Determining Joint Periodicities in Multi-time Data With Sampling Uncertainties

TL;DR

This paper presents a new sparse spectral estimation method for multiple non-uniformly sampled datasets with uncertain sampling times, demonstrated on paleoclimatology data, achieving near-optimal accuracy under high SNR.

Contribution

A novel joint spectral estimation approach that handles disjoint, partially known sampling times and uncertainties, advancing analysis of multi-source irregular data.

Findings

Method attains the derived Cramér-Rao lower bound at high SNR.

Outperforms existing approaches in simulated and real ice core data.

Robustly estimates periodicities despite sampling uncertainties.

Abstract

In this work, we introduce a novel approach for determining a joint sparse spectrum from several non-uniformly sampled data sets, where each data set is assumed to have its own, possibly disjoint, and only partially known, sampling times. The potential of the proposed approach is illustrated using a spectral estimation problem in paleoclimatology. In this problem, each data point derives from a separate ice core measurement, resulting in that even though all measurements reflect the same periodicities, the sampling times and phases differ among the data sets. In addition, sampling times are only approximately known. The resulting joint estimate exploiting all available data is formulated using a sparse reconstruction framework allowing for a reliable and robust estimate of the underlying periodicities. The corresponding misspecified Cram\'er-Rao lower bound, accounting for the expected sampling uncertainties, is derived and the proposed method is shown to attain the resulting bound when the signal to noise ratio is sufficiently high. The performance of the proposed method is illustrated as compared to other commonly used approaches using both simulated and measured ice core data sets.