Reduced Order Kalman Filtering

Dan Simon
Department of Electrical and Computer Engineering
Cleveland State University
Cleveland, Ohio

Kalman filters are commonly used to estimate the states of a noisy dynamic system. However, computational constraints can make the full order Kalman filter unamenable to real time implementation, especially when the implementation platform is a microcontroller or DSP. In addition, some Kalman filter applications (e.g., meteorology and oceanography applications) can involve millions of states. This has led to considerable effort on methods of reducing the order of the Kalman filter.

 

The earliest efforts at reduced order Kalman filters recognized that the Kalman filter for a system where some of the measurements were noise-free is equivalent to a Kalman filter for a system with a reduced number of states. On a related note, the Riccati equation associated with the Kalman filter can be reduced if some of the states are unobservable although the resulting filter still estimates all the states. Similarly, the Riccati equation can be reduced if a matrix decomposition is performed on some of the matrices in the Kalman filter, especially if the those matrices are rank deficient.

 

Most reduced order filters are designed on the basis of a reduction in the order of the system model. If we can find a reduced order system model that approximates the full order system model, then we can design a state estimator on the basis of the reduced order system model that approximates the full order Kalman filter. This web page makes available available a paper and an m-file (that can be run in the MATLAB environment) that demonstrates a new approach to reduced order Kalman filtering. 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.

Reduced.zip - 2 kilobytes

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

References

  1. D. Simon, “Reduced Order Kalman Filtering without Model Reduction,” Control and Intelligent Systems, vol. 35, no. 2, pp. 169-174, April 2007 - pdf, 585 KB

Professor Simon’s Home Page

Department of Electrical and Computer Engineering

Cleveland State University


Last Revised: December 14, 2013