based threshold can beused as the minimum CPA for collision avoidance. An exampleof calculating collision avoidance threshold (CAT) for level-turnmaneuvers of the unmanned aircraft (UA) is presented alongwith the results.
I. INTRODUCTION
The capacity to sense-and-avoid other air-traffic has been
identified as an important capability of unmanned aircraft
systems (UAS) to improve the safety when operating in an
integrated national airspace system (NAS). This paper outlines
a method to estimate the alerting thresholds for SAA that is
in alignment with the recommendations of the FAA sponsored
workshop in SAA in 2009 [1]. In this paper, we describe the
method of calculation, the assumptions, their justification, and
a set of example results. Research outlined in this paper is
conducted under the RAVEN II project at Memorial University
of Newfoundland in St. Johns, Newfoundland, Canada.
A. RAVEN II
RAVEN (Remote Aerial Vehicles for Environment Mon-
itoring) is a research project tasked with developing sense-
and-avoid capability for small UAS (sUAS). Under RAVEN
I, the predecessor to the current project, the RAVEN team
acquired capability and capacity to conduct sUAS research.
Currently, we operate two Aerosonde Mk4.2 airframes along
with an assortment of modified RC airframes that are used
for testing. The flight tests are carried out under special flight
operations certificate (SFOC, similar to a COA in the US)
from Transport Canada with the permission to conduct 4-
D synchronized air-to-air encounters using non-type specific
small unmanned aircraft (sUA) airframes on a year-around
basis.
Fig. 1. RAVEN II project is based at Memorial University of Newfoundland,St. John’s. Newfoundland, Canada with the flight test facility at Argentiaairfield.
B. Sense-and-Avoid Research
Primary research objective of the RAVEN II is to develop
sense-and-avoid capability for sUAS. Currently, the two main
regularity restrictions for sUAS operations are: visual range
operations and maximum takeoff weight (TOW) limitation
of 35kg1. In order to perform beyond visual range (BVR)
operations midair collision risk has to be mitigated with sense-
and-avoid capability or equivalent measures. In RAVEN II
project, we are developing analytical and simulation models
to understand the nature of the sense-and-avoid problem and
the core requirements of a SAA system that is in alignment
with the existing and developing standards. The ultimate goal
is to develop a unique technology solution that would suit low
altitude long endurance (LALE) sUAs and that would meet the
expected level of safety for the given operating environments.
C. Prior Work
Work reported in this paper is primarily motivated by [1]
and [2]. The stipulated guidelines to use time-based specifi-
cations is mainly due to the precedent set in the development
of traffic alert and collision avoidance system (TCAS) [3].
1http://www.tc.gc.ca/eng/civilaviation/standards/general-recavi-brochures-uav-2270.htm
978-1-4244-7148-5/10/$26.00 ©2010 IEEE
Several other methods are available to calculate the alerting
threshold. [1] itself outlines a method to calculate collision
avoidance threshold (CAT) and self-separation threshold (SST)
for limited encounter geometries. Wasla/HALE project ad-
dressed the same problem using a similar approach to TCAS
[4]. An optimal method based on game-theoritic formulation
is presented in [2] which, calculates the backward-reachability
set to identify all possible initial conditions of the Intruder.
Although [2] was originally demonstrated for air traffic conflict
identification it can be used to calculate the alerting threshold
using the level-set framework. However, method in [2] has
limited applicability when detailed kinematic or dynamic
models of the aircrafts are used. In this work we have used
a simulation based method to calculate backward-reachability
set using forward simulation in time by adopting the defini-
tions in [1]. The proposed method can accomodate arbitrarily
complex aircraft models as well as avoidance trajectories.
D. Outline
Next section presents the summary of the definitions in [1]
and our interpretation of them such that they lends themselves
to simulation-based calculation. In section III, the method of
estimation is presented followed by results of a case study to
calculate CAT for level-turn maneuvers.
