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time distribution, in comparison, has less support but a comparable conditional mean
of 17.12 s. Only 15% of the probability mass is concentrated on
τ
≥
40
s. The point
estimate of
τ
using the simple method is 21.65 s.
After the descend advisory is issued, the intruder begins to increase its descent, caus-
ing the DP logic to reverse the descend to a climb 20 seconds into the encounter. The
pilot begins the climb maneuver three seconds later. Once the aircraft are safely sep-
arated, the DP logic discontinues the advisory at
t
=31
s. The minimum horizontal
separation is 342 ft, at which time the vertical separation is 595 ft. No conflict occurs.
TCAS initially issues a climb advisory four seconds into the encounter because it an-
ticipates, using straight-line projection, that by climbing it can safely pass above the in-
truder. Nine seconds later, when the own aircraft is executing its climb advisory, TCAS
reverses the climb to a descend because it projects that maintaining the climb will not
provide the required separation. TCAS strengthens the advisory three seconds later, but
fails to resolve the conflict. The aircraft miss each other by 342 ft horizontally and 44 ft
vertically. Although the TCAS logic alerts earlier and more often, the DP logic still
outperforms it in this example encounter.
·
10
4
DP logic
TCAS logic
No logic
Intruder
4
.
4
4
.
2
−
40
−
20
0
20
40
Time (s)
Fig. 3.
Example encounter comparing the system with the DP entry time distribution against
TCAS
6.3
Performance Evaluation
Table 4 summarizes the results of simulating the DP logic and the TCAS logic on one
million encounters generated by the model of Section 5. The table summarizes the
number of conflicts, alerts, strengthenings, and reversals.
As the table shows, the DP logic can provide a much lower conflict rate while sig-
nificantly reducing the alert rate. The Monte Carlo entry time distribution results in a
greater number of conflicts, but it alerts less frequently than the other methods. Increas-
ing the number of samples used generally improves performance but increases online
