Samenvatting

Conceptual mathematical models play a crucial role
in the development of engineering specifications required in the
detailed design process and in the test and evaluation of avionics
equipment. Specifying aircraft proximity is a precursor to the
development of aircraft Detect and Avoid (DAA) systems that are, in
turn, critical to enabling Unmanned Aircraft Systems (UAS) greater
access to non-segregated airspace. Such specifications can also
significantly enhance the safety of conventionally piloted aircraft
operations. A more rigorous mathematical approach to specifying
aircraft proximity functions is now possible based on the Apollonian
Proximity Circle (APC) paradigm. In turn, this paradigm is based on
the Cylindrical Bipolar Co-ordinate system that can be used to
formally establish a framework of situational Quadrant Equivalence
Sets and Test Regimes that exhibit differing proximity and
geometrical behaviour. Some Test Regimes only require a sparse
allocation of test points while others, because of functional
characteristics such as asymptotic behaviour and contour spacing,
require a far more intense allocation of test points. Having addressed
the static specification of proximity the dynamic aspects related to
short-term intent and Conflict Probing also need to be addressed and
this leads to the identification of various anomalous behaviours. In
this paper the examples identified are: False Positives; Turn Policy
Reversals; the role of Decision Delays; and the nature of operational
guidance within Well Clear Volumes. Selected examples show how
this behaviour can be better characterized by reference to the APC
paradigm and, in particular, with reference to the role of the Line of
Sight vector between the aircraft in proximity. The APC paradigm
presented in this paper is analytic thus enabling a far more complete
and accurate specification of proximity than has previously been
reported in the literature. The systematic approach provides a
foundational basis for resolving the differing and contrary