## 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 language | English |
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Title of host publication | Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking |

Publisher | Wiley-IEEE Press |

Pages | 361-370 |

Number of pages | 10 |

ISBN (Electronic) | 9780470544198 |

ISBN (Print) | 0470120959, 9780470120958 |

DOIs | |

State | Published - 1 Jan 2007 |

## Keywords

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