Aerospace and Electronic Systems Magazine April 2018 - 43

Tang, Zhu, and Fan
Table 2.

2 is changing, the distance criteria are used as the main threshold
to detect conflict. At 9:37:30, their horizontal and vertical distance

Waypoints of Partial Trajectories of the Involved
Aircraft

are respectively:

Time

Aircraft

X(NM)

Y(NM)

Z(ft)

9:37:19

Aircraft 1

12.37

6.41

15,100.00

9:37:19

Aircraft 2

19.87

6.41

15,350.00

9:37:19

Aircraft 3

12.38

6.39

15,350.00

9:37:20

Aircraft 1

12.47

6.49

15,096.67

9:37:20

Aircraft 2

19.72

6.49

15,348.33

9:37:20

Aircraft 3

12.73

6.47

15,352.00

9:37:21

Aircraft 1

12.57

6.57

15,093.33

9:37:21

Aircraft 2

19.57

6.57

15,346.67

9:37:21

Aircraft 3

13.08

6.55

15,354.00

9:37:22

Aircraft 1

12.67

6.65

15,090.00

9:37:22

Aircraft 2

19.42

6.65

15,345.00

9:37:22

Aircraft 3

13.43

6.63

15,356.00

9:37:23

Aircraft 1

12.77

6.73

15,086.67

9:37:23

Aircraft 2

19.27

6.73

15,343.33

9:37:23

Aircraft 3

13.78

6.71

15,358.00

9:37:24

Aircraft 1

12.87

6.81

15,083.33

9:37:24

Aircraft 2

19.12

6.81

15,341.67

9:37:24

Aircraft 3

14.13

6.79

15,360.00

9:37:25

Aircraft 1

12.97

6.89

15,080.00

9:37:25

Aircraft 2

18.97

6.89

15,340.00

9:37:25

Aircraft 3

14.48

6.87

15,362.00

9:37:26

Aircraft 1

13.07

6.97

15,076.67

9:37:26

Aircraft 2

18.82

6.97

15,338.33

9:37:26

Aircraft 3

14.83

6.95

15,364.00

9:37:27

Aircraft 1

13.17

7.05

15,073.33

9:37:27

Aircraft 2

18.67

7.05

15,336.67

9:37:27

Aircraft 3

15.18

7.03

15,366.00

9:37:28

Aircraft 1

13.27

7.13

15,070.00

9:37:28

Aircraft 2

18.52

7.13

15,335.00

9:37:28

Aircraft 3

15.53

7.11

15,368.00

9:37:29

Aircraft 1

13.57

7.37

15,060.00

9:37:29

Aircraft 2

18.07

7.37

15,330.00

9:37:29

Aircraft 3

16.58

7.35

15,374.00

9:37:30

Aircraft 1

13.67

7.45

15,056.67

9:37:30

Aircraft 2

17.92

7.45

15,328.33

9:37:30

Aircraft 3

16.93

7.43

15,376.00

APRIL 2018

(17.92 − 16.93) + ( 7.45 − 7.43)
2

2

= 0.99 < 1.00

and 15376.00 − 15328.33 = 47.67 < 850, thus a secondary threat is
detected as the domino influence.
Last, we keep the direction of the wind unchanged and adjust
the value of wind speed, to explore the relationship between wind
speed and secondary conflict. The simulation results indicate that
when V30 is set in the interval [45, 120], Aircraft 2 in the previous
RA process would encounter Aircraft 3. It shows that there is a big
difference in the scenario evolution with/without considering the
wind disturbance, and validates the accuracy and practicality of the
encounter model proposed in this article for illustrating realistic
TCAS/TCAS scenarios.

FURTHER ANALYSIS
In the simulation model, the set of data components is D = {d1, d2,
..., dj, ..., da}, j = 1, 2, ..., a, the set of function components is H
= {h1, h2, ..., hv, ..., hm}, v = 1, 2, ..., m. The set of reachable states
K(G, M0) = {m0, m1, ..., mk−1} is defined as the collection of all state
identifiers that can be reached from the initial state identification
M0 according to the activation rules. The corresponding function
components, activating probability and activating consuming time
of the generated timing states {m1, ..., mk−1} based on m0 are respectively set as h1, ..., hk−1, r1, ..., rk−1, and t1, ..., tk−1, and therein,
there may be the same function components of hs(s = 1, 2, ..., k −
1). The average consuming time of a specific function component
is defined as the quotient between the sum of its activating probability multiplied by consuming time and the possible activation
number. The higher the value, the more time is consumed for each
activation during the simulation, i.e., the more time-consuming are
the processes of the complex system. Assume t(hv) as the average
consuming time of function component hv and it can be computed:
t ( hv ) =




rt

hs = hv s s
hs = hv

1

, v = 1,..., m; s = 1,...k − 1

(21)

The calculation of this factor is convenient for system developers to analyze and optimize the process, which has great influence
on the system's working efficiency. Figure 3 shows the average
consuming time of function components in the GMAS-based encounter model and submodel h1′ with the test case of different initial
states (averaged over 75 runs). The total average consuming time
is 1.98 seconds for the three-aircraft scenarios.
Figure 3a illustrates that the highest average consuming time is
the nested function component h1′ which is used as the approaching aircraft filter. The second one is h8, which updates the fight
state with the interval of 1 s until all threats are resolved or a new
secondary threat is detected; its average consuming time can be
adjusted through changing the updating intervals (e.g., turn 1 s to
2 s). The SL evaluation based on altitude is evident, thus the average consuming time of h3 is relatively low. Figure 3b, represents
the average consuming time of the three function components
( h1,1′ , h1,2′ , h1,3′ ) of h1′. And xeast = V ·cos γ·cos ψ − Vwind ·cos χ wind pos-

IEEE A&E SYSTEMS MAGAZINE

43



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