In NMPC strategies, the estimated state of the system is required for the solution of the NMPC or regulator problem from which feedback is obtained. An important observation is that, in order to retain the stabilizing properties of the controller, both the large-scale MHE and NMPC problems should be solved in real-time. However, this is not currently possible in most practical applications. In this work, we revisit a previously proposed real-time MHE algorithm . Here, the main idea is to provide instantaneous state estimates obtained from NLP sensitivity approximations constructed around the solution of a continuously updated nominal MHE problem. This fast optimization strategy allows for the implementation of large-scale MHE applications while avoiding undesired effects of computational delays. We extend these ideas further through a deeper analysis of the Karush-Kuhn-Tucker conditions of the MHE problem. As a result, we propose a common stability analysis framework for fast MHE algorithms and develop fast strategies for the computation of large-scale covariance information. Finally, we discuss implementation details of fast optimization capabilities in large-scale NLP algorithms.
 Zavala, V. M.; Laird, C.D. and Biegler, L.T. A Fast Computational Framework for Large-Scale Moving Horizon Estimation. Proceedings of the 8th International Symposium on Dynamics and Control of Process Systems, 2007.