Robust Extended Kalman Filter For State Estimation Of Nonlinear Dynamic Systems

State estimation is of great importance in real-time optimization,process monitoring and control.Although the extended Kalman filter(EKF)can estimate the desired states from noisy measurements by reconciling the measured data to fit the nonlinear dynamics described by state-space models,it needs to know the mathematical models of nonlinear dynamic systems and requires the measurement noise to obey Gaussian distribution.However,for some complex and unknown dynamic systems,the acquisition of their mechanism models is often difficult and even impossible;what is more,devices used for collecting and transmitting data will not only introduce the inherent Gaussian random noise,but also usually be corrupted by different types of gross errors.The presence of gross errors makes the measurement noise no longer obey Gaussian distribution and even results in the complete destruction of statistical characteristics.To solve the above problems,this paper proposes and designs several robust EKF methods for the state estimation of nonlinear dynamic systems,the main research works and innovations are as follows:(1)A measurement compensation based robust EKF method is proposed to deal with the three types of gross errors(outliers,bias and drift)or their different combinations that often occur in the dynamic systems.Above all,normal measurement data are distinguished from the abnormal ones by statistical test.Then,according to the characteristics of various gross errors,gross error identification and their magnitude estimation are accomplished.Finally,the accurate system states are re-estimated using the compensated measurements.(2)For the problem that EKF can’t be applied to the state estimation with non-Gaussian measurement noise,the EKF algorithm is re-formulated using the framework of dynamic data reconciliation(DDR)and the mutual transformation of the two methods is realized,which forms the basic DDR based EKF(DEKF).Subsequently,based on the Bayes formula and the maximum likelihood estimate,the application field of DEKF is extended from the Gaussian measurement noise to the non-Gaussian one.The proposed robust EKF provides a feasible state estimation scheme to consider the EKF with any noise distribution.(3)Aiming at the nonlinear dynamic system with complex or unknown models,a dynamic data reconciliation strategy combining Elman neural network with EKF is proposed,in which the advantages of the two methods complement each other.Without complex rigorous modeling process,a dynamic model of the investigated system is obtained using data-driven modeling.Based on the outputs of model prediction and the current measurement,accurate dynamic data reconciliation can be derived.This strategy not only improves the prediction accuracy,but also shows strong adaptability to the changes of measurement environment.Considering the different application scenarios of EKF,this study provides solutions to the robust state estimation problem of nonlinear dynamic systems with abnormal measurement and unknown models,and further extends the serviceable range of KF technology.