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Extensibility. Changing the probabilistic model to better re.ect the evolving airspace char-acteristics and pilot behavior is relatively straightforward, and re-optimizing the logic in response to these changes does not require any human e.ort. Modifying TCAS pseudocode is much more complicated. The primary limitation of the DP approach is that the model must be Markovian and must be capable of being approximated well by a discrete state space of manageable size. Other DP methods could be employed besides the one used in this report to help scale the method to more complex models.

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Validation. The validation of the DP logic will likely involve many of the same steps used to validate TCAS, including Monte Carlo simulation and .ight tests. Additional validation techniques can be employed due to the fact that the model used by DP is Markovian. This report showed to e.ciently compute the probability of NMAC as well as other performance metrics across the entire state space in under a minute. Performing the same computation using Monte Carlo, which is what would be required for a logic like TCAS, would have required months of continuous computation.

.
Veri.cation. The correctness of a manufacturer’s implementation of the TCAS pseudocode is veri.ed against a set of test encounters. The DP logic can be veri.ed in the same way. However, just because an implementation satis.es all test cases does not mean that it is cor-rect since it is not possible to test every possible encounter situation. With the DP logic, the complexity of the logic can be encoded using numerical lookup tables that can be standard-ized and delivered to manufacturers. Because there is very little code for manufacturers to implement, there is less opportunity for errors to be introduced.

This report has answered the primary research questions left open in Project Report ATC-360, but additional study of multiple threat encounters and interoperability is still required. Further study will also compare the behavior of the DP logic to other approaches, such as geometric optimization, that do not leverage probabilistic models to infer the optimal course of action. Before committing to a particular development strategy for future TCAS it is important to evaluate the relative merits of di.erent approaches from the perspective of development cost and risk over the entire life cycle of the system, in addition to anticipated safety and operational performance. A future paper will address these issues.

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APPENDIX A
EXPECTED COST FILE FORMAT

This appendix describes the .le format for the expected cost table. The expected cost table contains the expected costs stored using the 64bit IEEE 754-1985 double precision .oating point format. Because the number of available actions from a particular state is small compared to the total number of actions (e.g., one cannot strengthen or reverse until an initial advisory is issued), memory may be more e.ciently utilized by only storing the costs for the available actions.
An index .le is used to e.ciently locate the position in the expected cost table. The index .le contains a sequence of unsigned 32bit integers, containing o.sets into the cost table. For example, in
Fig.
A-1,
the
expected
costs
for
the
second
state
can
be
found
by
skipping
the
.rst
three
entries
in the table, corresponding to 3 × 64 bits from the beginning of the .le. If more than 232 . 1 state-action pairs are needed, then the representation of the index .le would need to be increased from 32 bits. If there are N states, then there are N + 1 entries in the index .le. The last entry contains the o.set to one entry past the last.
For each state, the cost table contains a sequence of values. To determine which value corresponds to which action, a table of actions is used. Because there are no more than 255 actions, the action .le uses unsigned 8bit numbers. The action .le contains the same number of entries as the cost table, but it is eight times smaller because it uses an 8bit instead of a 64bit representation.
　
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