Periodic encoding of HCAS angular inputs

Construct a sine–cosine encoding for the periodic bearing-angle and relative-heading inputs of the Horizontal Collision Avoidance System (HCAS), and determine whether removing the artificial wrap-around discontinuity reduces the size of the HCAS lookup table in a Safety Net.

Background

The HCAS neural-network inputs include the bearing angle and relative heading, both of which span the circular interval from −180° to 180°. The paper argues that representing these periodic variables directly can introduce an artificial discontinuity at the wrap-around boundary, which may cause fully connected networks to produce more errors and consequently enlarge the Safety Net lookup table.

The authors identify sine–cosine encoding as a potential remedy but do not evaluate it in the reported experiments. Establishing its effectiveness would clarify whether an alternative representation of the angular variables can improve HCAS compression while preserving the Safety Net’s correctness guarantee on the discretized input space.

References

A natural remedy, left to future work, is to encode the periodic angular inputs \theta{} and \psi{} by their sine and cosine components, removing the artificial discontinuity at the \ang{\pm180} wrap-around boundary that fully connected networks with standard initialization represent poorly; this would be expected to reduce the HCAS LUT even further.

— On the Applicability of Safety Nets: A Safety-By-Design Solution for Certifying Neural Networks  (2608.20053 - Christensen et al., 20 Aug 2026) in Section 4, Performance Study