Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization
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...
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9957005/ |
| _version_ | 1797986720242728960 |
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| author | Benjamin Siebler Stephan Sand Uwe D. Hanebeck |
| author_facet | Benjamin Siebler Stephan Sand Uwe D. Hanebeck |
| author_sort | Benjamin Siebler |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T07:37:25Z |
| format | Article |
| id | doaj.art-77753935734549fca787c8a6e73380f3 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-11T07:37:25Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-77753935734549fca787c8a6e73380f32022-12-22T04:36:41ZengIEEEIEEE Access2169-35362022-01-011012308012309310.1109/ACCESS.2022.32236939957005Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based LocalizationBenjamin Siebler0https://orcid.org/0000-0002-1745-408XStephan Sand1https://orcid.org/0000-0001-9502-5654Uwe D. Hanebeck2German Aerospace Center (DLR), Institute of Communications and Navigation, Oberpfaffenhofen, GermanyGerman Aerospace Center (DLR), Institute of Communications and Navigation, Oberpfaffenhofen, GermanyIntelligent Sensor-Actuator-Systems Laboratory, Karlsruhe Institute of Technology (KIT), Karlsruhe, GermanyIn 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.https://ieeexplore.ieee.org/document/9957005/Bayesian Cramér-Rao lower boundfinger-printingGaussian processindoor localizationmagnetic field-based localizationparticle filter |
| spellingShingle | Benjamin Siebler Stephan Sand Uwe D. Hanebeck Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization IEEE Access Bayesian Cramér-Rao lower bound finger-printing Gaussian process indoor localization magnetic field-based localization particle filter |
| title | Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization |
| title_full | Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization |
| title_fullStr | Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization |
| title_full_unstemmed | Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization |
| title_short | Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization |
| title_sort | bayesian cram x00e9 r rao lower bound for magnetic field based localization |
| topic | Bayesian Cramér-Rao lower bound finger-printing Gaussian process indoor localization magnetic field-based localization particle filter |
| url | https://ieeexplore.ieee.org/document/9957005/ |
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