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A Modified Cramér-Rao Bound for Discrete-Time Markovian Dynamic Systems

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Název: A Modified Cramér-Rao Bound for Discrete-Time Markovian Dynamic Systems
Autoři: El Bouch, Sara, Galy, Jérôme, Chaumette, Éric, Vilà-Valls, Jordi
Přispěvatelé: Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Hors Équipe (LIRMM, Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Département Electronique, Optronique et Signal (DEOS)
Zdroj: ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing ; https://hal-lirmm.ccsd.cnrs.fr/lirmm-04834020 ; ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2024, Seoul, South Korea. pp.9706-9710, ⟨10.1109/icassp48485.2024.10446252⟩
Informace o vydavateli: CCSD
IEEE
Rok vydání: 2024
Sbírka: LIRMM: HAL (Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier)
Témata: Estimation, Radar, Signal processing, Probability density function, Real-time systems, Acoustics, Random variables, Modified Cramér-Rao Bound, Markovian Dynamic Systems, [INFO]Computer Science [cs]
Geografické téma: Seoul, South Korea
Popis: International audience ; It is well-known that the Modified Cramér-Rao Bound (MCRB) holds particular value in nonstandard deterministic estimation scenarios. Specifically, it proves invaluable when, in addition to estimating deterministic parameters, one needs to determine the probability density function (p.d.f) of the data through the marginalization of a joint p.d.f over random variables. In general, this process of marginalization is mathematically intractable, which restricts the utility of the conventional CRB. This limitation is especially pertinent in the context of discrete-time Markovian dynamic systems. However, we demonstrate that for such systems, the MCRB can be computed recursively with minimal computational burden, provided certain mild regularity conditions are met for the random nuisance parameters. Although this computational advantage may entail a degree of looseness in the bound, we present evidence showcasing the practical relevance of the proposed expressions in a scenario where the MCRB and CRB align.
Druh dokumentu: conference object
Jazyk: English
DOI: 10.1109/icassp48485.2024.10446252
Dostupnost: https://hal-lirmm.ccsd.cnrs.fr/lirmm-04834020
https://doi.org/10.1109/icassp48485.2024.10446252
Přístupové číslo: edsbas.EEBAA991
Databáze: BASE
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  Data: A Modified Cramér-Rao Bound for Discrete-Time Markovian Dynamic Systems
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  Data: <searchLink fieldCode="AR" term="%22El+Bouch%2C+Sara%22">El Bouch, Sara</searchLink><br /><searchLink fieldCode="AR" term="%22Galy%2C+Jérôme%22">Galy, Jérôme</searchLink><br /><searchLink fieldCode="AR" term="%22Chaumette%2C+Éric%22">Chaumette, Éric</searchLink><br /><searchLink fieldCode="AR" term="%22Vilà-Valls%2C+Jordi%22">Vilà-Valls, Jordi</searchLink>
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  Data: Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO)<br />Hors Équipe (LIRMM<br />Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM)<br />Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)<br />Département Electronique, Optronique et Signal (DEOS)
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  Data: ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing ; https://hal-lirmm.ccsd.cnrs.fr/lirmm-04834020 ; ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2024, Seoul, South Korea. pp.9706-9710, ⟨10.1109/icassp48485.2024.10446252⟩
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  Data: 2024
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  Data: International audience ; It is well-known that the Modified Cramér-Rao Bound (MCRB) holds particular value in nonstandard deterministic estimation scenarios. Specifically, it proves invaluable when, in addition to estimating deterministic parameters, one needs to determine the probability density function (p.d.f) of the data through the marginalization of a joint p.d.f over random variables. In general, this process of marginalization is mathematically intractable, which restricts the utility of the conventional CRB. This limitation is especially pertinent in the context of discrete-time Markovian dynamic systems. However, we demonstrate that for such systems, the MCRB can be computed recursively with minimal computational burden, provided certain mild regularity conditions are met for the random nuisance parameters. Although this computational advantage may entail a degree of looseness in the bound, we present evidence showcasing the practical relevance of the proposed expressions in a scenario where the MCRB and CRB align.
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  Data: 10.1109/icassp48485.2024.10446252
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  Data: https://hal-lirmm.ccsd.cnrs.fr/lirmm-04834020<br />https://doi.org/10.1109/icassp48485.2024.10446252
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