Log-PF: Particle Filtering in Logarithm Domain
This paper presents a particle filter, called Log-PF, based on particle weights represented on a logarithmic scale. In practical systems, particle weights may approach numbers close to zero which can cause numerical problems. Therefore, calculations using particle weights and probability densities i...
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Series: | Journal of Electrical and Computer Engineering |
Online Access: | http://dx.doi.org/10.1155/2018/5763461 |
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doaj-61ce5e425f294ed4b2e41f1d43cb5d032021-07-02T02:49:44ZengHindawi LimitedJournal of Electrical and Computer Engineering2090-01472090-01552018-01-01201810.1155/2018/57634615763461Log-PF: Particle Filtering in Logarithm DomainChristian Gentner0Siwei Zhang1Thomas Jost2German Aerospace Center (DLR), Institute of Communications and Navigation, Oberpfaffenhofen, 82234 Wessling, GermanyGerman Aerospace Center (DLR), Institute of Communications and Navigation, Oberpfaffenhofen, 82234 Wessling, GermanyGerman Aerospace Center (DLR), Institute of Communications and Navigation, Oberpfaffenhofen, 82234 Wessling, GermanyThis paper presents a particle filter, called Log-PF, based on particle weights represented on a logarithmic scale. In practical systems, particle weights may approach numbers close to zero which can cause numerical problems. Therefore, calculations using particle weights and probability densities in the logarithmic domain provide more accurate results. Additionally, calculations in logarithmic domain improve the computational efficiency for distributions containing exponentials or products of functions. To provide efficient calculations, the Log-PF exploits the Jacobian logarithm that is used to compute sums of exponentials. We introduce the weight calculation, weight normalization, resampling, and point estimations in logarithmic domain. For point estimations, we derive the calculation of the minimum mean square error (MMSE) and maximum a posteriori (MAP) estimate. In particular, in situations where sensors are very accurate the Log-PF achieves a substantial performance gain. We show the performance of the derived Log-PF by three simulations, where the Log-PF is more robust than its standard particle filter counterpart. Particularly, we show the benefits of computing all steps in logarithmic domain by an example based on Rao-Blackwellization.http://dx.doi.org/10.1155/2018/5763461 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Christian Gentner Siwei Zhang Thomas Jost |
spellingShingle |
Christian Gentner Siwei Zhang Thomas Jost Log-PF: Particle Filtering in Logarithm Domain Journal of Electrical and Computer Engineering |
author_facet |
Christian Gentner Siwei Zhang Thomas Jost |
author_sort |
Christian Gentner |
title |
Log-PF: Particle Filtering in Logarithm Domain |
title_short |
Log-PF: Particle Filtering in Logarithm Domain |
title_full |
Log-PF: Particle Filtering in Logarithm Domain |
title_fullStr |
Log-PF: Particle Filtering in Logarithm Domain |
title_full_unstemmed |
Log-PF: Particle Filtering in Logarithm Domain |
title_sort |
log-pf: particle filtering in logarithm domain |
publisher |
Hindawi Limited |
series |
Journal of Electrical and Computer Engineering |
issn |
2090-0147 2090-0155 |
publishDate |
2018-01-01 |
description |
This paper presents a particle filter, called Log-PF, based on particle weights represented on a logarithmic scale. In practical systems, particle weights may approach numbers close to zero which can cause numerical problems. Therefore, calculations using particle weights and probability densities in the logarithmic domain provide more accurate results. Additionally, calculations in logarithmic domain improve the computational efficiency for distributions containing exponentials or products of functions. To provide efficient calculations, the Log-PF exploits the Jacobian logarithm that is used to compute sums of exponentials. We introduce the weight calculation, weight normalization, resampling, and point estimations in logarithmic domain. For point estimations, we derive the calculation of the minimum mean square error (MMSE) and maximum a posteriori (MAP) estimate. In particular, in situations where sensors are very accurate the Log-PF achieves a substantial performance gain. We show the performance of the derived Log-PF by three simulations, where the Log-PF is more robust than its standard particle filter counterpart. Particularly, we show the benefits of computing all steps in logarithmic domain by an example based on Rao-Blackwellization. |
url |
http://dx.doi.org/10.1155/2018/5763461 |
work_keys_str_mv |
AT christiangentner logpfparticlefilteringinlogarithmdomain AT siweizhang logpfparticlefilteringinlogarithmdomain AT thomasjost logpfparticlefilteringinlogarithmdomain |
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