Paper Info
Title
Cramér-Rao-Leibniz Lower Bound — A new estimation bound for finite support measurement noise
Abstract
In this paper we introduce a new bound on an estimator's error, derived from the classical Cramér-Rao Lower Bound (CRLB), for cases where the support of the likelihood function (LF) exhibits parameter-dependence. Parameter-dependent support of the LF arises here when an unknown parameter is observed in the presence of additive measurement noise and the measurement noise pdf has a finite support. This new modified CRLB - designated as the Cramér-Rao-Leibniz Lower Bound (CRLLB), since it relies on Leibniz integral rule - is presented and its use illustrated. The CRLLB is shown to provide, for example, a valid bound for the problem of uniform measurement noise for which the CRLB was shown in the literature as not valid. Furthermore, it is demonstrated that, in light of the CRLLB, the ML estimator in the uniform measurement noise case is statistically efficient, i.e., the estimator's variance is equal to the CRLLB.
Year
DOI
Venue
2014
10.1109/CDC.2014.7039788
Decision and Control
Keywords
Field
DocType
estimation theory,noise,parameter estimation,CRLB,CRLLB,Cramer-Rao-Leibniz lower bound,Leibniz integral rule,ML estimator,additive measurement noise,estimation bound,estimator error,finite support measurement noise,likelihood function support,measurement noise pdf,parameter estimation,parameter-dependent support,uniform measurement noise,Cramér-Rao Lower Bound,Parameter estimation,measurement noise pdf with finite support
Cramér–Rao bound,Mathematical optimization,Likelihood function,Leibniz integral rule,Upper and lower bounds,Estimation theory,Gaussian noise,Mathematics,Estimator
Conference
ISSN
Citations 
PageRank 
0743-1546
0
0.34
References 
Authors
1
6
Name
Order
Citations
PageRank
Yaakov Bar-Shalom146099.56
Richard W. Osborne III2156.05
Peter Willett31962224.14
Frederick E. Daum400.34
Bar-Shalom, Y.500.34
Osborne, R.W.600.34