Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 105

Fasano et al.

B. CONFLICT DETECTION
Tracking outputs are the basic information used for threat assessment. Conflict detection strategies conceptually depend both on
the quantity and on the quality of tracking information. This subsection discusses these two aspects.
First, let us consider the collision geometry in Fig. 18.
In Fig. 18, is the relative position vector of the obstacle,
is the
current UAV velocity vector,
is the current obstacle velocity
vector, and
is the velocity vector of the UA with respect to
the obstacle (i.e.,
).
If it is assumed that both vehicles will move along a straight
line path, then the closest point of approach will be located in the
plane formed by current UAV and obstacle positions, and the relative velocity vector
. In vectorial terms, the distance at
closest point of approach
is given by

Fig. 18.

Collision geometry and distance at closest point of approach (in general,
absolute velocity vectors do not lie in minimum distance plane.)

(41)

where it has also been considered that the time to closest point of
approach tCPA is given by

(42)

Since (41) is a vectorial equation, it can be projected along coordinate
axes to obtain components (e.g., horizontal and vertical components).
Equations (41) and (42) represent the basic conflict detection
for any surveillance system providing 3D information that is accurate enough. In fact, it can be demonstrated, and it is intuitive, that
two aircraft are headed for a collision if and only if dCPA is smaller
than the bubble distance and the range rate is negative [42].
Based on Table III, sensing architectures exploiting radars, stereovision, passive ranging approaches, ADS-B, scanning LIDARs,
or multisensor systems including these sources, can estimate the
threat level based on these relations.
Also, in the case of multiple conflicts, which may happen in
separation assurance applications based on cooperative information sources,
and tCPA offer a way to prioritize conflicts. In
these cases, tCPA for any incoming obstacle is typically compared
with a maximum look-ahead time, so that intruders with large time
to closest point of approach are discarded and considered as nonimmediate threats. Various prioritization logics can be then used.
As shown in what follows, (41) can also be used as a mathematical basis for sensing architectures that do not provide 3D position and velocity information that is accurate enough.
In the case of TCAS, the coarse horizontal accuracy actually prevents an accurate estimate of dCPA. Thus, conflict detection logic is
based on τ, which approximates tCPA on the basis of

(43)

The equation is exact for zero dCPA.
τ is actually complemented by a "vertical τ," which is computed
as the ratio between the altitude separation divided by the vertical
NOVEMBER 2016, Part II of II

Fig. 19.

Geometry for scale change.

closing speed of the two aircraft. Moreover, τ and vertical τ criteria
are modified for small closure rates, to avoid an aircraft becoming very close without activating any traffic advisory or resolution
advisory [43].
A vision-based system cannot exploit 3D information for collision threat evaluation, unless we consider stereovision, shapebased ranging, or passive ranging strategies (all having significant
limitations for the problem under analysis as stated above).
For the sake of completeness, it is worth recalling that monocular systems can provide in theory a range-less tCPA estimate based
on scale change. Considering for simplicity a one-dimensional
geometry (Fig. 19), if obstacle physical dimension along azimuth

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Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine November 2016 Tutorial X