A discretized nonlinear state estimator for batch processes

Computing arrival cost parameters in moving horizon estimation using sampling based filters

“…Poorly formulated arrival cost forces large horizons, which pose hindrances for fast, realtime estimation [2]. The Gaussian assumptions also break down for many nonlinear systems because of the tendency to exhibit multi ple modes in both the a priori and conditional densities [9][10][11]. The initialization of MHE with the best choice of arrival cost term is an open issue, which also leaves the computational complexity of MHE implementation as an open challenge.…”

“…They include the deterministic sampling based unscented Kalman filter (UKF), the random sampling based class of nonlinear filters called particle filter (PF) and the aggregate Markov chain based cell filter (CF). The choice of these three methods is motivated by their rela tively small online computational demand compared to other non traditional filters such as the grid based approaches [9,[12][13][14].…”

Particle filters for state and parameter estimation in batch processes

“…polymer properties in a batch polymerization process [3]). In addition, some of the parameters in a state space model cannot be specified exactly a priori [3,4,5]. These issues are discussed and addressed in this paper.…”

“…However when state equations are highly non-linear and the posterior density is non-Gaussian, the EKF may give a high estimation error. To avoid the Gaussian assumption, one approach that was originally presented in the 1970's was to approximate the posterior density by discretizing the continuous state variables into grids [5,8,9]. This methodology was termed point-mass filters or probability-grid filters.…”

Guaranteed Robust Nonlinear State Estimator with Application to Global Vehicle Tracking

“…A first such approximation is extended Kalman filtering [1], [7], based on a linearization of the model around its estimated trajectory in state space. The fact that this approach cannot accurately describe situations where the model is highly nonlinear and the pdf of the state is far from Gaussian has motivated the development of grid-based methods [4], [21], where the state space is partitioned a priori into cells and integrals are replaced by discrete approximations. This approach lacks flexibility, as it does not allow the partition to be adapted dynamically so as to get more resolution in regions with high probability.…”