Lower bounds on the mean square error derived from mixture of linear and non-linear transformations of the unbiasness definition

It is well known that in non-linear estimation problems the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR or number of snapshots. This effect is caused by outliers and is not captured by standard tools such as the Cramer-Rao bound (CR...

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Bibliographic Details
Main Authors: Chaumette, E., Renaux, A., Larzabal, P.
Format: Conference Proceeding
Language:English
Subjects:
Computational efficiency
Design optimization
Electric breakdown
Integral equations
Maximum likelihood estimation
Mean square error methods
mean-square-error bounds
Parameter estimation
SNR threshold
System analysis and design
Testing
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Summary:It is well known that in non-linear estimation problems the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR or number of snapshots. This effect is caused by outliers and is not captured by standard tools such as the Cramer-Rao bound (CRB). The search of the SNR threshold value can be achieved with the help of approximations of the Barankin bound (BB) proposed by many authors. These approximations result from a linear transformation (discrete or integral) of the uniform unbiasness constraint introduced by Barankin. Nevertheless, non-linear transformations can be used as well for some class of p.d.f. including the Gaussian case. The benefit is their combination with existing linear transformation to get tighter lower bounds improving the SNR threshold prediction.
ISSN:1520-6149
2379-190X
DOI:10.1109/ICASSP.2009.4960266