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Cramér–Rao Lower Bound for Magnetic Field Localization around Elementary Structures

Dammann, Armin and Siebler, Benjamin and Sand, Stephan (2024) Cramér–Rao Lower Bound for Magnetic Field Localization around Elementary Structures. Sensors, 24 (8). Multidisciplinary Digital Publishing Institute (MDPI). doi: 10.3390/s24082402. ISSN 1424-8220.

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Official URL: https://www.mdpi.com/1424-8220/24/8/2402


The determination of a mobile terminal’s position with high accuracy and ubiquitous coverage is still challenging. Global satellite navigation systems (GNSSs) provide sufficient accuracy in areas with a clear view to the sky. For GNSS-denied environments like indoors, complementary positioning technologies are required. A promising approach is to use the Earth’s magnetic field for positioning. In open areas, the Earth’s magnetic field is almost homogeneous, which makes it possible to determine the orientation of a mobile device using a compass. In more complex environments like indoors, ferromagnetic materials cause distortions of the Earth’s magnetic field. A compass usually fails in such areas. However, these magnetic distortions are location dependent and therefore can be used for positioning. In this paper, we investigate the influence of elementary structures, in particular a sphere and a cylinder, on the achievable accuracy of magnetic positioning methods. In a first step, we analytically calculate the magnetic field around a sphere and a cylinder in an outer homogeneous magnetic field. Assuming a noisy magnetic field sensor, we investigate the achievable positioning accuracy when observing these resulting fields. For our analysis, we calculate the Cramér–Rao lower bound, which is a fundamental lower bound on the variance of an unbiased estimator. The results of our investigations show the dependency of the positioning error variance on the magnetic sensor properties, in particular the sensor noise variance and the material properties, i.e., the relative permeability of the sphere with respect to the cylinder and the location of the sensor relative to the sphere with respect to the cylinder. The insights provided in this work make it possible to evaluate experimental results from a theoretical perspective.

Item URL in elib:https://elib.dlr.de/203644/
Document Type:Article
Title:Cramér–Rao Lower Bound for Magnetic Field Localization around Elementary Structures
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Dammann, ArminUNSPECIFIEDhttps://orcid.org/0000-0002-7112-1833UNSPECIFIED
Siebler, BenjaminUNSPECIFIEDhttps://orcid.org/0000-0002-1745-408XUNSPECIFIED
Sand, StephanUNSPECIFIEDhttps://orcid.org/0000-0001-9502-5654UNSPECIFIED
Date:9 April 2024
Journal or Publication Title:Sensors
Refereed publication:Yes
Open Access:Yes
Gold Open Access:Yes
In ISI Web of Science:Yes
Publisher:Multidisciplinary Digital Publishing Institute (MDPI)
Series Name:Wireless Sensors and Machine-Learning-Based Algorithms, Systems, and Applications for Practical Positioning and Navigation Systems
Keywords:navigation, position estimation; estimation theory; magnetic field; magnetic sensor; estimation error; Fisher information; Cramér–Rao lower bound
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Communication, Navigation, Quantum Technology
DLR - Research area:Raumfahrt
DLR - Program:R KNQ - Communication, Navigation, Quantum Technology
DLR - Research theme (Project):R - Project HIGAIN [KNQ], V - ProCo - Propulsion and Coupling
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Communication and Navigation > Communications Systems
Deposited By: Dammann, Dr.-Ing. Armin
Deposited On:17 Apr 2024 09:54
Last Modified:24 Apr 2024 12:28

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