The Constrained CramÉr-Rao Bound From the Perspective of Fitting a Model

Stoica and Ng (1998) presented a simple expression for the constrained Cramer-Rao bound (CCRB) when the constraints are given by a differentiable function of the parameter to be estimated. This letter considers the parallel case in developing the CCRB when the parameters are locally fitted to a lowe...

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Bibliographic Details
Published in:IEEE signal processing letters 2007-08, Vol.14 (8), p.564-567
Main Authors: Moore, T.J., Kozick, R.J., Sadler, B.M.
Format: Article
Language:English
Subjects:
Constrained CramÉr-Rao bound (CCRB)
Constraints
Covariance matrix
Cramer-Rao bounds
Derivation
equality constraints
Fittings
Laboratories
Lagrangian functions
Mathematical analysis
Mathematical models
Maximum likelihood estimation
model fitting
Null space
Parameter estimation
Parametric statistics
Regularity
Taylor series
Testing
Vectors (mathematics)
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Summary:Stoica and Ng (1998) presented a simple expression for the constrained Cramer-Rao bound (CCRB) when the constraints are given by a differentiable function of the parameter to be estimated. This letter considers the parallel case in developing the CCRB when the parameters are locally fitted to a lower-dimensional parametric model, i.e., the parameters are locally assumed to be functions of a distinct reduced parameter vector. We employ classical elements of CRB theory on the locally fitted model to present a very simple derivation of the CCRB, conditions for attaining the bound, and a regularity condition. Examples illustrate the key ideas.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2006.891316