II. DEFINITIONS
In this section, the definitions of alerting thresholds are
outlined. These thresholds are important in defining boundaries
that a UA equipped with a sense-and-avoid system has to
maintain vigilance over, and take appropriate action such that
it maintains the required level of separation with other users
of the airspace.
A. Definitions of Thresholds
In 2009, Federal Aviation Administration (FAA) and De-
partment of Defence (DOD) in United States has recom-
mended that a layered approach, as shown notionally in
Fig. 2, has to be adopted developing SAA solutions. At the
outer layer, UA should take action, before a given separation
threshold, to remain well-clear of air traffic using standard
operating procedures that apply to the airspace class which,
is termed self-separation threshold (SST); and at the inner
layer it should maneuver in any way that is safe to avoid near
midair collisions (NMAC), before a given separation threshold
which, is termed collision avoidance threshold (CAT). These
definitions use a common concept that UA should initiate
action before a given threshold (SST or CAT), to preclude
the intruder from penetrating the inner layer (CAT or collision
volume (CV), resp.).
B. Interpretation of Threshold
In order to compute each threshold, they can be interpreted
as follows. If the intruder is outside the threshold, the UA will
have at least one maneuver to evade to safety for all possible
maneuvers of the intruder. If Intruder is inside the threshold,
UA will not have any maneuvers that could take it to safety
Fig. 2. Layered model of the airspace surrounding the UA.
for all possible maneuvers of the intruder. This interpretation
is compliant with the definition of both SST and CAT in the
SAA workshop report and can be formally represented as:
1. CAT: ∀ xInt.(τ2) and ∀ m ∈ uInt., ∃ m ∈ uCAUA s.t. CV
2. SST: ∀ xInt.(τ1) and ∀ m ∈ uInt., ∃ m ∈ uSSUA s.t. CAT
where, for co-altitude encounters xInt. = [x, y, ψ, v, ψ̇] and
m = [v, ψ̇]. uSSUA is the set of all moves of the UA that
can be used for self-separation and uCAUA is the same for
collision avoidance. Thus, this interpretation defines an in-
terface between two regions (between safe and unsafe initial
conditions) in the intruder initial condition state-space. In
the above expressions of the CAT and SST the only known
threshold is the CV itself which, is a UA centered cylinder with
a 500 ft radius and 200 ft height in height. Therefore, first,
CAT and has to be calculated using CV and then, SST using
CAT. An encounter simulation based approach, as described
in the next section, is used to calculate the safe and unsafe
initial conditions of the intruder.
III. IMPLEMENTATION
A computer program has been implemented to estimate the
alerting thresholds based on the interpretation outlined in the
previous section. In order to concretely define the alerting
thresholds, the variables that are used in its declaration should
be concretely defined. This section, first defines the maneuvers
of both UA and the Intruder and then describe the method of
estimation.
A. Types Maneuvers
In order to estimate the alerting thresholds, all possible
maneuvers of the intruder, uInt. and the maneuvers that can
be used by UA for CA and SS, uCAUA and uSS
UA resp., has to be
defined.
1) UA Maneuvers: All users of the NAS are expected to
follow a set of rules and thus are expected to demonstrate
a predictable behaviour. In accordance with this principle,
SAA workshop report recommends that when performing SS,
UA could only use regular maneuvers that is used in mission
scenarios. However in CA, UA is allowed to operate outside its
mission performance envelope as a last-ditch effort to maintain
aircraft separation.
2) Intruder Maneuvers: Although “all possible maneuvers
of intruder” as defined in Section II-B are computationally
intractable to implement, the intruder maneuvers can be
categorized based on its intention and typical operational
procedures. Five possible categories of intruder maneuvers has
been identified and outlined in Table 1.
TABLE ITYPES OF INTRUDERS BASED ON THEIR INTENT AND TYPICAL
OPERATIONAL PROCEDURES.
