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Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization

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Title: Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization
Authors: Siebler, Benjamin, Sand, Stephan, Hanebeck, Uwe D.
Source: IEEE Access, 10, 123080–123093 ; ISSN: 2169-3536
Publisher Information: Institute of Electrical and Electronics Engineers
Publication Year: 2022
Collection: KITopen (Karlsruhe Institute of Technologie)
Subject Terms: Bayesian Cramér-Rao lower bound, finger-printing, Gaussian process, indoor localization, magnetic field-based localization, particle filter, ddc:004, DATA processing & computer science, info:eu-repo/classification/ddc/004
Description: In this paper, we show how to analyze the achievable position accuracy of magnetic localization based on Bayesian Cramér-Rao lower bounds and how to account for deterministic inputs in the bound. The derivation of the bound requires an analytical model, e.g., a map or database, that links the position that is to be estimated to the corresponding magnetic field value. Unfortunately, finding an analytical model from the laws of physics is not feasible due to the complexity of the involved differential equations and the required knowledge about the environment. In this paper, we therefore use a Gaussian process (GP) that approximates the true analytical model based on training data. The GP ensures a smooth, differentiable likelihood and allows a strict Bayesian treatment of the estimation problem. Based on a novel set of measurements recorded in an indoor environment, the bound is evaluated for different sensor heights and is compared to the mean squared error of a particle filter. Furthermore, the bound is calculated for the case when only the magnetic magnitude is used for positioning and the case when the whole vector field is considered. For both cases, the resulting position bound is below 10cm indicating an high potential accuracy of magnetic localization.
Document Type: article in journal/newspaper
File Description: application/pdf
Language: English
Relation: info:eu-repo/semantics/altIdentifier/wos/000892887400001; info:eu-repo/semantics/altIdentifier/issn/2169-3536; https://publikationen.bibliothek.kit.edu/1000154188; https://publikationen.bibliothek.kit.edu/1000154188/149916208; https://doi.org/10.5445/IR/1000154188
DOI: 10.5445/IR/1000154188
Availability: https://publikationen.bibliothek.kit.edu/1000154188
https://publikationen.bibliothek.kit.edu/1000154188/149916208
https://doi.org/10.5445/IR/1000154188
Rights: https://creativecommons.org/licenses/by/4.0/deed.de ; info:eu-repo/semantics/openAccess
Accession Number: edsbas.CD6FDBAE
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  Data: Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization
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  Data: <searchLink fieldCode="AR" term="%22Siebler%2C+Benjamin%22">Siebler, Benjamin</searchLink><br /><searchLink fieldCode="AR" term="%22Sand%2C+Stephan%22">Sand, Stephan</searchLink><br /><searchLink fieldCode="AR" term="%22Hanebeck%2C+Uwe+D%2E%22">Hanebeck, Uwe D.</searchLink>
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  Data: IEEE Access, 10, 123080–123093 ; ISSN: 2169-3536
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  Data: Institute of Electrical and Electronics Engineers
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  Data: 2022
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  Data: <searchLink fieldCode="DE" term="%22Bayesian+Cramér-Rao+lower+bound%22">Bayesian Cramér-Rao lower bound</searchLink><br /><searchLink fieldCode="DE" term="%22finger-printing%22">finger-printing</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+process%22">Gaussian process</searchLink><br /><searchLink fieldCode="DE" term="%22indoor+localization%22">indoor localization</searchLink><br /><searchLink fieldCode="DE" term="%22magnetic+field-based+localization%22">magnetic field-based localization</searchLink><br /><searchLink fieldCode="DE" term="%22particle+filter%22">particle filter</searchLink><br /><searchLink fieldCode="DE" term="%22ddc%3A004%22">ddc:004</searchLink><br /><searchLink fieldCode="DE" term="%22DATA+processing+%26+computer+science%22">DATA processing & computer science</searchLink><br /><searchLink fieldCode="DE" term="%22info%3Aeu-repo%2Fclassification%2Fddc%2F004%22">info:eu-repo/classification/ddc/004</searchLink>
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  Data: In this paper, we show how to analyze the achievable position accuracy of magnetic localization based on Bayesian Cramér-Rao lower bounds and how to account for deterministic inputs in the bound. The derivation of the bound requires an analytical model, e.g., a map or database, that links the position that is to be estimated to the corresponding magnetic field value. Unfortunately, finding an analytical model from the laws of physics is not feasible due to the complexity of the involved differential equations and the required knowledge about the environment. In this paper, we therefore use a Gaussian process (GP) that approximates the true analytical model based on training data. The GP ensures a smooth, differentiable likelihood and allows a strict Bayesian treatment of the estimation problem. Based on a novel set of measurements recorded in an indoor environment, the bound is evaluated for different sensor heights and is compared to the mean squared error of a particle filter. Furthermore, the bound is calculated for the case when only the magnetic magnitude is used for positioning and the case when the whole vector field is considered. For both cases, the resulting position bound is below 10cm indicating an high potential accuracy of magnetic localization.
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      – SubjectFull: indoor localization
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