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Nonlinear Kalman filtering for censored observations

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  • Arthur, Joseph
  • Attarian, Adam
  • Hamilton, Franz
  • Tran, Hien

Abstract

The use of Kalman filtering, as well as its nonlinear extensions, for the estimation of system variables and parameters has played a pivotal role in many fields of scientific inquiry where observations of the system are restricted to a subset of variables. However in the case of censored observations, where measurements of the system beyond a certain detection point are impossible, the estimation problem is complicated. Without appropriate consideration, censored observations can lead to inaccurate estimates. Motivated by previous work on censored filtering in linear systems, we develop a modified version of the extended Kalman filter to handle the case of censored observations in nonlinear systems. We validate this methodology in a simple oscillator system first, showing its ability to accurately reconstruct state variables and track system parameters when observations are censored. Finally, we utilize the nonlinear censored filter to analyze censored datasets from patients with hepatitis C and human immunodeficiency virus.

Suggested Citation

  • Arthur, Joseph & Attarian, Adam & Hamilton, Franz & Tran, Hien, 2018. "Nonlinear Kalman filtering for censored observations," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 155-166.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:155-166
    DOI: 10.1016/j.amc.2017.08.002
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    1. Alan S. Perelson & Avidan U. Neumann & Martin Markowitz & John M. Leonard & David D. Ho, 1996. "HIV-1 Dynamics In Vivo: Virion Clearance Rate, Infected Cell Lifespan, and Viral Generation Time," Working Papers 96-02-004, Santa Fe Institute.
    2. Ghanim Ullah & Steven J Schiff, 2010. "Assimilating Seizure Dynamics," PLOS Computational Biology, Public Library of Science, vol. 6(5), pages 1-12, May.
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    Cited by:

    1. Bi Liu & Yunlong Teng & Qi Huang, 2020. "RETRACTED: A novel imprecise reliability prediction method for incomplete lifetime data based on two-parameter Weibull distribution," Journal of Risk and Reliability, , vol. 234(1), pages 208-218, February.

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