3 Jun 2010
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. The addition of state constraints to a Kalman filter can significantly improve the estimation accuracy of the filter.
There are many ways to incorporate state constraints into the Kalman filter. These include the following for linear systems/constraints:
Constraint incorporation includes the following possibilities for nonlinear systems/constraints:
This web page makes available m-files (that can be run in the MATLAB environment) that demonstrate the application of constrained Kalman filtering to some simple example problems.