Suboptimal estimation of signals from uncertain observations using approximations of mixtures

doi:10.1016/j.dsp.2006.08.004

Digital Signal Processing

Volume 17, Issue 1, January 2007, Pages 4-16

https://doi.org/10.1016/j.dsp.2006.08.004 Get rights and content

Abstract

In this paper, we propose a suboptimal filtering algorithm for the estimation of a Gaussian signal from uncertain observations, using covariance information. The suboptimal estimators are obtained as the expectation of the signal, given the observations, when a certain approximation is considered for the conditional distribution. The approximation is carried out via successive approximations of mixtures of Gaussian distributions by Gaussian distributions. On the other hand, by assuming that the uncertainty probability is unknown, a recursive estimation algorithm is proposed for that probability. This algorithm is obtained under a Bayesian viewpoint; specifically, by considering a Beta as the a priori distribution for the unknown parameter, the proposed estimators provide approximations for the mean of the a posteriori distributions.

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Seiichi Nakamori was born in Kagoshima prefecture in 1951. He received the B.E. degree in electronic engineering from Kagoshima University in 1974, and the degree of Dr. of Eng. in applied mathematics and physics from Kyoto University in 1982. He was with the Faculty of Engineering, Ohita University, from 1974 to 1987, where he was promoted to a Lecturer, Interdisciplinary Chair (Applied Mathematics) in 1985. He joined Kagoshima University in 1987, as an Associate Professor in the Department of Technology (Electric Technology), Faculty of Education, where he was promoted to a Professor of the Graduate School of Education in 1994. He is mainly interested in the stochastic signal estimation problem. He is a member of the Society of Instrument and Control Engineers, the Institute of Systems, Control and Information Engineers, and the Japanese Society of Technology Education.

Aurora Hermoso-Carazo received the M.Sc. degree in mathematics (statistics) and the Ph.D. degree in likelihood test in log normal processes, both from the University of Granada, Spain, in 1979 and 1984, respectively. In 1986, she became an Associate Professor at the Department of Statistics and Operations Research, University of Granada, Spain. Her current research interests include stochastic systems, filtering, and prediction.

Josefa Linares-Pérez received the M.Sc. degree in mathematics (statistics) and the Ph.D. degree in stochastic differential equations, both from the University of Granada, Spain, in 1980 and 1982, respectively. She is currently a Professor at the Department of Statistics and Operations Research, University of Granada, Spain. Her research interest involves the areas of stochastic calculus and estimation in stochastic systems.

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Suboptimal estimation of signals from uncertain observations using approximations of mixtures

Abstract

Section snippets

Signal Process.

Digital Signal Process.

Linear estimation for discrete-time systems in the presence of time-correlated disturbances and uncertain observations

IEEE Trans. Automat. Control

Recursive estimator for linear and nonlinear systems with uncertain observations

Signal Process.

A view of three decades of linear filtering theory

IEEE Trans. Inform. Theory