TABLE 10
Performance evaluation on the correlated encounter model

TCAS Sensor Perfect Sensor
DP/DP Entry DP/Simple Entry TCAS DP/DP Entry DP/Simple Entry TCAS

Pr(Alert) 2.01 · 10.1 3.92 · 10.1 5.03 · 10.1 1.16 · 10.1 4.02 · 10.1 4.66 · 10.1 Pr(Reversal) 7.99 · 10.4 1.88 · 10.3 3.26 · 10.3 2.60 · 10.4 1.70 · 10.3 2.63 · 10.3 E[RA duration] 2.46 · 100 8.14 · 100 1.10 · 101 1.48 · 100 8.13 · 100 1.04 · 101

White-noise model Correlated encounter model

×10.4 ×10.4

00.20.40.60.81 00.20.40.60.81 ×106 ×106

00.20.40.60.81 00.20.40.60.81
×106 ×106

00.20.40.60.81 00.20.40.60.81
×106  ×106 
Number of encounters  Number of encounters 
DP/DP
Entry
(TCAS
Sensor)
DP/Simple
Entry
(TCAS
Sensor)
TCAS
(TCAS
Sensor)
 DP/DP Entry (Perfect Sensor) DP/Simple Entry (Perfect Sensor) TCAS (Perfect Sensor) 
Figure 28. Convergence curves for DP and TCAS with and without sensor noise.

White-noise model Correlated encounter model
×10.4 ×10.4 1 1.5
1
0.5
0.5
0

0 5 10150 5 1015
σχ (deg) σχ (deg)
Pr(NMAC)

DP/DP Entry (TCAS Sensor) DP/DP Entry (Perfect Sensor) DP/Simple Entry (TCAS Sensor) DP/Simple Entry (Perfect Sensor) TCAS (TCAS Sensor) TCAS (Perfect Sensor)
Figure 29. Sensor noise robustness. Each point on the curves was estimated from 500,000 simulations.

7.5 DISCUSSION

This section considered the extension of the logic presented in previous sections to account for state uncertainty using the QMDP method. The method was evaluated using the TCAS sensor with realistic sensor noise parameters. The results of simulations of realistic encounter scenarios suggest that the method works well, surpassing the performance of TCAS in terms of safety and other operational considerations.
Future work could explore the use of other approximation methods and sensor systems. For example, exploitation of GPS-based systems that have the potential of providing more accurate position estimates as well as velocities is likely to enhance the performance of the dynamic program-ming logic. The measurements from such systems can also be used to supplement the information currently provided by TCAS, thus improving its performance. It is important to note that the methodology proposed in this section can accommodate di.erent sensor systems, as the solution of the MDP remains the same regardless of the particular sensor suite installed on the aircraft; no additional o.ine development is required.

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8. COORDINATION

The formulation of the collision avoidance problem in the previous sections assumed that the own aircraft, equipped with a collision avoidance system, encountered a single unequipped intruder. The collision avoidance system could in.uence the trajectory of the own aircraft by issuing advisories to the pilot, but it could not in.uence the intruder aircraft. In situations where both aircraft are equipped with collision avoidance systems, it is important that the advisories be coordinated to reduce the risk of inducing collision.
One way to model the problem of coordinating resolution maneuvers over a communication channel between multiple aircraft equipped with the same system is as a decentralized POMDP with communication
(Dec-POMDP-Com),
but
solving
them
optimally
is
infeasible
in
general
[47–49].
This section discusses a variety of di.erent coordination strategies that di.er in the policies they compute o.ine, their state estimation method, and how they select actions. These strategies are not necessarily optimal but they provide a lower NMAC rate and alert rate than the coordination strategy embedded in TCAS.
　
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