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

Ilan Reuven, Hagit Messer

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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
Title of host publicationBayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
PublisherWiley-IEEE Press
Number of pages10
ISBN (Electronic)9780470544198
ISBN (Print)0470120959, 9780470120958
StatePublished - 1 Jan 2007

Bibliographical note

Publisher Copyright:
© 2007 by the Institute of Electrical and Electronics Engineers, Inc. All rights reserved.


  • Bayesian methods
  • Covariance matrix
  • Finite element methods
  • Linear matrix inequalities
  • Matrices


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