Robust Airborne Collision Avoidance through Dynamic Programm(42)

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Compatibility Action Selection
Another strategy is to force the aircraft with the higher ICAO address to select a compatible action. If there are multiple compatible actions, then the one with the lowest expected cost is selected. Of course, the expected costs are computed assuming that future actions are unimpeded by compatibility restrictions dictated by another aircraft with a potentially di.erent state estimate. Although the expected costs may be inaccurate, performance is not expected to be signi.cantly impaired. The current TCAS logic uses forced compatibility, although it does not choose compatible actions based on expected cost.

8.5 EXAMPLE ENCOUNTER
Figure
31
shows
an
example
encounter
simulated
from
the
correlated
encounter
model.
Both aircraft are equipped with the TCAS-like sensor. The performance of TCAS is compared with two coordination strategies. The .rst strategy, Joint-Indep, consists of using the joint policy with independent action selection based on independent state estimation. Each aircraft maintains a belief state inferred from its own observations, computes the joint action, and selects its portion of the joint action. The second strategy, Joint-Cent, consists of using the joint policy with centralized action selection based on independent state estimation. The aircraft with the lower ICAO address computes the joint action using the belief state inferred from its own observations, selects its portion of
the
joint
action,
and
transmits
the
other
portion
to
the
other
aircraft.
In
Fig.
31(a),
the
aircraft
approaching from the left has the lower ICAO address. It will be referred to as Aircraft 1; the other aircraft will be referred to as Aircraft 2.
Because the aircraft can disagree about the belief state, the Joint-Indep strategy can poten-tially cause the aircraft to issue incompatible advisories. Indeed, at t = 24s both aircraft receive descend advisories because they both believe they are at the higher altitude. An NMAC occurs at t =40s;theaircraftcomewithin15ftverticallyand356fthorizontally. IntheJoint-Centstrategy, however, because the action selection is centralized, the maneuvers are compatible. At t = 23s, Aircraft 1 issues a descend advisory and transmits a climb advisory to Aircraft 2, which receives it one second later. At the next time step, both advisories are strengthened. The advisories are weakened nine seconds later. The aircraft safely pass each other. TCAS, similarly, selects the same senses: TCAS commands Aircraft 1 to descend at t = 30s and Aircraft 2 to climb at t = 31s. The aircraft come within 87ft vertically and 316ft horizontally.

8.6 SIMULATION RESULTS
The following three coordination strategies were evaluated in the absence of sensor noise on 500,000 encounters from the correlated encounter model:
.
joint policy / independent action selection (Joint-Indep),

.
uncoordinated policy / independent action selection (Uncoord-Indep), and

.
uncoordinated policy / compatibility action selection (Uncoord-Compat).

The
policies
were
generated
using
the
same
model
parameters
and
costs
from
Section
5
with
the
addition of .ve terminal cycles and no clear-of-con.ict reward. The entry distribution is identical to
the
one
used
in
Section
6
and
Section
7.
The
results
are
summarized
in
Table
11,
which
shows
the probability of NMAC and other alert metrics for both aircraft (denoted AC1 and AC2).
TABLE 11
Performance evaluation of coordination strategies with no noise
　
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