Kalman Filtering with State Constraints

Dan Simon
of Electrical Engineering
Cleveland State University

1960 East 24th Street
Cleveland, OH 44115


Kalman filters are commonly used to estimate the states of a dynamic system.  However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically.  For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter.  The constraints may be time-varying or nonlinear.  Dr. Tien-Li Chia showed in his PhD disseratation that, given a dynamic system with state constraints, a constrained Kalman filter estimate can be obtained at each time step by projecting the unconstrained Kalman filter solution onto the state constraint surface.  This significantly improves the estimation accuracy of the filter. 

This web page makes available an m-file (that can be run in the MATLAB environment) that demonstrates the application of constrained Kalman filtering to a simple nonlinear vehicle tracking problem. M-files are written in a very high-level language that can be easily read, almost like pseudo code. The m-file is contained in the following zip file.

KalmanConstrained.zip - 2 kilobytes

If you download KalmanConstrained.zip to your hard drive by clicking on the above link, then unzip the file (using, for example, WinZip), you can run a constrained Kalman filter experiment and reproduce the results in reference [1].  If you don't have software to unzip the file, you can download a free evaluation version of WinZip from www.winzip.com.


  1. D. Simon and T. Chia, “Kalman Filtering with State Equality Constraints,” IEEE Transactions on Aerospace and Electronic Systems, vol. 39, pp. 128-136, January 2002 - pdf, 211 KB - postscript, 3.26 MB
  2. D. Simon and D.L. Simon, “Kalman Filtering with Inequality Constraints for Turbofan Engine Health Estimation,” submitted for publication - pdf, 528 KB - postscript, 4.33 MB
  3. D. Simon and D.L. Simon, “Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering,” ASME Turbo Expo 2003, Atlanta, GA, paper GT2003-38584, June 2003 – pdf paper, 174 KBpdf overheads, 195 KB

Professor Simon’s Home Page

Department of Electrical and Computer Engineering

Cleveland State University

Last Revised: December 14, 2013