View source for NCS: Moving Horizon Estimation

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In this lecture, we give an introduction to moving horizon estimation (MHE) and extended Kalman filters (EKF). These filter stuctures can be used with nonlinear models and are therefore more general than the standard Kalman filter. Furthermore, MHE can also take constraints on the noise and the state space, as well as asymmetric probability distributions, into account. MHE is dual to receding horizon control (RHC) and also relies on optimization software. The lecture ends with a brief discussion on stability properties of MHE.

== Lecture Materials ==
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[[Media:L4-2_MHE.pdf|Lecture: Moving Horizon Estimation]]

== Reading ==
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* <p>[http://pubs.acs.org/cgi-bin/abstract.cgi/iecred/2005/44/i08/abs/ie034308l.html Critical evaluation of extended Kalman filtering and moving horizon estimation], E.L. Haseltine and J.B. Rawlings, ''Ind. Eng. Chem. Res.'', vol. 44, no.8, 2005. Contains several examples where EKF and MHE have been applied. Discusses the differences between the methods and when EKF is likely to fail.</p>

* <p>[http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=26479&arnumber=1178905&count=27&index=5 Constrained State Estimation for Nonlinear Discrete-Time Systems: Stability and Moving Horizon Approximations], C.V. Rao, J.B. Rawlings, and D.Q. Mayne, ''IEEE Transactions on Automatic Control'', vol.48, no.2, 2003. A mathematical treatment of MHE and stability conditions are derived. Everybody should read at least Section I.</p>

* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. Gives an introduction to the extended Kalman filter in discrete time.</p>

== Additional Resources ==
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* <p>[http://jbrwww.che.wisc.edu/theses/rao.ps Moving Horizon Strategies for the Constrained Monitoring and Control of Nonlinear Discrete-Time Systems] C.V. Rao. Rao's PhD thesis contains a lot of material on MHE. There is also a discussion on MAP estimates.</p>
* <p>[http://www.eng.newcastle.edu.au/eecs/cdsc/books/cce/ Constrained Control and Estimation - An Optimisation Approach], G. C. Goodwin, M. M. Seron, J. A. De Dona.  Springer Verlag, 2005.  This is a recent book treating constrained control and estimation in a unified framework (including finite horizon optimal control and RHC) using discrete-time formulation.  The website has a lot of additional useful and interesting material.</p>