Comparison of unconstrained nonlinear state estimation techniques on a MMA polymer reactor

A particle filter for ammonia coverage ratio and input simultaneous estimations in Diesel-engine SCR system

“…Considering the system nonlinearities and measurement noises, the EKF algorithm is the most classic and widely-used method. However, the method requires that the linearization of the nonlinear model to which the KF can be applied keeps small deviation, the nonlinearity of the model is not big and the noise is Gaussian or independent and identically distributed which are hard to satisfy in the SCR system[ 19 , 20 ]. Therefore, the observer based on EKF algorithm may not perform well in the state estimation of the SCR system.…”

“…Therefore, how to develop an observer that provides an exact optimal solution to the SCR system remains an open problem. Though the modified KF, also known as extended Kalman filter(EKF), is the most traditional estimator for nonlinear systems, it has been demonstrated to perform poorly in the non-Gaussian posterior estimates obtained when the system is nonlinear[ 20 ]. The EKF requires that the nonlinear state transition equations and measurement equations are approximated to linear equations by using the first-order Taylor series expansion, so that the KF can be applied to estimate the states.…”

“…The EKF requires that the nonlinear state transition equations and measurement equations are approximated to linear equations by using the first-order Taylor series expansion, so that the KF can be applied to estimate the states. Moreover, it requires the nonlinearity of the model is small and the deviation of the approximation is not big[ 20 ], which is however not exhibited by the SCR system that involves complicate chemical reaction processes and time-varying reaction conditions. Therefore, though the EKF works well in many cases, an alternate observer needs to be developed to provide a better estimation in the SCR system.…”

“…To address the uncertainties especially in strong nonlinear and non-Gaussian systems, particle filter(PF) algorithm has been given relatively more efforts. Unlike the EKF, PF relies on fitting an approximate solution to the nonlinear equation rather than solving the linear equations obtained by approximating the nonlinear system[ 20 ]. It makes use of the Bayesian filter and Monte Carlo method to estimate the states.…”

“…The state distribution is represented by a set of random samples with associated weights. High probability density is represented by a huge number of particles, low probability by a low number or no particles[ 20 ]. It refers from many researchers that for strong nonlinear and non-Gaussian systems, if the model is not accurate enough, then the PF algorithm is considered very useful to do the state estimation[ 21 , 22 ].…”