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Observable
Markov
Decision
Processes
11
2.3 Full
Observability
Approximation
12
2.4 Discussion
12
3. COLLISION
AVOIDANCE
IN
TWO
SPATIAL
DIMENSIONS
13
3.1 Action
Space
13
3.2 State
Space
15
3.3 Dynamic
Model
17
3.4 Cost
Function
18
3.5 Optimal
Policy
19
3.6 Example
Encounter
21
3.7 Performance
Assessment
21
3.8 Safety
Curve
22
3.9 E.ciently
Evaluating
Performance
Metrics
23
3.10
Discussion
23
4. ROBUSTNESS
ANALYSIS
25
4.1 White-Noise
Encounter
Model
25
4.2 Correlated
Encounter
Model
26
4.3 Robustness
to
Model
Parameter
Variation
26
4.4 Robustness
to
Model
Structure
Variation
28
4.5 Robust
Dynamic
Programming
28
4.6 State-Based
Robustness
Analysis
31
4.7 Discussion
32
5. COLLISION
AVOIDANCE
IN
THREE
SPATIAL
DIMENSIONS
35
5.1 Partial
Control
Assumptions
35
5.2 Controlled
Subproblem
36
5.3 Uncontrolled
Subproblem
37
5.4 Online
Solution
39
5.5 Example
Encounter
41
5.6 Performance
Assessment
41
5.7 Safety
Curve
44
5.8 Terminal
Cycling
44
5.9 Discussion
45
6. PROBABILISTIC
PILOT
RESPONSE
MODELS
47
6.1 Pilot
Response
Models
47
6.2 Optimal
Policy
49
6.3 Belief
State
Filtering
49
6.4 Example
Encounter
51
6.5 Simulation
Results
53
6.6 Discussion
55
7. STATE
ESTIMATION
57
7.1 Sensing
57
7.2 State
Estimation
Process
57
7.3 Simulation
Results
59
7.4 Sensor
Noise
Robustness
59
7.5 Discussion
63
8. COORDINATION
65
8.1 TCAS
Coordination
65
8.2 Policy
65
8.3 State
Estimation
68
8.4 Action
Selection
69
8.5 Example
Encounter
70
8.6 Simulation
Results
71
8.7 Discussion
73
9. MULTIPLE
THREAT
ENCOUNTERS
75
9.1 Command
Arbitration
75
9.2 Utility
Fusion
76
9.3 Example
Encounter
77
9.4 Simulation
Results
80
9.5 Discussion
80
10. CONCLUSIONS
83
A. EXPECTED
COST
FILE
FORMAT
87
B. TRACKING
89
B.1 Kalman
Filter
89
B.2 Unscented
Kalman
Filter
92
B.3 Horizontal
Tracker
93
B.4 Vertical
Tracker
96
B.5 Discussion
98
References
99
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LIST OF ILLUSTRATIONS
Figure
Page
No.
1 Trajectory
propagation
methods.
4 2 Advisory
transition
model
when
DES1500
is
issued.
15 3 Advisory
transition
model
when
SDES1500
is
issued.
16 4 Optimal
action
plots
for
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