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A comparison of nonlinear filtering approaches in the context of an HIV model

1. Center for Research in Scientific Computation, Raleigh, NC 27695-8205

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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Keywords HIV.; Gauss-Hermite filter; unscented Kalman filter; extended Kalman filter

Citation: H. Thomas Banks, Shuhua Hu, Zackary R. Kenz, Hien T. Tran. A comparison of nonlinear filtering approaches in the context of an HIV model. Mathematical Biosciences and Engineering, 2010, 7(2): 213-236. doi: 10.3934/mbe.2010.7.213


This article has been cited by

  • 1. András Hartmann, Susana Vinga, João M. Lemos, Online Bayesian Time-varying Parameter Estimation of HIV-1 Time-series*, IFAC Proceedings Volumes, 2012, 45, 16, 1294, 10.3182/20120711-3-BE-2027.00277

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