Name Descriptoin
Non-
maneuve-
ring
In this mode, intruder continues in a straight
line throughout the encounter. i.e. v = con-
stant and ψ̇ = 0Open-
loop
The Intruder will continue at the same input
throughout the encounter. i.e. assuming that
intruder is oblivious to the presence of the
UA ( v = constant and ψ̇ = constant).
State-
feedback
Intruder attempts to intercept the UA, given
that it has the current state information of
the UA. This case is same as an intruder
that continuously monitors the UA in order
to intercept it.
Non-
anticipat-
ory
Intruder attempts to intercept the UA, given
that is has the current state information of the
UA and the current input to the UA. In this
scenario intruder can accurately anticipate
the next immediate move of the UA.
Anticipat-
ory
Intruder attempts to intercept the UA, given
that is has the complete trajectory informa-
tion into the future. This type of intruder is
the most lethal of all antagonistic intruders.
From the above categorizations, only first two represent the
most realistic scenarios in the current airspace. Thus, only
those two have been used in the simulations presented later in
this paper.
3) Encounter Simulations: Once maneuvers for each air-
craft are selected, UA and Intruder can be simulated using
the preferred dynamic or kinematic model that lends itself
to fast-time simulation. Each encounter is simulated with
the required number of simulated intruders and UAs. All
simulated intruders start from the same initial pose ([x, y, ψ])and heading velocity. All UAs start at the origin and facing
east with the same UA heading velocity. As shown in Fig. 3,
an encounter between a single simulated intruder and a UA can
result in either with a safe CPA or with a NMAC. Simulation
terminates when one of these conditions occurs. If all escape
maneuvers of the UA become invalidated through NMACs, the
initial condition of the intruder is labeled as unsafe. If there
are one or more safe escape maneuvers for the intruder then
the initial condition of the intruder will be labeled as safe.
Fig. 3. Unsafe and safe encounters.
Fig. 4. A example encounter simulation where Intruder starts from a unsafeinitial condition.
Fig. 4 shows a simulated encounter for one intruder initial
pose that results in a NMAC for all escapes maneuvers of
the UA. It is simulated with unmanned aircraft velocity of
60 knots, turn rate of 12 deg/sec, intruder velocity of 120
knots, and turn rate of 3 deg/sec. Simulated UA and intruder
trajectories are shown in green and blue, respectively. The UA
trajectories change their color to red when they get invalidated
through NMAC by at least one intruder trajectory.
B. Estimation of Range-based Alerting Thresholds
In order to estimate the shape and form of the interface
between safe and unsafe regions, two methods are used to
organize the simulations: grid-based method and tracking
method.
1) Grid-based Method: In grid-based computation of alert-
ing thresholds, entire neighborhood of the UA is tested to
discover the interface between safe and unsafe regions. Fig. 5
shows a result of a grid-based simulation. Grid-based method
can be used to study the time to safety in safe region as well
as time to NMAC in unsafe regions of the entire neighbor-
hood that is tested. Although, all the tests can be performed
in parallel, grid-based simulations can become prohibitively
computationally expensive especially when large number of
intruders and UAs are used in a single simulation, as well as
when denser grids are used to increase the resolution of the
boundary.
Fig. 5 shows the plot of all initial conditions in grid-based
calculations of the safe (red) and unsafe (blue) regions with
the UA at the center and moving eastwards. The red area in the
center represents the unsafe areas surrounding the UA and the
red area in front shows the initial conditions of the Intruder,
Fig. 5. Results of a grid-based simulation.
where if UA acts early, that is unsafe.
2) Boundary Tracking Method: Compared to grid-based
method, the alerting thresholds can be searched and tracked
much faster by testing lesser number of initial conditions.
Although it is faster and can discover the thresholds at higher
resolutions, it cannot detect the other regions outside of CAT,
which are not safe as shown in Fig. 5. Also tracking method
might suffer from inconsistencies in the boundary due to
discretization in intruder and UA inputs as well as time. A
typical threshold generated through tracking is shown in Fig. 6.
