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Modeling and Interpolation of the Ambient Magnetic Field by Gaussian Processes
Department of Computer Science, Aalto University, Espoo, Finland.
Department of Engineering, University of Cambridge, Cambridge, U.K..
Department of Information Technology, Uppsala University, Uppsala, Sweden.
Department of Information Technology, Uppsala University, Uppsala, Sweden.
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2018 (English)In: IEEE Transactions on robotics, ISSN 1552-3098, E-ISSN 1941-0468, Vol. 34, no 4, p. 1112-1127Article in journal (Refereed) Published
Abstract [en]

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell’s equations, we derive and present a Bayesian nonparametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by imposing a Gaussian process (GP) prior to the latent scalar potential of the magnetic field. By rewriting the GP model in terms of a Hilbert space representation, we circumvent the computational pitfalls associated with GP modeling and provide a computationally efficient and physically justified modeling tool for the ambient magnetic field. The model allows for sequential updating of the estimate and time-dependent changes in the magnetic field. The model is shown to work well in practice in different applications. We demonstrate mapping of the magnetic field both with an inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2018. Vol. 34, no 4, p. 1112-1127
Keywords [en]
Magnetometers;Magnetic domains;Magnetosphere;Computational modeling;Interpolation;Mathematical model;Simultaneous localization and mapping;Gaussian process (GP);magnetic field;mapping;Maxwell’s equations;online representation
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-150520DOI: 10.1109/TRO.2018.2830326OAI: oai:DiVA.org:liu-150520DiVA, id: diva2:1241564
Available from: 2018-08-24 Created: 2018-08-24 Last updated: 2018-08-24Bibliographically approved
In thesis
1. Probabilistic modeling for sensor fusion with inertial measurements
Open this publication in new window or tab >>Probabilistic modeling for sensor fusion with inertial measurements
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In recent years, inertial sensors have undergone major developments. The quality of their measurements has improved while their cost has decreased, leading to an increase in availability. They can be found in stand-alone sensor units, so-called inertial measurement units, but are nowadays also present in for instance any modern smartphone, in Wii controllers and in virtual reality headsets.

The term inertial sensor refers to the combination of accelerometers and gyroscopes. These measure the external specific force and the angular velocity, respectively. Integration of their measurements provides information about the sensor's position and orientation. However, the position and orientation estimates obtained by simple integration suffer from drift and are therefore only accurate on a short time scale. In order to improve these estimates, we combine the inertial sensors with additional sensors and models. To combine these different sources of information, also called sensor fusion, we make use of probabilistic models to take the uncertainty of the different sources of information into account. The first contribution of this thesis is a tutorial paper that describes the signal processing foundations underlying position and orientation estimation using inertial sensors.

In a second contribution, we use data from multiple inertial sensors placed on the human body to estimate the body's pose. A biomechanical model encodes the knowledge about how the different body segments are connected to each other. We also show how the structure inherent to this problem can be exploited. This opens up for processing long data sets and for solving the problem in a distributed manner.

Inertial sensors can also be combined with time of arrival measurements from an ultrawideband (UWB) system. We focus both on calibration of the UWB setup and on sensor fusion of the inertial and UWB measurements. The UWB measurements are modeled by a tailored heavy-tailed asymmetric distribution. This distribution naturally handles the possibility of measurement delays due to multipath and non-line-of-sight conditions while not allowing for the possibility of measurements arriving early, i.e. traveling faster than the speed of light.

Finally, inertial sensors can be combined with magnetometers. We derive an algorithm that can calibrate a magnetometer for the presence of metallic objects attached to the sensor. Furthermore, the presence of metallic objects in the environment can be exploited by using them as a source of position information. We present a method to build maps of the indoor magnetic field and experimentally show that if a map of the magnetic field is available, accurate position estimates can be obtained by combining inertial and magnetometer measurements.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. p. 46
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1814
National Category
Control Engineering Medical Laboratory and Measurements Technologies Signal Processing
Identifiers
urn:nbn:se:liu:diva-133083 (URN)10.3384/diss.diva-133083 (DOI)9789176856215 (ISBN)
Public defence
2017-01-13, Visionen, House B, Campus Valla, Linköping, 10:15 (English)
Supervisors
Funder
EU, FP7, Seventh Framework ProgrammeSwedish Research Council
Available from: 2016-12-15 Created: 2016-12-09 Last updated: 2019-10-29Bibliographically approved

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