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Cramer–Rao lower bounds for change points in additive and multiplicative noise

Tourneret, Jean-Yves and Ferrari, André and Swami, Ananthram Cramer–Rao lower bounds for change points in additive and multiplicative noise. (2004) Signal Processing, 8 (7). 1071-1088. ISSN 0165-1684

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Official URL: http://dx.doi.org/10.1016/j.sigpro.2004.03.009


The paper addresses the problem of determining the Cramer–Rao lower bounds (CRLBs) for noise and change-point parameters, for steplike signals corrupted by multiplicative and/or additive white noise. Closed-form expressions for the signal and noise CRLBs are first derived for an ideal step with a known change point. For an unknown change-point, the noise-free signal is modeled by a sigmoidal function parametrized by location and step rise parameters. The noise and step change CRLBs corresponding to this model are shown to be well approximated by the more tractable expressions derived for a known change-point. The paper also shows that the step location parameter is asymptotically decoupled from the other parameters, which allows us to derive simple CRLBs for the step location. These bounds are then compared with the corresponding mean square errors of the maximum likelihood estimators in the pure multiplicative case. The comparison illustrates convergence and efficiency of the ML estimator. An extension to colored multiplicative noise is also discussed.

Item Type:Article
Additional Information:This publication is available at http://www.sciencedirect.com/science/journal/01651684
HAL Id:hal-03602345
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Observatoire de la Côte d'Azur (FRANCE)
Other partners > Université Nice Sophia Antipolis (FRANCE)
Laboratory name:
Deposited On:15 Sep 2009 13:55

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