Various deterministic sampling-based constrained state estimation techniques for nonlinear dynamical  systems have been proposed in the literature. These algorithms mainly focus on correcting the estimated (or filtered) states such that they satisfy all of the given constraints. However, the aspect of correcting  redicted states (after model propagation) such that they satisfy all of the constraints has not been given much attention in the literature. These states are obtained by propagating deterministically chosen points (called sigma points) through the process model. Most approaches either do not incorporate constraints during the generation of these sigma points or use arbitrary strategies for constraint incorporation. Further, the weights associated with these points are not systematically updated after incorporation of any state constraint. In this article, we propose an optimization-based sigma points selection approach that overcomes these limitations. Additionally, we incorporate the effect of constraints by directly working with truncated probability density functions. The efficacy of the proposed approach is demonstrated by comparing its performance against those of various strategies available in the literature on several simulation case studies.