American Institute of Mathematical Sciences

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2010, 7(2): 213-236. doi: 10.3934/mbe.2010.7.213

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

H. Thomas Banks 1, , Shuhua Hu 1, , Zackary R. Kenz 1, and  Hien T. Tran 1,

1. 

Center for Research in Scientific Computation, Raleigh, NC 27695-8205, United States, United States, United States

Received  July 2009 Revised  January 2010 Published  April 2010

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.
Keywords: HIV., Gauss-Hermite filter, unscented Kalman filter, extended Kalman filter.
Mathematics Subject Classification: 65C30, 92D30, 93E1.
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 & Engineering, 2010, 7 (2) : 213-236. doi: 10.3934/mbe.2010.7.213
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