Minimax
Filtering with State Constraints

**Dan Simon**

Department of Electrical Engineering

Cleveland State University

Cleveland, Ohio

Kalman filters are commonly used to estimate the states of a dynamic system. Alternatively, H-infinity filters (also called minimax filters) can be used if the designer wants to incorporate more robustness into the filter. However, in the application of H-infinity 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. I have recently shown that, given a dynamic system with state constraints, a constrained H-infinity filter estimate can be obtained at each time step by projecting the unconstrained 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 H-infinity filtering to a simple linear 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.

MinimaxConstrained.zip - 2 kilobytes

If you download MinimaxConstrained.zip to your hard drive by clicking on the above link, then unzip the file (using, for example, WinZip), you can run a constrained Minimax 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.

*References*

- D. Simon, “A Game Theory
Approach to Constrained Minimax State Estimation,”
*IEEE Transactions on Signal Processing*, vol. 54, no. 2, pp. 405-412, February 2006 - pdf, 281 KB - D. Simon, “Lemma proofs for ‘A game theory approach to constrained minimax state estimation’ ” - pdf, 71 KB
- D. Simon, “H-infinity Filtering
with Inequality Constraints for Aircraft Turbofan Engine Health
Estimation,”
*IEEE Conference on Decision and Control*, San Diego, CA, pp. 3291-3296, December 2006 - pdf paper, 88.3 KB - pdf overheads, 835 KB

Department of Electrical and Computer Engineering

Last Revised: December 14, 2013