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Cramér-Rao bound for a mixture of real- and integer-valued parameter vectors and its application to the linear regression model

Medina, Daniel and Vilà-Valls, Jordi and Chaumette, Eric and Vincent, François and Closas, Pau Cramér-Rao bound for a mixture of real- and integer-valued parameter vectors and its application to the linear regression model. (2021) Signal Processing, 179. 107792. ISSN 0165-1684

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Official URL: https://doi.org/10.1016/j.sigpro.2020.107792

Abstract

Performance lower bounds are known to be a fundamental design tool in parametric estimation theory. A plethora of deterministic bounds exist in the literature, ranging from the general Barankin bound to the well-known Cramér-Rao bound (CRB), the latter providing the optimal mean square error performance of locally unbiased estimators. In this contribution, we are interested in the estimation of mixed real- and integer-valued parameter vectors. We propose a closed-form lower bound expression leveraging on the general CRB formulation, being the limiting form of the McAulay-Seidman bound. Such formulation is the key point to take into account integer-valued parameters. As a particular case of the general form, we provide closed-form expressions for the Gaussian observation model. One noteworthy point is the as- sessment of the asymptotic efficiency of the maximum likelihood estimator for a linear regression model with mixed parameter vectors and known noise covariance matrix, thus complementing the rather rich literature on that topic. A representative carrier-phase based precise positioning example is provided to support the discussion and show the usefulness of the proposed lower bound.

Item Type:Article
HAL Id:hal-02973927
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > German Aerospace Center - DLR (GERMANY)
Other partners > DLR Institute of Communications and Navigation (GERMANY)
Other partners > Northeastern University (USA)
Laboratory name:
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Deposited On:21 Oct 2020 11:48

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