Abstract
Ordinary differential equation (ODE) models are widely used to model dynamic processes in many scientific fields. Parameter estimation is usually a challenging problem, especially in nonlinear ODE models. The most popular method, nonlinear least square estimation, is shown to be strongly sensitive to outliers. In this paper, robust estimation of parameters using M-estimators is proposed, and their asymptotic properties are obtained under some regular conditions. The authors also provide a method to adjust Huber parameter automatically according to the observations. Moreover, a method is presented to estimate the initial values of parameters and state variables. The efficiency and robustness are well balanced in Huber estimators, which is demonstrated via numerical simulations and chlorides data analysis.
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This research is supported by the Natural Science Foundation of China under Grant Nos. 11201317, 11028103, 11231010, 11471223, Doctoral Fund of Ministry of Education of China under Grant No. 20111108120002, the Beijing Municipal Education Commission Foundation under Grant No. KM201210028005, and the Key project of Beijing Municipal Educational Commission.
This paper was recommended for publication by Editor LIU Yungang.
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Qiu, Y., Hu, T., Liang, B. et al. Robust estimation of parameters in nonlinear ordinary differential equation models. J Syst Sci Complex 29, 41–60 (2016). https://doi.org/10.1007/s11424-015-4045-9
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DOI: https://doi.org/10.1007/s11424-015-4045-9