7.3 SIMULATION RESULTS

The DP logic, extended to account for state uncertainty using the QMDP method, was evaluated in simulation
and
compared
against
TCAS.
Table
9
summarizes
the
results
of
simulating
one
million
encounters using the white-noise encounter model. The white-noise model used 8 ft/s2 horizontal acceleration and 3ft/s2 vertical acceleration standard deviations. The performance of DP using the DP and simple entry distributions is presented alongside TCAS. The performance of the systems without sensor noise serves as a baseline. During evaluation, the pilot responded deterministically to advisories.
The DP logic was computed using a unit NMAC cost, an alert cost of 0.001, a reversal cost of 0.01, a strengthening cost of 0.009, and a clear-of-con.ict reward of 1 × 10.6. Five terminal cycles were used. The logic was optimized using deterministic pilot response. The same entry distribution as
in
Section
6
was
used.

The DP logic outperforms TCAS on all metrics except for strengthening. Even with the level of sensor noise expected by the current TCAS sensor, the DP logic still leads to greater safety while alerting less frequently. The DP logic also, on average, disrupts the pilot with fewer changes to the advisory and keeps advisories on display for a shorter period of time.
Table
10
summarizes
the
same
performance
metrics,
this
time
estimated
using
the
correlated
encounter model. The DP logic was optimized using an alert cost of 0.01, keeping all other pa-rameters the same. In realistic encounter scenarios with realistic levels of sensor noise, the DP logic
is
twice
as
safe
as
TCAS
even
though
it
alerts
less
than
half
the
time.
Figure
28
shows
the
convergence curves for several metrics from the tables.

7.4 SENSOR NOISE ROBUSTNESS
Because the sensor error may deviate signi.cantly from the sensor error model assumed in Sec-tion
7.1,
it
is
necessary
for
the
logic
to
be
robust
to
di.erent
degrees
of
state
uncertainty.
Figure
29
illustrates the e.ect bearing noise has on the probability of NMAC and of alert for both the DP logic and TCAS. The bearing sensor introduces the most noise in the state estimates, and it is used directly to estimate the DP entry distribution.
The TCAS logic is relatively insensitive to bearing noise because bearing measurements are only used to disable alerting in situations where the projected miss distance is large. The DP logic using the simple entry distribution is also relatively insensitive because it, like TCAS, uses range and range rate to estimate τ . The DP logic using the DP entry distribution is most sensitive to bearing noise because it uses bearing measurements to localize the intruder. In simulations using the correlated encounter model, performance is not signi.cantly degraded with increased noise. The DP logic still results in fewer NMACs and fewer alerts than TCAS. The DP logic appears to be more sensitive to bearing error when evaluated on white-noise encounters. This is due to the fact that many of the white-noise encounters are head-on. A high level of sensor noise causes the system to misjudge the intruder heading and therefore not alert even when the intruder poses a signi.cant threat.
TABLE 9
Performance evaluation on the white-noise encounter model

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

Pr(Alert) 7.51 · 10.1 9.00 · 10.1 9.94 · 10.1 7.16 · 10.1 9.91 · 10.1 9.94 · 10.1 Pr(Reversal) 9.40 · 10.3 4.16 · 10.3 1.91 · 10.1 2.66 · 10.3 3.29 · 10.4 1.93 · 10.1 E[RA duration] 1.15 · 101 1.94 · 101 3.96 · 101 1.32 · 101 2.65 · 101 3.99 · 101
　
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