NDLI: Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering

Content Provider	IEEE Xplore Digital Library
Author	Schrempf, O.C. Brunn, D. Hanebeck, U.D.
Copyright Year	2006
Description	Author affiliation: Inst. of Comput. Sci. & Eng., Univ. Karlsruhe (Schrempf, O.C.; Brunn, D.; Hanebeck, U.D.)
Abstract	A deterministic procedure for optimal approximation of arbitrary probability density functions by means of Dirac mixtures with equal weights is proposed. The optimality of this approximation is guaranteed by minimizing the distance of the approximation from the true density. For this purpose a distance measure is required, which is in general not well defined for Dirac mixtures. Hence, a key contribution is to compare the corresponding cumulative distribution functions. This paper concentrates on the simple and intuitive integral quadratic distance measure. For the special case of a Dirac mixture with equally weighted components, closed-form solutions for special types of densities like uniform and Gaussian densities are obtained. Closed-form solution of the given optimization problem is not possible in general. Hence, another key contribution is an efficient solution procedure for arbitrary true densities based on a homotopy continuation approach. In contrast to standard Monte Carlo techniques like particle filters that are based on random sampling, the proposed approach is deterministic and ensures an optimal approximation with respect to a given distance measure. In addition, the number of required components (particles) can easily be deduced by application of the proposed distance measure. The resulting approximations can be used as basis for recursive nonlinear filtering mechanism alternative to Monte Carlo methods
Starting Page	1709
Ending Page	1714
File Size	509621
Page Count	6
File Format	PDF
ISBN	1424401712
DOI	10.1109/CDC.2006.376759
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Particle measurements Particle filters Filtering Probability density function Distribution functions Measurement standards Monte Carlo methods Density measurement Optimal control USA Councils
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Dirac Mixture Density Approximation Based on Minimization of the Weighted Cramer-von Mises Distance

Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering (2006)

Progressive correction for deterministic Dirac mixture approximations

A new quasi-Monte Carlo filtering algorithm based on number theoretical method

Greedy algorithms for dirac mixture approximation of arbitrary probability density functions

Incremental density approximation and kernel-based Bayesian filtering for object tracking

Recursive Prediction of Stochastic Nonlinear Systems Based on Optimal Dirac Mixture Approximations

Deterministic approximation of circular densities with symmetric Dirac mixtures based on two circular moments

Comments on Gaussian particle filtering

Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering

Similar Documents

Dirac Mixture Density Approximation Based on Minimization of the Weighted Cramer-von Mises Distance

Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering (2006)

Progressive correction for deterministic Dirac mixture approximations

A new quasi-Monte Carlo filtering algorithm based on number theoretical method

Greedy algorithms for dirac mixture approximation of arbitrary probability density functions

Incremental density approximation and kernel-based Bayesian filtering for object tracking

Recursive Prediction of Stochastic Nonlinear Systems Based on Optimal Dirac Mixture Approximations

Deterministic approximation of circular densities with symmetric Dirac mixtures based on two circular moments

Comments on Gaussian particle filtering

Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering