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On Lower Bounds for Non Standard Deterministic Estimation

Kbayer, Nabil and Galy, Jerome and Chaumette, Eric and Vincent, François and Renaux, Alexandre and Larzabal, Pascal On Lower Bounds for Non Standard Deterministic Estimation. (2017) IEEE Transactions on Signal Processing, 65 (6). 1538-1553. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2016.2645538

Abstract

We consider deterministic parameter estimation and the situation where the probability density function (p.d.f.) parameterized by unknown deterministic parameters results from the marginalization of a joint p.d.f. depending on random variables as well. Unfortunately, in the general case, this marginalization is mathematically intractable, which prevents from using the known standard deterministic lower bounds (LBs) on the mean squared error (MSE). Actually the general case can be tackled by embedding the initial observation space in a hybrid one where any standard LB can be transformed into a modified one fitted to nonstandard deterministic estimation, at the expense of tightness however. Furthermore, these modified LBs (MLBs) appears to include the submatrix of hybrid LBs which is an LB for the deterministic parameters. Moreover, since in the nonstandard estimation, maximum likelihood estimators (MLEs) can be no longer derived, suboptimal nonstandard MLEs (NSMLEs) are proposed as being a substitute. We show that any standard LB on the MSE of MLEs has a nonstandard version lower bounding the MSE of NSMLEs. We provide an analysis of the relative performance of the NSMLEs, as well as a comparison with the MLBs for a large class of estimation problems. Last, the general approach introduced is exemplified, among other things, with a new look at the well-known Gaussian complex observation models.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Conservatoire National des Arts et Métiers - CNAM (FRANCE)
French research institutions > Centre National d'Études Spatiales - CNES (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Ecole Nationale de l'Aviation Civile - ENAC (FRANCE)
Other partners > Ecole Normale Supérieure de Cachan - ENS Cachan (FRANCE)
French research institutions > Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux - IFSTTAR (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Rockwell Collins (FRANCE)
Other partners > Thales (FRANCE)
Other partners > Telecom ParisTech (FRANCE)
Other partners > Université de Cergy-Pontoise (FRANCE)
Other partners > CentraleSupélec (FRANCE)
Other partners > Direction Générale de l’Aviation Civile - DGAC (FRANCE)
Other partners > Ecole Normale Supérieure de Rennes - ENS Rennes (FRANCE)
Other partners > Université de Montpellier (FRANCE)
Other partners > Université Paris-Sud 11 (FRANCE)
Laboratory name:
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Deposited By: Francois VINCENT
Deposited On:23 Mar 2017 09:24

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