1.3.2 Real-Time Usage
At some update rate, the surveillance system will measure the positions of the intruder aircraft. The current TCAS surveillance system measures range and bearing of the local air tra.c and decodes the altitude information transmitted by their transponders. Other surveillance inputs, such as satellite-based position reports, may be used in the future, but this report focuses on the surveillance data currently provided by the TCAS surveillance system.
The current state of the world cannot be known exactly; it can only be inferred from the sensor measurements with some degree of con.dence. The collision avoidance system updates a probability distribution over the set of possible states based on the sensor measurements. This probability distribution is used to compute the current expected costs for the various actions. The system simply executes the action with the lowest cost.

1.4 RECENT ADVANCES
The general approach pursued in this report was originally proposed in Project Report ATC-360
[12].
Although
this
report
will
review
the
important
concepts
from
Project
Report
ATC-360,
the focus will be on recent advances, which include:
.
Advisory changes. The previous report assumed that once an advisory is issued, it cannot be changed. However, depending on how an encounter evolves, TCAS will either strengthen or reverse the original advisory. Because it is impossible to know exactly the future trajectories of aircraft, the provision for strengthening and reversing advisories is critical to reducing collision risk.

.
Motion in three spatial dimensions. The model used to derive the logic in the previous report was essentially two dimensional. This report models aircraft motion in three spatial dimensions. Enhancing the realism of the model used to optimize the logic results in improved performance when deployed in the real world.

.
Probabilistic pilot response models. The previous report assumed a deterministic pilot re-sponse to resolution advisories. The response model was based on that used by TCAS, which assumes that the pilot responds to an initial advisory in exactly 5 s with 1/4g acceleration. Because pilots respond to their advisories with variable delay and strength, this report at-tempts to model this variability explicitly when optimizing the logic. Accounting for the relative likelihood of di.erent pilot responses improves the robustness of the optimized logic.

.
State estimation. The previous report assumed that the current state of the world, which includes the positions and velocities of the aircraft, is perfectly known. However, the TCAS sensor is imperfect, and so the state can only be estimated. This report uses a sensor model and dynamic model together to estimate a probability distribution over states based on sensor measurements. This distribution is then used to decide when to alert and which advisory to issue. Leveraging an explicit sensor model allows the logic to be robust against noisy measurements.

.
Coordination. The previous report assumed that the intruder was not equipped with a colli-sion avoidance system. If both aircraft are equipped with a collision avoidance system, they can coordinate their advisories over a communication channel to further enhance safety. This report explains how the logic can be optimized for coordination with other aircraft.

.
Multiple threat encounters. The previous report assumed a single intruder, but as the density of the airspace increases, encounters with multiple intruder aircraft will become increasingly likely. This report explains how to accommodate encounter scenarios where multiple aircraft pose a collision threat.

1.5 OVERVIEW
Section
2
introduces
Markov
decision
processes
(MDPs)
as
a
way
　
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