mlsanityData to 14 Oct 2026

Modeling and interpolation of the ambient magnetic field by Gaussian processes

arXiv 1509.04634 ↗First posted 15 Sep 2015cs.RO stat.MLcited by 28

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Abstract (arXiv)

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 non-parametric 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 on 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.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 Sep 2015.

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Citing papers per year: 2021: 6; 2022: 8; 2023: 4; 2024: 7; 2025: 1; 2026: 2.

28 papers.

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  1. 2022Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficientscited by 17
  2. 2021High-Dimensional Gaussian Process Inference with Derivativescited by 16
  3. 2022Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equationscited by 14
  4. 2023A spectrum of physics-informed Gaussian processes for regression in engineeringcited by 14
  5. 2021Grey-box models for wave loading predictioncited by 13
  6. 2023Gaussian processes at the Helm(holtz): A more fluid model for ocean currentscited by 12
  7. 2023Memory-Based Dual Gaussian Processes for Sequential Learningcited by 11
  8. 2022Scalable First-Order Bayesian Optimization via Structured Automatic Differentiationcited by 10
  9. 2021Fusion-DHL: WiFi, IMU, and Floorplan Fusion for Dense History of Locations in Indoor Environmentscited by 8
  10. 2022Physics-informed machine learning for Structural Health Monitoringcited by 8
  11. 2024Physics-Informed Variational State-Space Gaussian Processescited by 7
  12. 2022On boundary conditions parametrized by analytic functionscited by 4
16 more
  1. 2025Uncertainty-Aware Diagnostics for Physics-Informed Machine Learningcited by 3
  2. 2021Uncertainty Quantification and Experimental Design for Large-Scale Linear Inverse Problems under Gaussian Process Priorscited by 2
  3. 2022Incorporating Sum Constraints into Multitask Gaussian Processescited by 2
  4. 2024Gaussian Process Priors for Boundary Value Problems of Linear Partial Differential Equationscited by 2
  5. 2021Hierarchical Non-Stationary Temporal Gaussian Processes With L1-Regularizationcited by 1
  6. 2021Efficient methods for Gaussian Markov random fields under sparse linear constraintscited by 1
  7. 2022Magnetic Field Prediction Using Generative Adversarial Networkscited by 1
  8. 2022Indoor SLAM Using a Foot-mounted IMU and the local Magnetic Fieldcited by 1
  9. 2024Stochastic Inference of Plate Bending from Heterogeneous Data: Physics-informed Gaussian Processes via Kirchhoff-Love Theorycited by 1
  10. 2024Adjusting Model Size in Continual Gaussian Processes: How Big is Big Enough?cited by 1
  11. 2024Enhancing Visual Inertial SLAM with Magnetic Measurementscited by 1
  12. 2023Large-scale magnetic field maps using structured kernel interpolation for Gaussian process regressioncited by 0
  13. 2024Exploiting Hankel-Toeplitz Structures for Fast Computation of Kernel Precision Matricescited by 0
  14. 2024Tensor network square root Kalman filter for online Gaussian process regressioncited by 0
  15. 2026Fast Reconstruction of Exact Maxwell Dynamics from Sparse Datacited by 0
  16. 2026GINIO: A Geometric SO(3)-Equivariant Interface for Neural Inertial Odometrycited by 0