Posterior Cramér-Rao bounds for discrete-time nonlinear filtering

Autores
Tichavský, Petr; Muravchik, Carlos Horacio; Nehorai, Arye
Año de publicación
1998
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.
Facultad de Ingeniería
Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales
Materia
Ingeniería
Electrotecnia
Adaptive estimation
Kalman filtering
nonlinear filters
time-varying systems
tracking filters
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/122993
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/122993
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Posterior Cramér-Rao bounds for discrete-time nonlinear filteringTichavský, PetrMuravchik, Carlos HoracioNehorai, AryeIngenieríaElectrotecniaAdaptive estimationKalman filteringnonlinear filterstime-varying systemstracking filtersA mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.Facultad de IngenieríaInstituto de Investigaciones en Electrónica, Control y Procesamiento de Señales1998-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1386-1396http://sedici.unlp.edu.ar/handle/10915/122993enginfo:eu-repo/semantics/altIdentifier/issn/1053-587Xinfo:eu-repo/semantics/altIdentifier/doi/10.1109/78.668800info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:29:14Zoai:sedici.unlp.edu.ar:10915/122993Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:29:15.172SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Posterior Cramér-Rao bounds for discrete-time nonlinear filtering
title Posterior Cramér-Rao bounds for discrete-time nonlinear filtering
spellingShingle Posterior Cramér-Rao bounds for discrete-time nonlinear filtering
Tichavský, Petr
Ingeniería
Electrotecnia
Adaptive estimation
Kalman filtering
nonlinear filters
time-varying systems
tracking filters
title_short Posterior Cramér-Rao bounds for discrete-time nonlinear filtering
title_full Posterior Cramér-Rao bounds for discrete-time nonlinear filtering
title_fullStr Posterior Cramér-Rao bounds for discrete-time nonlinear filtering
title_full_unstemmed Posterior Cramér-Rao bounds for discrete-time nonlinear filtering
title_sort Posterior Cramér-Rao bounds for discrete-time nonlinear filtering
dc.creator.none.fl_str_mv Tichavský, Petr
Muravchik, Carlos Horacio
Nehorai, Arye
author Tichavský, Petr
author_facet Tichavský, Petr
Muravchik, Carlos Horacio
Nehorai, Arye
author_role author
author2 Muravchik, Carlos Horacio
Nehorai, Arye
author2_role author
author
dc.subject.none.fl_str_mv Ingeniería
Electrotecnia
Adaptive estimation
Kalman filtering
nonlinear filters
time-varying systems
tracking filters
topic Ingeniería
Electrotecnia
Adaptive estimation
Kalman filtering
nonlinear filters
time-varying systems
tracking filters
dc.description.none.fl_txt_mv A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.
Facultad de Ingeniería
Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales
description A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.
publishDate 1998
dc.date.none.fl_str_mv 1998-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/122993
url http://sedici.unlp.edu.ar/handle/10915/122993
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1053-587X
info:eu-repo/semantics/altIdentifier/doi/10.1109/78.668800
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
1386-1396
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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score 13.070432

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