In situ adaptive tabulation or ISAT based moving horizon estimation (MHE) is suggested as a fast and robust approach for state estimation. Computational issues with a moving horizon constrained state estimation technique like MHE are discussed. Implementation of storage and retrieval approach of ISAT for state estimation is proposed to maintain the accuracy and robustness of MHE, while generating the estimates at a reduced computational cost (similar to 300 times faster). Comparison with the widely used nonlinear state estimation technique of extended Kalman filtering (EKF) shows better performance using ISAT-MHE. Case studies with nonlinear discrete-time and continuous-time systems are carried out using ISAT, which is tailored for solving the optimal estimation problem. Published by Elsevier Ltd.