Aerospace and Electronic Systems Magazine April 2018 - 38

Simulation Modelling of Traffic Collision Avoidance System
and straight way. Influenced by wind, the speeds of all three
aircraft involved in the previous scenario would be different
from planned and potentially changing constantly. The scenario
would evolve differently and have to be resolved differently depending on the presence or absence of wind disturbance. For
instance, with the different values for wind speed, Aircraft 2
may or may not have the potential to induce a secondary threat
with Aircraft 3 in Figure 1. Thus, an automated process for constructing TCAS logic considering wind disturbance is appealing
because of the potential to display flight situations more realistically. However, most of the existing analyses of TCAS in the
literature do not take into account the impact of wind. Though in
[13], the correlation between wind perturbations and aircraft positions was considered, only the probability of conflict between
two aircraft was computed, not the whole process of collision
avoidance in a complex airspace involving multiple aircraft.
And, in [14] the spatial environment, including wind, temperature, and cloud was compositely taken into consideration in a
short-term path forecast.

The TCAS processor uses radar
data and discrete aircraft state
inputs from its own aircraft to
control the collision-avoidance
logic parameters that determine
the protective volume around
the vehicle. Two TCAS-equipped
aircraft would act in coordination
to avoid a collision.
The specific modelling framework used in this research is the
graphical modelling and analysis software (GMAS), and the aim of
the research described in this article is threefold:
C

C

C

38

to cover TCAS II logic as well as the pilot response, the
wind disturbance (the main analytical factor), and the interactions between these model agents;
to develop a systematic validation process for TCAS operations taking into account their evaluation needs, especially resolving the potential collision risk in multi-threat
scenarios;
to provide a paradigm of building encounter models consisting of several agents, which could expediently absorb the
other influence factors and improvement strategies into the
newly-developed TCAS versions.

AIRCRAFT DYNAMICS AND TCAS OPERATIONS
The TCAS processor uses radar data and discrete aircraft state inputs from its own aircraft to control the collision avoidance logic
parameters that determine the protection volume around the vehicle. If the intruder aircraft is also TCAS equipped, the avoidance
maneuver will be in coordination.

AIRCRAFT MODEL
The motion equations to model the aircraft dynamics are based
on the three-dimensional (3D) point-mass differential equations
which result in a set of 7 state variables (γ, V, h, φ, ψ, xeast, xnorth)
[15]. Here, γ is the flight path angle, V the true air speed, h vertical
distance or altitude, φ is the bank angle, ψ the heading angle, xeast
the east position and xnorth the north position.
γ =

L + T ·sin α
g
·cos φ − ·cos γ
mV
·
V

(1)

T ·cos α − D
V =
− g·sin γ
m

(2)

h = V ·sin γ

(3)

φ= p

(4)

ψ =

g·tan ψ
V

(5)

xeast = V ·cos γ·cos ψ − Vwind ·cos χ wind

(6)

xnorth = V ·cos γ·sin ψ − Vwind ·sin χ wind

(7)

wherein, D is the drag, T is the engine thrust, α is the angle of attack, χwind and Vwind are the wind direction and speed, L is the lift, p
is the roll rate, and g is gravity.
Independent of any ground inputs, TCAS performs surveillance of nearby aircraft to provide information on the position,
altitude, and speed of these aircraft so the collision avoidance algorithms can perform their function. Given that TCAS executes
with local scope and within a short period, the involved airspace
can be regarded as a Euclidean 3D space (not a curved space)
whose definition criteria could be based on the range of reliable
surveillance that the aircraft supports. Thus, a planar projection
of the airspace has been considered by using a Cartesian coordinate system and with a minimum distortion [4]. The region
formed by x and y axes indicates the horizontal plane, and z
stands for the altitude h. In brief, the above motion equations to
model the basic dynamic characteristics of Aircraft i (i = 1, 2,
..., n) at time t can be expressed in the simplified representation
sti = pti , vti =  xti , yti , zti , vti, x , vti, y , vti, z .
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IEEE A&E SYSTEMS MAGAZINE

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APRIL 2018



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