Journal
IEEE TRANSACTIONS ON ROBOTICS
Volume 34, Issue 4, Pages 1112-1127Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TRO.2018.2830326
Keywords
Gaussian process (GP); magnetic field; mapping; Maxwell's equations; online representation
Categories
Funding
- Academy of Finland [266940, 273475, 308640]
- CADICS, a Linnaeus Center
- project Probabilistic Modelling of Dynamical Systems [621-2013-5524]
- Swedish Research Council (VR)
- Swedish Foundation for Strategic Research under the project Cooperative Localization
- EPSRC Grant Autonomous Behaviour and Learning in an Uncertain World [EP/J012300/1]
- Academy of Finland (AKA) [273475] Funding Source: Academy of Finland (AKA)
- EPSRC [EP/J012300/1] Funding Source: UKRI
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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.
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