It shows a plot of the CAT boundary calculated using boundary
tracking method for a head-on encounter (UA: v = 60 knots,
turn rate= 12 deg/sec Intruder: v = 120 knots, zero turn rate).
Fig. 6. Results of the tracking method for a head-on encounter.
Owing to its computational efficiency, tracking method was
used throughout this study. Grid-based method was used only
to gain insight into the structure of the unsafe regions in few
specific cases.
C. Deriving Time-based Alerting Thresholds
While range-based specifications have their own advantages,
size of the range-based CAT varies significantly with the
closure rate of the aircrafts. In order to reduce this dependency
and simplify the specification of the thresholds, a time-based
specification is derived from the range-based specification.
For each initial condition of the range-based threshold, time
to straight line CPA [5] of the UA and the converging Intruder
can be calculated. As shown in the Fig. 7, the CPA time
varies for each initial condition on the range-based threshold.
Thus, for each relative heading angle, CPA time for each
initial condition that makeup the range-based threshold can be
tabulated. The main parameter that attributes to the changes
in CPA value is the lateral offset of the Intruder and it can
be abstracted out by selecting the maximum CPA value for
a particular relative heading. For relative angle ψ = 180◦ as
shown in Fig. 7, abstracted time based CAT will be 7 seconds.
Fig. 7. Variation of the CPA time from different points on the CAT (UA: v= 60 knots, turn rate= 12 deg/sec Intruder: v = 120 knots, zero turn rate).
D. Procedure for Estimating Alerting Thresholds
The method described in this section can be summarized as
a step-by-step procedure as listed below:
1) Select the set of collision avoidance or self-separation
maneuvers for UA.
2) Select the set of maneuvers for Intruder.
3) Select the method of estimation (grid-based or tracker-
based).
4) Select parameters for: (a) UA and Intruder performance
envelopes, (b) encounter parameters (simulation time
and spatial resolution, encounter heading, etc.), and (c)
CV and CAT for estimating CAT and SST, resp.
5) Run the simulation.
6) Derive range-based alerting thresholds at a suitable level
of abstraction.
7) Calculate CPA for range-based thresholds.
8) Derive time-based alerting thresholds from CPA values,
at a suitable level of abstraction.
IV. COLLISION AVOIDANCE THRESHOLD (CAT)
The procedure outlined in the previous section was used to
estimate the CAT for level-turn co-altitude encounters between
UA and Intruders. In this section results of the CAT estimation
methods are presented along with the assumptions.
A. Assumptions
Following assumptions are made in the process of calculat-
ing the CAT:
1) Co-altitude Encounters: Only co-altitude encounters are
studied in this work. Thus, the state of UA and intruder can
be reduced to [x, y, ψ, v, ψ̇] where, variables are longitude,
latitude, heading, heading velocity, and turn rate, respectively;
and heading velocity and turn rate controls each aircraft. In
this study heading velocity is assumed to be constant in all
conditions unless otherwise mentioned.
2) Intruder Turn Rate Restrictions: It is noted that as the
maximum allowable intruder turn rate increases, the CAT
grows outward and becomes unbounded. Thus in the simula-
tions intruder turn rates have to be restricted to lower values.
However, this threshold in turn rate varies according to the
intruder and UA heading velocity. Thus, in this work only
non-maneuvering (zero turn rate) intruders are considered.
3) UA Evasive Maneuvers: A simpler evasive maneuever is
selected for UA that turns the aircraft to a chosen heading at
its maximum turn rate and maintains the heading. Thus, once
evasive maneuver is initiated it is assumed that UA is able
to maintain the required separation without any further active
monitoring of the Intruder.
B. Range-based CAT
Using above assumptions and the tracking method, CAT
is estimated for different relative heading, between intruder
and UA. Following parameters were used in the simulations:
spatial resolution = 30 ft, time resolution = 50 ms, number
samples for UA = 720, number samples for Intruders = 1
(minimum requirement for non-manuvering case), and heading
resolution = 2◦.
