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


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.
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

Alexander Bibov, Heikki Haario, Antti Solonen. Stabilized BFGS approximate Kalman filter. Inverse Problems and Imaging, 2015, 9 (4) : 1003-1024. doi: 10.3934/ipi.2015.9.1003


Russell Johnson, Carmen Núñez. The Kalman-Bucy filter revisited. Discrete and Continuous Dynamical Systems, 2014, 34 (10) : 4139-4153. doi: 10.3934/dcds.2014.34.4139


Andreas Bock, Colin J. Cotter. Learning landmark geodesics using the ensemble Kalman filter. Foundations of Data Science, 2021, 3 (4) : 701-727. doi: 10.3934/fods.2021020


Junyoung Jang, Kihoon Jang, Hee-Dae Kwon, Jeehyun Lee. Feedback control of an HBV model based on ensemble kalman filter and differential evolution. Mathematical Biosciences & Engineering, 2018, 15 (3) : 667-691. doi: 10.3934/mbe.2018030


Mojtaba F. Fathi, Ahmadreza Baghaie, Ali Bakhshinejad, Raphael H. Sacho, Roshan M. D'Souza. Time-resolved denoising using model order reduction, dynamic mode decomposition, and kalman filter and smoother. Journal of Computational Dynamics, 2020, 7 (2) : 469-487. doi: 10.3934/jcd.2020019


Wawan Hafid Syaifudin, Endah R. M. Putri. The application of model predictive control on stock portfolio optimization with prediction based on Geometric Brownian Motion-Kalman Filter. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021119


Sebastian Reich, Seoleun Shin. On the consistency of ensemble transform filter formulations. Journal of Computational Dynamics, 2014, 1 (1) : 177-189. doi: 10.3934/jcd.2014.1.177


Jin-Won Kim, Amirhossein Taghvaei, Yongxin Chen, Prashant G. Mehta. Feedback particle filter for collective inference. Foundations of Data Science, 2021, 3 (3) : 543-561. doi: 10.3934/fods.2021018


Qiyu Jin, Ion Grama, Quansheng Liu. Convergence theorems for the Non-Local Means filter. Inverse Problems and Imaging, 2018, 12 (4) : 853-881. doi: 10.3934/ipi.2018036


Hai Huyen Dam, Kok Lay Teo. Variable fractional delay filter design with discrete coefficients. Journal of Industrial and Management Optimization, 2016, 12 (3) : 819-831. doi: 10.3934/jimo.2016.12.819


Xiaoying Han, Jinglai Li, Dongbin Xiu. Error analysis for numerical formulation of particle filter. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1337-1354. doi: 10.3934/dcdsb.2015.20.1337


Xueling Zhou, Bingo Wing-Kuen Ling, Hai Huyen Dam, Kok-Lay Teo. Optimal design of window functions for filter window bank. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1119-1145. doi: 10.3934/jimo.2020014


Anugu Sumith Reddy, Amit Apte. Stability of non-linear filter for deterministic dynamics. Foundations of Data Science, 2021, 3 (3) : 647-675. doi: 10.3934/fods.2021025


Valerii Maltsev, Michael Pokojovy. On a parabolic-hyperbolic filter for multicolor image noise reduction. Evolution Equations and Control Theory, 2016, 5 (2) : 251-272. doi: 10.3934/eect.2016004


Kody Law, Abhishek Shukla, Andrew Stuart. Analysis of the 3DVAR filter for the partially observed Lorenz'63 model. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 1061-1078. doi: 10.3934/dcds.2014.34.1061


Yi Xu, Wenyu Sun. A filter successive linear programming method for nonlinear semidefinite programming problems. Numerical Algebra, Control and Optimization, 2012, 2 (1) : 193-206. doi: 10.3934/naco.2012.2.193


Abdel-Rahman Hedar, Alaa Fahim. Filter-based genetic algorithm for mixed variable programming. Numerical Algebra, Control and Optimization, 2011, 1 (1) : 99-116. doi: 10.3934/naco.2011.1.99


Andrea Arnold, Daniela Calvetti, Erkki Somersalo. Vectorized and parallel particle filter SMC parameter estimation for stiff ODEs. Conference Publications, 2015, 2015 (special) : 75-84. doi: 10.3934/proc.2015.0075


Sahani Pathiraja, Wilhelm Stannat. Analysis of the feedback particle filter with diffusion map based approximation of the gain. Foundations of Data Science, 2021, 3 (3) : 615-645. doi: 10.3934/fods.2021023


Xin Li, Feng Bao, Kyle Gallivan. A drift homotopy implicit particle filter method for nonlinear filtering problems. Discrete and Continuous Dynamical Systems - S, 2022, 15 (4) : 727-746. doi: 10.3934/dcdss.2021097

2018 Impact Factor: 1.313


  • PDF downloads (37)
  • HTML views (0)
  • Cited by (1)

[Back to Top]