Least-squares Polynomial Estimation from Observations Featuring Correlated Random Delays
The least-squares polynomial filtering and fixed-point smoothing problems of discrete-time signals from randomly delayed observations is addressed, when the Bernoulli random variables modelling the delay are correlated at consecutive sampling times. Recursive estimation algorithms are deduced withou...
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| Published in: | Methodology and computing in applied probability Vol. 12; no. 3; pp. 491 - 509 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Springer US
01.09.2010
Springer Nature B.V |
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| ISSN: | 1387-5841, 1573-7713 |
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| Abstract | The least-squares polynomial filtering and fixed-point smoothing problems of discrete-time signals from randomly delayed observations is addressed, when the Bernoulli random variables modelling the delay are correlated at consecutive sampling times. Recursive estimation algorithms are deduced without requiring full knowledge of the state-space model generating the signal process, but only information about the delay probabilities and the moments of the processes involved. Defining a suitable augmented observation vector, the polynomial estimation problem is reduced to the linear estimation problem of the signal based on the augmented observations, which is solved by using an innovation approach. |
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| AbstractList | The least-squares polynomial filtering and fixed-point smoothing problems of discrete-time signals from randomly delayed observations is addressed, when the Bernoulli random variables modelling the delay are correlated at consecutive sampling times. Recursive estimation algorithms are deduced without requiring full knowledge of the state-space model generating the signal process, but only information about the delay probabilities and the moments of the processes involved. Defining a suitable augmented observation vector, the polynomial estimation problem is reduced to the linear estimation problem of the signal based on the augmented observations, which is solved by using an innovation approach.[PUBLICATION ABSTRACT] The least-squares polynomial filtering and fixed-point smoothing problems of discrete-time signals from randomly delayed observations is addressed, when the Bernoulli random variables modelling the delay are correlated at consecutive sampling times. Recursive estimation algorithms are deduced without requiring full knowledge of the state-space model generating the signal process, but only information about the delay probabilities and the moments of the processes involved. Defining a suitable augmented observation vector, the polynomial estimation problem is reduced to the linear estimation problem of the signal based on the augmented observations, which is solved by using an innovation approach. |
| Author | Caballero-Águila, R. Linares-Pérez, J. Hermoso-Carazo, A. |
| Author_xml | – sequence: 1 givenname: R. surname: Caballero-Águila fullname: Caballero-Águila, R. email: raguila@ujaen.es organization: Dpto. Estadística e I.O., Universidad de Jaén – sequence: 2 givenname: A. surname: Hermoso-Carazo fullname: Hermoso-Carazo, A. organization: Dpto. Estadística e I.O., Universidad de Granada – sequence: 3 givenname: J. surname: Linares-Pérez fullname: Linares-Pérez, J. organization: Dpto. Estadística e I.O., Universidad de Granada |
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| CitedBy_id | crossref_primary_10_1016_j_cam_2011_06_021 crossref_primary_10_1109_TAC_2013_2246474 |
| Cites_doi | 10.1109/18.335913 10.1016/S0165-1684(99)00154-1 10.1016/j.amc.2003.12.066 10.1016/S0167-6911(01)00132-3 10.1016/S0165-1684(97)00126-6 10.1109/TAC.2003.809771 10.1109/81.933327 10.1109/TAC.2004.834121 10.1016/S0005-1098(97)00170-2 10.1109/83.563326 10.1137/S0363012993252899 10.1080/00207720701777777 10.1016/j.dsp.2007.04.007 10.1007/s11045-005-4127-2 10.1109/9.400478 10.1109/78.774757 10.1093/ietfec/e89-a.2.486 10.1080/02286203.2003.11442252 |
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| DOI | 10.1007/s11009-008-9117-z |
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| Keywords | Filtering and smoothing algorithms Polynomial estimation 60G35 Least-squares estimation Randomly delayed observations 62M20 |
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| Title | Least-squares Polynomial Estimation from Observations Featuring Correlated Random Delays |
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