Constrained Unscented Gaussian Sum Filter for state estimation of nonlinear dynamical systems

This work presents a novel constrained Bayesian state estimation approach for nonlinear dynamical systems. The proposed approach uses the recently proposed Unscented Gaussian Sum Filter to represent the underlying non-Gaussian densities as sum of Gaussians, and explicitly incorporates constraints on states during the measurement update step. This approach, labeled Constrained-Unscented Gaussian Sum Filter (C-UGSF), can thus model non-Gaussianity in constrained, nonlinear state estimation problems. Its applicability is demonstrated using three nonlinear, constrained state estimation case studies taken from literature, namely, (i) a gas phase batch reactor, (ii) an isothermal batch process, and (iii) a continuous polymerization process. Results demonstrate superior estimation performance along with a significant improvement in computational time when compared to Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR), which is a popular nonlinear, constrained state estimation approach available in literature.