• Corpus ID: 239050313

Hyperspherical Dirac Mixture Reapproximation

@article{Li2021HypersphericalDM,
  title={Hyperspherical Dirac Mixture Reapproximation},
  author={Kailai Li and Florian Pfaff and Uwe D. Hanebeck},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.10411}
}
  • Kailai Li, F. Pfaff, U. Hanebeck
  • Published 20 October 2021
  • Computer Science, Mathematics, Engineering
  • ArXiv
We propose a novel scheme for efficient Dirac mixture modeling of distributions on unit hyperspheres. A so-called hyperspherical localized cumulative distribution (HLCD) is introduced as a local and smooth characterization of the underlying continuous density in hyperspherical domains. Based on HLCD, a manifold-adapted modification of the Cramér–von Mises distance (HCvMD) is established to measure the statistical divergence between two Dirac mixtures of arbitrary dimensions. Given a (source… 

Figures from this paper

References

SHOWING 1-10 OF 57 REFERENCES
Optimal Reduction of Dirac Mixture Densities on the 2-Sphere
This paper is concerned with optimal approximation of a given Dirac mixture density on the S2 manifold, i.e., a set of weighted samples located on the unit sphere, by an equally weighted Dirac
Clustering on the Unit Hypersphere using von Mises-Fisher Distributions
TLDR
A generative mixture-model approach to clustering directional data based on the von Mises-Fisher distribution, which arises naturally for data distributed on the unit hypersphere, and derives and analyzes two variants of the Expectation Maximization framework for estimating the mean and concentration parameters of this mixture.
Optimal Reduction of Multivariate Dirac Mixture Densities
TLDR
An alternative to the classical cumulative distribution, the Localized Cumulative Distribution, is defined, as a smooth characterization of discrete random quantities (on continuous domains), which provides the basis for various efficient nonlinear estimation and control methods.
Hyperspherical Deterministic Sampling Based on Riemannian Geometry for Improved Nonlinear Bingham Filtering
TLDR
A geometry-adaptive sampling scheme for generating equally weighted deterministic samples of Bingham distributions in arbitrary dimensions that gives better tracking accuracy and robustness for nonlinear orientation estimations.
Geometry-driven Deterministic Sampling for Nonlinear Bingham Filtering
TLDR
A geometry-driven deterministic sampling method for Bingham distributions in arbitrary dimensions that enables better accuracy and robustness for nonlinear Bingham filtering and integrates into a quaternion-based orientation estimation framework.
Progressive von Mises–Fisher Filtering Using Isotropic Sample Sets for Nonlinear Hyperspherical Estimation †
TLDR
A novel scheme for nonlinear hyperspherical estimation using the von Mises–Fisher distribution with deterministic sample sets with an isotropic layout is presented, considerably enhancing the filtering performance under strong nonlinearity.
Synchronizing Probability Measures on Rotations via Optimal Transport
TLDR
A new paradigm, `measure synchronization', for synchronizing graphs with measure-valued edges is introduced, which aims at estimating marginal distributions of absolute orientations by synchronizing the `conditional' ones on the Riemannian manifold of quaternions.
Grid-Based Quaternion Filter for SO(3) Estimation
TLDR
A novel discrete Bayesian filtering scheme is proposed on the manifold of unit quaternions for rotation estimation that allows non-parametric modeling of the underlying uncertainty using Dirac mixtures located on a hyperspherical grid.
Dual Quaternion Sample Reduction for SE(2) Estimation
TLDR
A novel sample reduction scheme for random variables belonging to the SE(2) group by means of Dirac mixture approximation, which shows superior tracking performance of the sample reduction-based filter compared with Monte Carlo-based as well as parametric model-based planar dual quaternion filters.
Nonlinear von Mises–Fisher Filtering Based on Isotropic Deterministic Sampling
  • Kailai Li, F. Pfaff, U. Hanebeck
  • Computer Science
    2020 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI)
  • 2020
TLDR
A novel deterministic sampling approach for von Mises–Fisher distributions of arbitrary dimensions where samples of configurable size are drawn isotropically on the hypersphere while preserving the mean resultant vector of the underlying distribution.
...
1
2
3
4
5
...