Determining joint periodicities in multi-time data with sampling uncertainties

David Svedberg*, Filip Elvander, Andreas Jakobsson

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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 Cramér-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.

Original languageEnglish
Article number109147
Number of pages10
JournalSignal Processing
Volume213
Early online date2023
DOIs
Publication statusPublished - Dec 2023
MoE publication typeA1 Journal article-refereed

Keywords

  • Irregular sampling
  • Misspecified modelling
  • Multi-time
  • Paleoclimatology

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