Template Matching with Ranks

TL;DR

This paper introduces a rank-based template matching method for noisy signals, demonstrating its asymptotic normality and parametric convergence rate through theoretical analysis and numerical simulations.

Contribution

It proposes a novel rank-based estimator for template matching that achieves optimal asymptotic properties, extending existing signal processing techniques.

Findings

Estimator achieves parametric rate of convergence

Estimator is asymptotically normal

Numerical simulations support theoretical results

Abstract

We consider the problem of matching a template to a noisy signal. Motivated by some recent proposals in the signal processing literature, we suggest a rank-based method and study its asymptotic properties using some well-established techniques in empirical process theory combined with H\'ajek's projection method. The resulting estimator of the shift is shown to achieve a parametric rate of convergence and to be asymptotically normal. Some numerical simulations corroborate these findings.