1) Results: Fig. 8 shows the range-based CAT for three
different relative heading angles. They have maximum ranges
of about 0.19, 0.34, and 0.35 nautical miles, respectively. Fig.
9 shows the plot of maximum range of the CAT for all relative
headings. For the type of intruder and the UA, the CAT has a
maximum range of about 0.4 nm.
Fig. 8. CATs for relative heading of 0◦ (tail-chase), 90◦ (side-on), and 180◦(head-on) (UA: v = 60 knots, turn rate= 12 deg/sec Intruder: v = 120 knots,zero turn rate).
Fig. 9. Plot of the maximum range of each CAT (convex hull of CATs forall relative headings) (UA: v = 60 knots, turn rate= 12 deg/sec Intruder: v =120 knots, zero turn rate).
2) Applications: Range-based CAT can be used as min-
imum sensor range requirement given it is the latest point
before which a converging intruder has to be detected. Also
when UA is in the air, the time CPA with a converging intruder
less the time-based CAT value will provide the available
time budget for tracking, estimation and collision avoidance
functions.
C. Time-based CAT
The time-based CAT is derived from the range-based CAT
using the method outlined in section III-C. The main parameter
that causes most change in CPA value is the lateral offset of the
intruder and it can be abstracted out by selecting the maximum
CPA value (τ2) for a particular relative heading. Fig. 10 shows
the variation of the τ2 with the relative heading angle. For the
type of aircrafts analyzed in Fig. 10, head-on encounters have
a τ2 of 7.0 seconds while tail-chase case has around 11.6 sec
τ2.
Given the information in Fig. 10 and assumptions, it can
be concluded that, if current relative heading of the intruder is
known and if it remains constant during the encounter, we can
assume a universal τ2 of 11.6 seconds for the type of aircrafts
that were analyzed.
1) Sensitivity: Fig. 11 and Fig. 12 shows the effect of
Intruder velocity has on range-based and time-based CAT,
resp. As can be seen, time-based CAT shows much less
variations compared with range-based CAT. In the head-on
encounters, the τ2 remains the same when intruder velocity
changes while range changes about 400%. When the aircraft
are in tail-chase scenarios, τ2 only decrease about 30% while
range increases about 375%.
V. CONCLUSION
We presented a method to estimate alerting thresholds for
co-altitude encounter as both range-based and time-based
Fig. 10. Maximum Tau2 for all relative headings of the intruder with amaximum of 11.6 seconds in the zero relative heading, tail-chase case. (UA:v = 60 knots, turn rate= 12 deg/sec Intruder: v = 120 knots, zero turn rate).
Fig. 11. CATs for various intruder velocities as shown (UA: v = 60 knots,turn rate= 12 deg/sec Intruder: v = [as shown], zero turn rate).
specifications. Based on our observations the following can
be stated as concluding remarks:
• Definitions of the SAA workshop report can be adopted
to formulate a method for estimating CAT and SST;
• The method proposed in this paper can be used to, first,
calculate CAT and then SST;
• Range-based CAT is found to be useful in deriving
minimum field of regard for sensors that will be used
for sense-and-avoid, and
• It can be concluded that, based on our artificial assump-
tions, a time-based CAT can be used as a single spec-
ification for collision avoidance for a range of intruder
Fig. 12. Variation in the tau2 boundary with intruder velocity (UA: v = 60knots, turn rate= 12 deg/sec Intruder: v = [as shown], zero turn rate).
types.
ACKNOWLEDGMENT
We would like to acknowledge the financial support from,
Atlantic Canada Opportunities Agency (ACOA), Memorial
University of Newfoundland (MUN), Natural Sciences and
Engineering Research Council of Canada (NSERC), Provincial
Aerospace Limited (PAL), Defence Research and Develop-
ment Canada (DRDC), and Government of Newfoundland and
Labrador.
REFERENCES
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