State estimation is the precondition and foundation of a bioprocess monitoring and optimal control. However,there are many difficulties in dealing with a non-linear system,such as the instability of process, un-modele...State estimation is the precondition and foundation of a bioprocess monitoring and optimal control. However,there are many difficulties in dealing with a non-linear system,such as the instability of process, un-modeled dynamics,parameter sensitivity,etc.This paper discusses the principles and characteristics of three different approaches,extended Kalman filters,strong tracking filters and unscented transformation based Kalman filters.By introducing the unscented transformation method and a sub-optimal fading factor to correct the prediction error covariance,an improved Kalman filter,unscented transformation based robust Kalman filter,is proposed. The performance of the algorithm is compared with the strong tracking filter and unscented transformation based Kalman filter and illustrated in a typical case study for glutathione fermentation process.The results show that the proposed algorithm presents better accuracy and stability on the state estimation in numerical calculations.展开更多
A new method of unscented extended Kalman filter （UEKF） for nonlinear system is presented. This new method is a combination of the unscented transformation and the extended Kalman filter （EKF）. The extended Kalman...A new method of unscented extended Kalman filter （UEKF） for nonlinear system is presented. This new method is a combination of the unscented transformation and the extended Kalman filter （EKF）. The extended Kalman filter is similar to that in a conventional EKF. However, in every running step of the EKF the unscented transformation is running, the deterministic sample is caught by unscented transformation, then posterior mean of non- lineadty is caught by propagating, but the posterior covariance of nonlinearity is caught by linearizing. The accuracy of new method is a little better than that of the unscented Kalman filter （UKF）, however, the computational time of the UEKF is much less than that of the UKF.展开更多
An adaptive unscented Kalman filter （AUKF） and an augmented state method are employed to estimate the timevarying parameters and states of a kind of nonlinear high-speed objects. A strong tracking filter is employed...An adaptive unscented Kalman filter （AUKF） and an augmented state method are employed to estimate the timevarying parameters and states of a kind of nonlinear high-speed objects. A strong tracking filter is employed to improve the tracking ability and robustness of unscented Kalman filter （UKF） when the process noise is inaccuracy, and wavelet transform is used to improve the estimate accuracy by the variance of measurement noise. An augmented square-root framework is utilized to improve the numerical stability and accuracy of UKF. Monte Carlo simulations and applications in the rapid trajectory estimation of hypersonic artillery shells confirm the effectiveness of the proposed method.展开更多
Filtering is a recursive estimation of hidden states of a dynamic system from noisy measurements.Such problems appear in several branches of science and technology,ranging from target tracking to biomedical monitoring...Filtering is a recursive estimation of hidden states of a dynamic system from noisy measurements.Such problems appear in several branches of science and technology,ranging from target tracking to biomedical monitoring.A commonly practiced approach of filtering with nonlinear systems is Gaussian filtering.The early Gaussian filters used a derivative-based implementation,and suffered from several drawbacks,such as the smoothness requirements of system models and poor stability.A derivative-free numerical approximation-based Gaussian filter,named the unscented Kalman filter(UKF),was introduced in the nineties,which offered several advantages over the derivativebased Gaussian filters.Since the proposition of UKF,derivativefree Gaussian filtering has been a highly active research area.This paper reviews significant developments made under Gaussian filtering since the proposition of UKF.The review is particularly focused on three categories of developments:i)advancing the numerical approximation methods;ii)modifying the conventional Gaussian approach to further improve the filtering performance;and iii)constrained filtering to address the problem of discrete-time formulation of process dynamics.This review highlights the computational aspect of recent developments in all three categories.The performance of various filters are analyzed by simulating them with real-life target tracking problems.展开更多
A new estimate method is proposed, which takes advantage of the unscented transform method, thus the true mean and covariance are approximated more accurately. The new method can be applied to non-linear systems witho...A new estimate method is proposed, which takes advantage of the unscented transform method, thus the true mean and covariance are approximated more accurately. The new method can be applied to non-linear systems without the linearization process necessary for the EKF, and it does not demand a Gaussian distribution of noise and what’s more, its ease of implementation and more accurate estimation features enables it to demonstrate its good performance in the experiment of satellite orbit simulation. Numerical experiments show that the application of the unscented Kalman filter is more effective than the EKF.展开更多
基金Supported by the National Natural Science Foundation of China （20476007, 20676013）.
