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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 (2021) Cramér-Rao bound for a mixture of real- and integer-valued parameter vectors and its application to the linear regression model. Signal Processing, 179. Elsevier. doi: 10.1016/j.sigpro.2020.107792. ISSN 0165-1684.

[img] PDF - Only accessible within DLR bis 16 September 2022 - Postprint version (accepted manuscript)

Official URL: https://www.sciencedirect.com/science/article/abs/pii/S0165168420303364


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 assessment 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 URL in elib:https://elib.dlr.de/136928/
Document Type:Article
Title:Cramér-Rao bound for a mixture of real- and integer-valued parameter vectors and its application to the linear regression model
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Medina, DanielDaniel.AriasMedina (at) dlr.dehttps://orcid.org/0000-0002-1586-3269
Vilà-Valls, JordiJordi.VILA-VALLS (at) isae-supaero.frhttps://orcid.org/0000-0001-7858-4171
Chaumette, EricEric.CHAUMETTE (at) isae-supaero.frUNSPECIFIED
Vincent, FrançoisFrancois.Vincent (at) isae-supaero.frUNSPECIFIED
Closas, Paupau.closas (at) northeastern.eduhttps://orcid.org/0000-0002-5960-6600
Date:February 2021
Journal or Publication Title:Signal Processing
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
DOI :10.1016/j.sigpro.2020.107792
Keywords:Cramér-Rao bound; McAulay-Seidman bound; Mixed real- integer parameter vector estimation; Linear regression; GNSS; Ambiguity resolution
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Communication and Navigation
DLR - Research area:Raumfahrt
DLR - Program:R KN - Kommunikation und Navigation
DLR - Research theme (Project):R - Project Navigation 4.0 (old)
Location: Neustrelitz
Institutes and Institutions:Institute of Communication and Navigation > Nautical Systems
Deposited By: Medina, Daniel
Deposited On:29 Oct 2020 11:47
Last Modified:29 Oct 2020 11:47

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