Aerospace and Electronic Systems Magazine September 2016 - 23

Zsedrovits et al.

(1)

Considering the intruder relative velocities (Vx ,Vy ,Vz) and tTC , the
above expressions can be reformulated and their derivatives obtained. From here, formulae are presented only for the x horizontal
direction because the y direction formulae are structurally the same
(note that Vz < 0 because of approaching airplanes).

D/E and G airspaces. This means that they can possibly collide
with intruders ranging from small UAV to large transport aircraft.
That's why the size-velocity characteristics of the whole range of
possible intruders should be characterized. This characterization is
done based on an aircraft database [24] by plotting the size-cruise
velocity pairs. A mean curve, a lower and an upper bound are fitted
to data as shown in Figure 6. Based on these curves, the limiting
values of Rv can be calculated and applied in the threshold selection procedure. For details see [15].

THE PROPOSED AVOIDANCE STRATEGY
(2)

In [19] a simple avoidance strategy is proposed based on the relative
bearing of the intruder. It proposes to turn into the direction of the
intruder to avoid it. This works well if the path of the intruder crosses
own path, but can lead to a collision if it does not (see Figure 7).

In a SAA scenario, the miss distance Xa should be estimated. This
would be possible from (dx/dt)/(dSx/dt) if the intruder size Rx were
known (see [17], for example). However, it is unknown. Inspecting
closer the ratio:

(3)
CPA performs well at characterizing the miss distance Xa relative
to intruder size Rx. This is a perfect parameter for collision estimation. If CPA = 0, MAC is sure. If 0 < CPA < CPAC (below a selected
threshold), NMAC can be defined. Above CPAC, there is no risk of
collision. However, dx/dt and dSx/dt can only be estimated from
measured x and S (from now Sx will be denoted as S and Rx as R for
simplicity); as a result, they can be noisy which may lead to false
CPA estimates. On the other hand, |dx/dt| ≫ 0 is good indicator
of non-collision (if own craft and intruder paths are straight and
velocities are constant it can be proven that dx/dt = 0 indicates
collision) and |dS/dt| → ∞ of collision (when intruder is very close
to own craft). This leads to the idea to select separate detection
thresholds for dx/dt and dS/dt. If dx/dt is large, this means that there
will be no collision. The question is, how long one has to wait until
observing dx/dt above the threshold? In a collision scenario, the
collision comes earlier than this observation. That's why a threshold should be selected for dS/dt. If it is above the threshold, there
is no time for further waiting; the avoidance should be activated.
The method of threshold selection is published in detail in [15],
where a hysteresis is introduced between non-collision and collision decisions, and a minimum CPA value is guaranteed below
which the avoidance is surely activated for any possible intruder
size and velocity. Here, only the characterization of possible intruder threats is introduced in detail.

Figure 6.

Size-cruising speed characteristics of possible intruder threats.

CHARACTERIZATION OF POSSIBLE INTRUDERS
Equation (2) shows that Rv = Rx /Vz is a key value in both dx/dt and
dSx /dt. This is the ratio of intruder physical size and velocity in the
direction of own craft. This ratio can highly change if one considers several types of possible intruders. Considering small UAVs as
the carriers of the SAA system, they are usually applied in Class
SEPTEMBER 2016

Figure 7.

Turning into the direction of the intruder and its risk.

IEEE A&E SYSTEMS MAGAZINE

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