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.
Highlights
The modeling of the physiologic and immunologic response to human immunodeficiency virus (HIV) infection in humans is generating a substantial amount of research effort, and significant progress has been made in the treatment of HIV-infected patients
Because HIV modeling generally involves partial observations and noisy measurements from combined compartments, the method by which the state is obtained at each sampling time is of special concern, and an efficient estimation technique is needed to develop a successful implementation of feedback control
For the case with only model states estimated, the Extended Kalman Filter (EKF) performs much better than both the Unscented Kalman Filter (UKF) and Gauss-Hermite Filter (GHF) in terms of estimation accuracy for all the measurement frequencies that we have investigated, and there is little difference in the estimation accuracy between the UKF and GHF
Summary
The modeling of the physiologic and immunologic response to HIV infection in humans is generating a substantial amount of research effort, and significant progress has been made in the treatment of HIV-infected patients. Because HIV modeling generally involves partial observations and noisy measurements from combined compartments, the method by which the state is obtained at each sampling time is of special concern, and an efficient estimation technique is needed to develop a successful implementation of feedback control. A number of challenges include development of filters for state and parameter estimation in the context of low frequency sampling and partial state observations that are censored Successful efforts in these areas must be combined with feedback control of nonlinear dynamics which are often only approximate for patient response. The EKF was found in [9] to have difficulty with state estimation even when the time span between measurements is only five days This motivates a need to consider alternative filtering methods.
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