A barankin-type lower bound on the estimation error of a hybrid parameter vector

Ilan Reuven*, Hagit Messer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The Barankin bound is a realizable lower bound on the mean-square error (mse) of any unbiased estimator of a (nonrandom) parameter vector. In this correspondence we present a Barankin-type bound which is useful in problems where there is a prior knowledge on some of the parameters to be estimated. That is, the parameter vector is a hybrid vector in the sense that some of its entries are deterministic while other are random variables. We present a simple expression for a positive-definite matrix which provides bounds on the covariance of any unbiased estimator of the nonrandom parameters and an estimator of the random parameters, simultaneously. We show that the Barankin bound for deterministic parameters estimation and the Bobrovsky-Zakai bound for random parameters estimation are special cases of our proposed bound.

Original languageEnglish
Pages (from-to)1084-1093
Number of pages10
JournalIEEE Transactions on Information Theory
Volume43
Issue number3
DOIs
StatePublished - 1997

Keywords

  • Barankin bound
  • Parameter estimation
  • Performance bounds

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