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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(Document in English)
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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 |
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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: | |
Statistics: | download |
Deposited On: | 21 Oct 2020 11:48 |
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