An Ensemble Kalman Filter for Systems Governed by Differential Algebraic Equations (DAEs)

Implementation of Kalman Filtering for Differential-Algebraic Equations

“…We now have the next state estimates x D,k|k and x A,k|k and covariance matrix P k|k . An DAE-compatible Ensemble Kalman filter can be found here [53] and a DAE-compatible Iterative Extended Kalman filter can be found here [54].…”

“…Mandela et al [39] improved upon this implementation of a DAE-compatible xxtended Kalman filter and introduced a DAE-compatible unscented Kalman filter. Purohit et al [53] and Puranik et al [54] developed a DAE-compatible Ensemble Kalman filter and a DAE-compatible iterative extended Kalman filter, respectively. An implementation of a DAE-compatible Kalman filter has been applied on the model of a lithium-ion cell [12].…”

Nonlinear Filters for State Estimation of UV Flash Processes

“…We discretize (41) with Euler's implicit method and (42) with the semi-implicit scheme described in Section III. For each of the N k time steps, we solve…”

“…For instance, it is common to assume that systems reach thermodynamic phase equilibrium instantaneously. Recently, authors have developed the EKF [32]- [34], the UKF [35]- [39], PFs [40], [41], and the EnKF [42] for DAE models.…”

Machine‐learning‐based predictive control of nonlinear processes. Part II: Computational implementation

“…In chemical process control, the constrained ensemble Kalman filter has been proposed for dealing with bounds and has been tested with a gas‐phase reactor and an isothermal batch reactor . Similarly, ensemble Kalman filter has been extended for systems described by differential algebraic equations . Despite the great efforts that have been done in state estimation using ensemble methods, ensemble learning has not been fully investigated in model predictive control, in which parallel computing can also be utilized to reduce computation time.…”