Cyclic Barankin-type bounds for non-Bayesian periodic parameter estimation

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28 Scopus citations

Abstract

In many practical periodic parameter estimation problems, the appropriate performance criteria are periodic in the parameter space. The existing mean-square-error (MSE) lower bounds, such as Cramér-Rao bound (CRB) and Barankin-type bounds do not provide valid lower bounds in such problems. In this paper, cyclic versions of the CRB and the Barankin-type bounds, Hammersley-Chapman-Robbins and McAulay-Seidman, are derived for non-Bayesian parameter estimation. The proposed bounds are lower bounds on the mean cyclic error (MCE) of any cyclic-unbiased estimator, where the cyclic-unbiasedness is defined by using Lehmann-unbiasedness. These MCE lower bounds can be readily obtained from existing MSE lower bounds and thus, can be easily calculated. The cyclic Barankin-type bounds and the performance of the maximum-likelihood (ML) estimator are compared in terms of MCE in Von-Mises distributed measurements problem and for frequency and amplitude estimation with Gaussian noise. In these problems, the ML estimator is found to be cyclic unbiased.

Original languageEnglish
Article number6808538
Pages (from-to)3321-3336
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume62
Issue number13
DOIs
StatePublished - 1 Jul 2014

Keywords

  • Cramér-Rao bound (CRB)
  • Frequency estimation
  • Large errors bounds
  • Lehmann-unbiased
  • Non-Bayesian parameter estimation
  • cyclic performance bounds
  • cyclic-unbiased
  • periodic parameter estimation

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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