A comparison of nonlinear filtering approaches in the context of an
HIV model
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Received:
01 July 2009
Accepted:
29 June 2018
Published:
01 April 2010
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MSC :
65C30, 92D30, 93E10.
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In this paper three different filtering methods, the Extended
Kalman Filter (EKF), the Gauss-Hermite Filter (GHF), and the
Unscented Kalman Filter (UKF), are compared for state-only and
coupled state and parameter estimation when used with log state
variables of a model of the immunologic response to the human
immunodeficiency virus (HIV) in individuals. The filters are
implemented to estimate model states as well as model parameters
from simulated noisy data, and are compared in terms of estimation
accuracy and computational time. Numerical experiments reveal that
the GHF is the most computationally expensive algorithm, while the
EKF is the least expensive one. In addition, computational
experiments suggest that there is little difference in the
estimation accuracy between the UKF and GHF. When measurements are
taken as frequently as every week to two weeks, the EKF is the
superior filter. When measurements are further apart, the UKF is the
best choice in the problem under investigation.
Citation: H. Thomas Banks, Shuhua Hu, Zackary R. Kenz, Hien T. Tran. A comparison of nonlinear filtering approaches in the context of anHIV model[J]. Mathematical Biosciences and Engineering, 2010, 7(2): 213-236. doi: 10.3934/mbe.2010.7.213
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Abstract
In this paper three different filtering methods, the Extended
Kalman Filter (EKF), the Gauss-Hermite Filter (GHF), and the
Unscented Kalman Filter (UKF), are compared for state-only and
coupled state and parameter estimation when used with log state
variables of a model of the immunologic response to the human
immunodeficiency virus (HIV) in individuals. The filters are
implemented to estimate model states as well as model parameters
from simulated noisy data, and are compared in terms of estimation
accuracy and computational time. Numerical experiments reveal that
the GHF is the most computationally expensive algorithm, while the
EKF is the least expensive one. In addition, computational
experiments suggest that there is little difference in the
estimation accuracy between the UKF and GHF. When measurements are
taken as frequently as every week to two weeks, the EKF is the
superior filter. When measurements are further apart, the UKF is the
best choice in the problem under investigation.
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