Bayesian Periodic Cramér-Rao Bound.

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5 Scopus citations


The Cramér-Rao bound (CRB) has been extensively used as a benchmark for estimation performance in both Bayesian and non-Bayesian frameworks. In many practical periodic parameter estimation problems, such as phase, frequency, and direction-of-arrival estimation, the observation model is periodic with respect to the unknown parameters and thus, the appropriate criterion is periodic in the parameter space. Consequently, Bayesian lower bounds on the mean-squared-error (MSE) are not valid bounds for periodic estimation problems. In addition, many Bayesian MSE lower bounds cannot be derived in the periodic case due to their restrictive regularity conditions. For example, the regularity conditions of the Bayesian CRB (BCRB) are not satisfied for parameters with uniform prior distribution. In this letter, we derive a Bayesian Cramér-Rao-type lower bound on the mean-squared-periodic-error (MSPE). The proposed periodic BCRB (PBCRB) is a lower bound on the MSPE of any estimator and has less restrictive regularity conditions than the BCRB. The PBCRB is compared with the MSPE of the minimum MSPE estimator for phase estimation in Gaussian noise and it is shown that the PBCRB is a valid and tight lower bound for this problem.
Original languageEnglish
Pages (from-to)1878-1882
Number of pages5
JournalIEEE Signal Processing Letters
StatePublished - 2022


  • Bayes methods
  • Gaussian noise
  • parameter estimation
  • phase estimation
  • System analysis and design
  • mean-squared-error (MSE)
  • Bayesian Cramér-Rao bound (BCRB) ,
  • periodic BCRB (PBCRB)

ASJC Scopus subject areas

  • Signal Processing
  • Applied Mathematics
  • Electrical and Electronic Engineering


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