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As
shown
in
Fig.
33(b),
this
guaranteed
cost
strategy
results
in
an
alerting
region
similar
to the closest command arbitration strategy, but it does not have the issue identi.ed earlier where the own aircraft descends to avoid the closer intruder but results in entering the path of another intruder.
The sum-collision/max-action (SCMA) strategy involves partitioning the expected cost due to collision from the expected cost due to alerting.4
Given an agent n and action a,
(n)(n)
J(n)(a)= Jcollision(a)+ Jaction(a). (33)
DP can be used o.ine to compute the collision cost and the action cost for every discrete state-action pair. The results would be stored in a table. During execution, f would combine these costs as follows:
(1) (1)(N)(N)(n)(n)
f(Jcollision(a),Jaction(a),...,JJcollision(a) + maxJaction(a). (34)
collision(a),Jaction(a)) =
n
n
Figure
33(c)
shows
the
alert
regions
for
SCMA.
It
does
not
double
count
alert
costs,
but
it
does
sum the collision costs. Because collision with two aircraft is twice as costly as collision with one aircraft, the alert region is enlarged.

9.3 EXAMPLE ENCOUNTER
Figure
34
exhibits
the
behavior
of
the
guaranteed
cost
strategy
and
the
TCAS
logic
in
an
example
multithreat encounter. The multithreat encounter was sampled from a multithreat model built from radar
data
[52].
There
is
no
sensor
noise,
and
both
intruders
are
unequipped.
Eleven
seconds
into
the encounter, the DP logic issues DES1500. The expected costs for issuing DES1500, CL1500, and COC are 0.00595, 0.00741, and 0.00601 for intruder 1, respectively. As intruder 2 is moving away from the own aircraft, thus posing no signi.cant threat, the expected costs are 0.001, 0.001, and 0 for intruder 2, respectively. Fourteen seconds later, the DP logic issues SDES2500. As the advisory is later terminated, the own aircraft levels o., safely passing between both intruders in altitude. One potential issue with the guaranteed cost strategy is that it can cause the own aircraft to pass between
the
intruders,
as
shown
in
Fig.
33(b).
If intruder 2 happened to be a more imminent threat, the own aircraft would have had to climb after its descent. The TCAS logic issues CL1500 and subsequently SCL2500 to pass over both intruders, but they are too late. An NMAC occurs with intruder 1.
4The SCMA strategy was originally proposed by Richard Williams from Lincoln Laboratory.

(a) Summation utility fusion strategy.

(b) Guaranteed cost strategy.

0 10203040
(c) SCMA strategy.
Figure 33. Utility fusion strategies. Two intruder aircraft are on the left. All aircraft are initially level and no advisory has been issued. Horizontal axis is time (s) and the vertical axis is altitude (ft). The parameters from
Section
3
with
zero
terminal
cycles
were
used.

Time (s)
(a) Vertical pro.le.
×104
1
North (ft)

.2 .1.5 .1 .0.50 0.51
East (ft)
.1
(b) Horizontal pro.le.

9.4 SIMULATION RESULTS

Table
13
and
Table
14
summarize
the
results
of
evaluating
the
guaranteed
cost
and
summation
util-
ity fusion strategies on 500,000 multithreat encounters. In these encounters one aircraft, equipped with the collision avoidance system, encounters two unequipped intruders. The tables summarize the performance of the strategies in the absence of sensor noise and when the equipped aircraft uses the TCAS-like sensor. The performance of the TCAS multithreat logic is also shown.
　
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