This work addresses optimal constrained state estimation problem for finite and infinite-dimensional chemical process systems. We consider cases when the prior information, in addition to the model parameters and the measurements, is available in the form of an inequality constraint with respect to the system's state. In the latest developments of the optimal state estimation theory, considerations of the state constraints have been often neglected since constraints do not fit easily in the structure of the optimal state estimator. Therefore, the issue of the state constraints being present needs to be addressed adequately, in particular, nonnegativity of concentration. Motivated by this, we developed a sequential, algorithmic optimal constrained state estimator for both finite and infinite-dimensional process systems commonly found in chemical process engineering (CSTR, tubular reactor). In this paper, we also designed an optimal constrained state estimator for a large class of dissipative infinite-dimensional systems which involve boundary actuation and point observation. Finally, illustrative examples of chemical process systems and proposed optimal state constrained estimation are presented. (C) 2015 Elsevier Ltd. All rights reserved.