2,393 research outputs found
Modeling and interpolation of the ambient magnetic field by Gaussian processes
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.Comment: 17 pages, 12 figures, to appear in IEEE Transactions on Robotic
Sequential non-rigid structure from motion using physical priors
© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We propose a new approach to simultaneously recover camera pose and 3D shape of non-rigid and potentially extensible surfaces from a monocular image sequence. For this purpose, we make use of the Extended Kalman Filter based Simultaneous Localization And Mapping (EKF-SLAM) formulation, a Bayesian optimization framework traditionally used in mobile robotics for estimating camera pose and reconstructing rigid scenarios. In order to extend the problem to a deformable domain we represent the object's surface mechanics by means of Navier's equations, which are solved using a Finite Element Method (FEM). With these main ingredients, we can further model the material's stretching, allowing us to go a step further than most of current techniques, typically constrained to surfaces undergoing isometric deformations. We extensively validate our approach in both real and synthetic experiments, and demonstrate its advantages with respect to competing methods. More specifically, we show that besides simultaneously retrieving camera pose and non-rigid shape, our approach is adequate for both isometric and extensible surfaces, does not require neither batch processing all the frames nor tracking points over the whole sequence and runs at several frames per second.Peer ReviewedPostprint (author's final draft
Convergence and Consistency Analysis for A 3D Invariant-EKF SLAM
In this paper, we investigate the convergence and consistency properties of
an Invariant-Extended Kalman Filter (RI-EKF) based Simultaneous Localization
and Mapping (SLAM) algorithm. Basic convergence properties of this algorithm
are proven. These proofs do not require the restrictive assumption that the
Jacobians of the motion and observation models need to be evaluated at the
ground truth. It is also shown that the output of RI-EKF is invariant under any
stochastic rigid body transformation in contrast to based EKF
SLAM algorithm (-EKF) that is only invariant under
deterministic rigid body transformation. Implications of these invariance
properties on the consistency of the estimator are also discussed. Monte Carlo
simulation results demonstrate that RI-EKF outperforms -EKF,
Robocentric-EKF and the "First Estimates Jacobian" EKF, for 3D point feature
based SLAM
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