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...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.展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.11201317,11028103,11231010,11471223Doctoral Fund of Ministry of Education of China under Grant No.20111108120002+1 种基金the Beijing Municipal Education Commission Foundation under Grant No.KM201210028005the Key project of Beijing Municipal Educational Commission
文摘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.
