The Constrained Misspecified Crér-Rao Bound

The aim of this letter is to provide a constrained version of the misspecified Crér-Rao bound (MCRB). Specifically, the MCRB is a lower bound on the error covariance matrix of any unbiased (in a proper sense) estimator of a deterministic parameter vector under misspecified models, i.e., when the tru...

Full description

Saved in:
Bibliographic Details
Published inIEEE signal processing letters Vol. 23; no. 5; p. 718
Main Authors tunati, Stefano, Gini, Fulvio, Greco, Maria S
Format Journal Article
LanguageEnglish
Published New York The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 01.05.2016
Online AccessGet full text

Cover

More Information
Summary:The aim of this letter is to provide a constrained version of the misspecified Crér-Rao bound (MCRB). Specifically, the MCRB is a lower bound on the error covariance matrix of any unbiased (in a proper sense) estimator of a deterministic parameter vector under misspecified models, i.e., when the true and the assumed data distributions are different. Here, we aim at finding an expression of the MCRB for estimation problems involving continuously differentiable equality constraints. Our proof generalizes the derivation of the classical constrained CRB (CCRB) by showing that the constrained MCRB (CMCRB) can be obtained by exploiting the building blocks of its unconstrained counterpart and a basis of the null space of the constraint's Jacobian matrix. The conditions for the existence of the CMCRB are also discussed.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2016.2546383