Fixed-Lag Smoothing Algorithm under Non-independent Uncertainty

Seiichi NAKAMORI; Aurora HERMOSO-CARAZO; Josefa LINARES-PEREZ

doi:10.1093/ietfec/e88-a.4.988

Fixed-Lag Smoothing Algorithm under Non-independent Uncertainty

Seiichi NAKAMORI, Aurora HERMOSO-CARAZO, Josefa LINARES-PEREZ

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This paper discusses the least-squares linear filtering and fixed-lag smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of not necessarily independent Bernoulli variables. It is assumed that the observations are perturbed by white noise and the autocovariance function of the signal is factorizable. Using an innovation approach we obtain the filtering and fixed-lag smoothing recursive algorithms, which do not require the knowledge of the state-space model generating the signal. Besides the observed values, they use only the matrix functions defining the factorizable autocovariance function of the signal, the noise autocovariance function, the marginal probabilities and the (2,2)-element of the conditional probability matrices of the Bernoulli variables. The algorithms are applied to estimate a scalar signal which may be transmitted through one of two channels.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.4 pp.988-995

Publication Date: 2005/04/01

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DOI: 10.1093/ietfec/e88-a.4.988

Type of Manuscript: PAPER

Category: Digital Signal Processing

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Seiichi NAKAMORI, Aurora HERMOSO-CARAZO, Josefa LINARES-PEREZ, "Fixed-Lag Smoothing Algorithm under Non-independent Uncertainty" in IEICE TRANSACTIONS on Fundamentals, vol. E88-A, no. 4, pp. 988-995, April 2005, doi: 10.1093/ietfec/e88-a.4.988.
Abstract: This paper discusses the least-squares linear filtering and fixed-lag smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of not necessarily independent Bernoulli variables. It is assumed that the observations are perturbed by white noise and the autocovariance function of the signal is factorizable. Using an innovation approach we obtain the filtering and fixed-lag smoothing recursive algorithms, which do not require the knowledge of the state-space model generating the signal. Besides the observed values, they use only the matrix functions defining the factorizable autocovariance function of the signal, the noise autocovariance function, the marginal probabilities and the (2,2)-element of the conditional probability matrices of the Bernoulli variables. The algorithms are applied to estimate a scalar signal which may be transmitted through one of two channels.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.4.988/_p

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@ARTICLE{e88-a_4_988,
author={Seiichi NAKAMORI, Aurora HERMOSO-CARAZO, Josefa LINARES-PEREZ, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Fixed-Lag Smoothing Algorithm under Non-independent Uncertainty},
year={2005},
volume={E88-A},
number={4},
pages={988-995},
abstract={This paper discusses the least-squares linear filtering and fixed-lag smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of not necessarily independent Bernoulli variables. It is assumed that the observations are perturbed by white noise and the autocovariance function of the signal is factorizable. Using an innovation approach we obtain the filtering and fixed-lag smoothing recursive algorithms, which do not require the knowledge of the state-space model generating the signal. Besides the observed values, they use only the matrix functions defining the factorizable autocovariance function of the signal, the noise autocovariance function, the marginal probabilities and the (2,2)-element of the conditional probability matrices of the Bernoulli variables. The algorithms are applied to estimate a scalar signal which may be transmitted through one of two channels.},
keywords={},
doi={10.1093/ietfec/e88-a.4.988},
ISSN={},
month={April},}

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TY - JOUR
TI - Fixed-Lag Smoothing Algorithm under Non-independent Uncertainty
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 988
EP - 995
AU - Seiichi NAKAMORI
AU - Aurora HERMOSO-CARAZO
AU - Josefa LINARES-PEREZ
PY - 2005
DO - 10.1093/ietfec/e88-a.4.988
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2005
AB - This paper discusses the least-squares linear filtering and fixed-lag smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of not necessarily independent Bernoulli variables. It is assumed that the observations are perturbed by white noise and the autocovariance function of the signal is factorizable. Using an innovation approach we obtain the filtering and fixed-lag smoothing recursive algorithms, which do not require the knowledge of the state-space model generating the signal. Besides the observed values, they use only the matrix functions defining the factorizable autocovariance function of the signal, the noise autocovariance function, the marginal probabilities and the (2,2)-element of the conditional probability matrices of the Bernoulli variables. The algorithms are applied to estimate a scalar signal which may be transmitted through one of two channels.
ER -