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In
Table
13,
the
DP
logic
was
optimized
using
a
clear-of-con.ict
reward
of
1
× 10.4. With the exception of the clear-of-con.ict reward, all the other parameters used to generate the logic were
identical
to
those
used
in
Section
8.
In
both
the
perfect
sensing
and
TCAS
sensing
scenarios,
the DP strategies resolve more NMACs than TCAS; they also issue fewer alerts. The summation strategy results in fewer alerts, and consequently more NMACs, than the guaranteed cost strategy because it double counts alert costs.
In Table
14,
the
DP
logic
was
optimized
using
no
clear-of-con.ict
reward.
This
has
the
e.ect
of
making the DP logic safer at the expense of increasing the alert rate and the mean time for which the system displays alerts. The guaranteed cost strategy is almost four times safer than TCAS when there is no sensor noise and twice as safe when there is TCAS-like sensor noise. Removing the clear-of-con.ict reward also has the added advantage of generally decreasing the strengthening and reversal rates of the DP logic.

9.5 DISCUSSION
The experiments demonstrate that combining the expected costs for individual threats can lead to e.ective avoidance behavior that surpasses TCAS in safety with fewer alerts. It appears that this approach has not been pursued in the literature for aircraft collision avoidance. Further analysis is required to identify potential vulnerabilities of this approach. This section focused on encounters where only a single aircraft is equipped with a collision avoidance system. Future work will involve incorporating coordination between equipped aircraft and studying its impact on overall safety.
TABLE 13
Multithreat performance evaluation with clear-of-con.ict reward

Perfect Sensor TCAS Sensor
Guaranteed cost Summation TCAS Guaranteed cost Summation TCAS

Pr(Alert) 6.07 · 10.1 5.46 · 10.1 7.47 · 10.1 7.12 · 10.1 6.38 · 10.1 7.64 · 10.1 Pr(Reversal) 7.35 · 10.3 5.41 · 10.3 5.50 · 10.3 1.63 · 10.2 1.06 · 10.2 6.55 · 10.3 E[RA duration] 1.14 · 101 9.10 · 100 1.92 · 101 1.18 · 101 9.80 · 100 1.95 · 101

TABLE 14
Multithreat performance evaluation with no clear-of-con.ict reward

Perfect Sensor TCAS Sensor
Guaranteed cost Summation TCAS Guaranteed cost Summation TCAS

Pr(Alert) 6.22 · 10.1 5.55 · 10.1 7.47 · 10.1 7.28 · 10.1 6.49 · 10.1 7.64 · 10.1 Pr(Reversal) 7.37 · 10.3 5.40 · 10.3 5.46 · 10.3 1.60 · 10.2 1.03 · 10.2 6.55 · 10.3 E[RA duration] 1.49 · 101 1.16 · 101 1.92 · 101 1.85 · 101 1.52 · 101 1.95 · 101

 

 

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10. CONCLUSIONS

This report has explored the use of dynamic programming (DP) as a method for automatically deriving robust airborne collision avoidance logic. The experiments demonstrate that this ap-proach has the potential to signi.cantly improve safety while reducing the rate of unnecessary alerts compared to the current TCAS logic. In addition, the method satis.es the collection of design considerations introduced at the beginning of the report. This section summarizes how the approach addresses these considerations and identi.es areas where further research is required.
.
Safety performance. The simulations in this report demonstrate that DP can further reduce the risk of near mid-air collision (NMAC) beyond what is currently provided by TCAS while reducing the alert rate. The experiments were conducted using a high-.delity encounter model derived from nine months of national radar data, and NMAC rates were estimated from millions of simulations. The safety provided by the DP logic is a function of the parameters of the cost function against which the logic is optimized. The NMAC rate can be reduced further at the expense of additional alerts, strengthenings, and reversals. Determining the cost function parameters will be an important area of discussion within the TCAS development community because of their impact on safety and operational performance. Further simulation studies will better inform the choice of cost function parameters.
　
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