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
The least trimmed squares estimator (LTS) is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. We show that the LT...The least trimmed squares estimator (LTS) is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. We show that the LTS estimate can be obtained by a simple algorithm with the complexity 0( N In N) for large N, where N is the number of measurements. We also show that though the LTS is robust in terms of the outliers, it is sensitive to the inliers. The concept of the inliers is introduced. Moreover, the Generalized Least Trimmed Squares estimator (GLTS) together with its solution are presented that reduces the effect of both the outliers and the inliers. Keywords Least squares - Least trimmed squares - Outliers - System identification - Parameter estimation - Robust parameter estimation This work was supported in part by NSF ECS — 9710297 and ECS — 0098181.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.
文摘The least trimmed squares estimator (LTS) is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. We show that the LTS estimate can be obtained by a simple algorithm with the complexity 0( N In N) for large N, where N is the number of measurements. We also show that though the LTS is robust in terms of the outliers, it is sensitive to the inliers. The concept of the inliers is introduced. Moreover, the Generalized Least Trimmed Squares estimator (GLTS) together with its solution are presented that reduces the effect of both the outliers and the inliers. Keywords Least squares - Least trimmed squares - Outliers - System identification - Parameter estimation - Robust parameter estimation This work was supported in part by NSF ECS — 9710297 and ECS — 0098181.
