This paper investigates the use of several nonlinear estimation algorithms such as extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF) in the problem of state estimation in chemical processes. Three simulation case studies are considered to evaluate the performance of the proposed method. The second case study uses the experimental data to investigate the accuracy of the CKF against the UKF in practical applications. Simulation results confirm the superiority of the CKF to the EKE and UKF. However, all of these approaches fail to handle the constraint issue in state estimation problems. Subsequently, a modified CKF is introduced to overcome the linear constraint in nonlinear estimation problems. The final part of the paper shows simulation results that confirm the effectiveness of the proposed constrained CKF (CCKF). Potential profits that can be achieved while applying the proposed approach in constrained estimation problems are shown compared to the conventional moving horizon estimation (MHE) algorithm.