文摘State estimation is the precondition and foundation of a bioprocess monitoring and optimal control. However,there are many difficulties in dealing with a non-linear system,such as the instability of process, un-modeled dynamics,parameter sensitivity,etc.This paper discusses the principles and characteristics of three different approaches,extended Kalman filters,strong tracking filters and unscented transformation based Kalman filters.By introducing the unscented transformation method and a sub-optimal fading factor to correct the prediction error covariance,an improved Kalman filter,unscented transformation based robust Kalman filter,is proposed. The performance of the algorithm is compared with the strong tracking filter and unscented transformation based Kalman filter and illustrated in a typical case study for glutathione fermentation process.The results show that the proposed algorithm presents better accuracy and stability on the state estimation in numerical calculations.
基金Supported by National Natural Science Foundation of China （61135001, 61075029, 61074179, 61074155） and the Postdoctoral Science Foundation of China （20110491692）
文摘A new method of unscented extended Kalman filter （UEKF） for nonlinear system is presented. This new method is a combination of the unscented transformation and the extended Kalman filter （EKF）. The extended Kalman filter is similar to that in a conventional EKF. However, in every running step of the EKF the unscented transformation is running, the deterministic sample is caught by unscented transformation, then posterior mean of non- lineadty is caught by propagating, but the posterior covariance of nonlinearity is caught by linearizing. The accuracy of new method is a little better than that of the unscented Kalman filter （UKF）, however, the computational time of the UEKF is much less than that of the UKF.
基金supported by the National Natural Science Foundation of China (61304254)the National Science Foundation for Distinguished Young Scholars of China (60925011)the Provincial and Ministerial Key Fund of China (9140A07010511BQ0105)
文摘An adaptive unscented Kalman filter （AUKF） and an augmented state method are employed to estimate the timevarying parameters and states of a kind of nonlinear high-speed objects. A strong tracking filter is employed to improve the tracking ability and robustness of unscented Kalman filter （UKF） when the process noise is inaccuracy, and wavelet transform is used to improve the estimate accuracy by the variance of measurement noise. An augmented square-root framework is utilized to improve the numerical stability and accuracy of UKF. Monte Carlo simulations and applications in the rapid trajectory estimation of hypersonic artillery shells confirm the effectiveness of the proposed method.
文摘Filtering is a recursive estimation of hidden states of a dynamic system from noisy measurements.Such problems appear in several branches of science and technology,ranging from target tracking to biomedical monitoring.A commonly practiced approach of filtering with nonlinear systems is Gaussian filtering.The early Gaussian filters used a derivative-based implementation,and suffered from several drawbacks,such as the smoothness requirements of system models and poor stability.A derivative-free numerical approximation-based Gaussian filter,named the unscented Kalman filter(UKF),was introduced in the nineties,which offered several advantages over the derivativebased Gaussian filters.Since the proposition of UKF,derivativefree Gaussian filtering has been a highly active research area.This paper reviews significant developments made under Gaussian filtering since the proposition of UKF.The review is particularly focused on three categories of developments:i)advancing the numerical approximation methods;ii)modifying the conventional Gaussian approach to further improve the filtering performance;and iii)constrained filtering to address the problem of discrete-time formulation of process dynamics.This review highlights the computational aspect of recent developments in all three categories.The performance of various filters are analyzed by simulating them with real-life target tracking problems.
基金Supported by the National Science Foundation of China(No.40674039) the DGLIGG(No.L06-06) the College Foundation of Surveying and MappingInstitute .
文摘A new estimate method is proposed, which takes advantage of the unscented transform method, thus the true mean and covariance are approximated more accurately. The new method can be applied to non-linear systems without the linearization process necessary for the EKF, and it does not demand a Gaussian distribution of noise and what’s more, its ease of implementation and more accurate estimation features enables it to demonstrate its good performance in the experiment of satellite orbit simulation. Numerical experiments show that the application of the unscented Kalman filter is more effective than the EKF.
