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...

Full description

Bibliographic Details
Main Authors: Christian Gentner, Siwei Zhang, Thomas Jost
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Journal of Electrical and Computer Engineering
Online Access:http://dx.doi.org/10.1155/2018/5763461
id doaj-61ce5e425f294ed4b2e41f1d43cb5d03
record_format Article
spelling 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
_version_ 1721342689469792256