Tau coupling investigation using positive wavelet analysis

Abstract

The investigation of motion guidance and its subsequent application using tau (τ) theory relies on the accurate
calculation of the coupling term between the τ (time to contact) of the motion and the appropriate τ guide. However,
the traditional approach for this calculation can be numerically unstable, requires experience and skill to execute in a
meaningful manner, is sensitive to the data selected, and has limited application when the motion information is
incomplete or deviates from the ideal. To deal with these issues, a new approach, based on positive wavelet analysis, is
proposed in this paper. The mother wavelet is constructed using the desired τ-guide shapes, with its scale considered to
be defined by the maneuver period. The scale and time information of interest are found by searching for the best local
correlation within the whitened original signal. An inverse dewhitening process is then used to reconstruct an
approximation to the original motion signal. The adequacy of the positive wavelet method has been demonstrated
using data obtained from piloted simulation test campaigns. The results show that the approach is not only feasible,
but it has better numerical stability, reliability, enhanced performance, and wider applicability than those that have
been used to date