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

[1] “Sense and Avoid (SAA) for Unmanned Aircraft Systems (UAS),” FAASharepoint Website [Accessed: November, 2009], FAA/DOD Sponsored”Sense-and-Avoid” workshop, October 2009.

[2] A. M. Bayen, S. Santhanam, I. Mitchell, and C. J. Tomlin, “A differentialgame formulation of alert levels in ETMS data for high altitude traffic,”in AIAA GN&C Conference, 2003.

[3] F. A. Administration, “Introduction to TCAS II Version 7,” U.S. Depart-ment of Transportation, Tech. Rep., November 2000.

[4] J. Meyer, D. Altenkirch, R. Knorr, A. Lenz, and T. Schattel, “Sense &Avoid for UAVs,” in 22nd Bristol UAV Systems Conference, April 2007.

[5] D. H. Eberly, 3D Game Engine Design: A Practical Approach to Real-Time Computer Graphics. Morgan Kaufmann, 2000.