Frequency estimation based on the cumulated Lomb-Scargle periodogram

TL;DR

This paper introduces a new estimator for the period of a periodic function observed in noise at irregular sampling times, demonstrating its consistency and asymptotic properties through theoretical proofs and simulations.

Contribution

The paper proposes a novel cumulated Lomb-Scargle periodogram-based estimator for period estimation in irregularly sampled noisy data, with proven statistical properties.

Findings

Estimator is consistent and asymptotically Gaussian.

Explicit formula for the asymptotic variance.

Monte-Carlo experiments validate theoretical results.

Abstract

We consider the problem of estimating the period of an unknown periodic function observed in additive noise sampled at irregularly spaced time instants in a semiparametric setting. To solve this problem, we propose a novel estimator based on the cumulated Lomb-Scargle periodogram. We prove that this estimator is consistent, asymptotically Gaussian and we provide an explicit expression of the asymptotic variance. Some Monte-Carlo experiments are then presented to support our claims.