A comparison of nonlinear filtering approaches in the context of anHIV model - H. Thomas Banks; Shuhua Hu; Zackary R. Kenz; Hien T. Tran (Mathematical Biosciences and Engineering)
In this paper three different filtering methods, the ExtendedKalman Filter (EKF), the Gauss-Hermite Filter (GHF), and theUnscented Kalman Filter (UKF), are compared for state-only andcoupled state and parameter estimation when used with log statevariables of a model of the immunologic response to the humanimmunodeficiency virus (HIV) in individuals. The filters areimplemented to estimate model states as well as model parametersfrom simulated noisy data, and are compared in terms of estimationaccuracy and computational time. Numerical experiments reveal thatthe GHF is the most computationally expensive algorithm, while theEKF is the least expensive one. In addition, computationalexperiments suggest that there is little difference in theestimation accuracy between the UKF and GHF. When measurements aretaken as frequently as every week to two weeks, the EKF is thesuperior filter. When measurements are further apart, the UKF is thebest choice in the problem under investigation.