4.2 CORRELATED ENCOUNTER MODEL
The white-noise encounter model is useful for evaluating the robustness of the logic as the process
noise parameter σ¨
white-noise acceleration model is the same as that assumed in the logic optimization process. To
determine the robustness of the logic to a signi.cantly di.erent model structure, the performance
of the logic is evaluated on a higher-.delity encounter model, called the correlated encounter model,
derived
from
nine
months
of
recorded
radar
data
[39,40].
The correlated encounter model represents the variables governing the initialization of the encounter
as
a
Bayesian
network
[41].
The
Bayesian
network
represents
a
probability
distribution
over sixteen variables such as airspace class, category of aircraft, initial airspeed, and acceleration. The dynamics of the aircraft are represented by a dynamic Bayesian network, which captures the changes in turn rate and vertical rate over time.
4.3 ROBUSTNESS TO MODEL PARAMETER VARIATION
This section analyzes the robustness of the optimized logic on the white-noise encounter model with varying process noise parameter. In the following discussion, the modeled noise parameter refers
h
is varied. However, the assumption that the vertical motion is governed by a
h
to σ¨ used when optimizing the logic, and the environment noise parameter refers to σ¨ the white-noise encounter model during evaluation.
Inthe.rstsetofexperiments, themodelednoiseparameteriskept.xedat8ft/s2. Two policy
h
used in
h
slices for this setting of σ¨ 0ft/s2 to 15ft/s2
are
shown
in
Fig.
8.
The environment noise parameter is varied from
. The
performance
of
both
the
optimized
logic
and
TCAS
are
shown
in
Fig.
9.
Each point on the curves was estimated from one million simulations.
Due to the way encounters are initialized, trajectories with zero acceleration noise will always result in an NMAC unless an advisory is issued. When the environment noise parameter is zero, both TCAS and the DP logic alert in every encounter and successfully prevent NMAC. As the environment noise parameter increases, the system predictability decreases and some encounter trajectories diverge, initially causing the alert rate to decrease and the NMAC rate to increase for both the TCAS logic and the DP logic. The DP logic reaches its lowest alert rate when the environment noise matches its optimized value of 8ft/s2.
Increasing the environment noise above the modeled noise degrades performance, but the logic remains robust regardless of whether the noise is over-or under-estimated. Regardless of the actual environment noise, the DP logic is su.ciently robust to signi.cantly outperform TCAS.
0 5 101520253035
τ (s)
(a) h˙0 = 0ft/min,h˙1 = 0ft/min,sRA = COC
0 5 101520253035
τ (s)
(b) h˙0 = 1000ft/min,h˙1 = 0ft/min,sRA = COC
Figure 8. Optimal action plots when σ¨ = 8ft/s2.
h
×10.3
1
0.8
6
Pr(Alert)
Pr(NMAC)
4
0.6
0.4
2
0.2
00 5 10 15 00 5 10 15
Environment noise (ft/s2) Environment noise (ft/s2)
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