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.
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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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