Kim, J orcid.org/0000-0002-3456-6614 and Richardson, R (2016) Negative-free approximation of probability density function for nonlinear projection filter. In: 2016 IEEE 55th Conference on Decision and Control (CDC). 55th IEEE Conference on Decision and Control, 12-14 Dec 2016, Las Vegas, Nevada, United States. IEEE , pp. 3738-3743. ISBN 978-1-5090-1837-6
Abstract
Several approaches have been developed to estimate probability density functions (pdfs). The pdf has two important properties: the integration of pdf over whole sampling space is equal to 1 and the value of pdf in the sampling space is greater than or equal to zero. The first constraint can be easily achieved by the normalisation. On the other hand, it is hard to impose the non-negativeness in the sampling space. In a pdf estimation, some areas in the sampling space might have negative pdf values. It produces unreasonable moment values such as negative probability or variance. A transformation to guarantee the negative-free pdf over a chosen sampling space is presented and it is applied to the nonlinear projection filter. The filter approximates the pdf to solve nonlinear estimation problems. For simplicity, one-dimensional nonlinear system is used as an example to show the derivations and it can be readily generalised for higher dimensional systems. The efficiency of the proposed method is demonstrated by numerical simulations. The simulations also show that, for the same level of approximation error in the filter, the required number of basis functions with the transformation is a lot smaller than the ones without transformation. This would largely benefit the computational cost reduction.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, IEEE. This is an author produced version of a paper published in 2016 IEEE 55th Conference on Decision and Control (CDC). Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, 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 components of this work in other works. Uploaded in accordance with the publisher’s self-archiving policy. |
Keywords: | Probability density function, Kalman filters, Estimation, Space vehicles, Nonlinear systems, Mathematical model, Atmospheric measurements |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Systems and Design (iESD) (Leeds) |
Funding Information: | Funder Grant number EPSRC EP/N010523/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 12 Aug 2016 08:18 |
Last Modified: | 13 Apr 2017 21:58 |
Published Version: | https://doi.org/10.1109/CDC.2016.7798832 |
Status: | Published |
Publisher: | IEEE |
Identification Number: | 10.1109/CDC.2016.7798832 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:103369 |