Some results on linear equality constrained state filtering

Abstract

This paper addresses the linear equality constrained state filtering for linear dynamic systems from different perspectives. First, by integrating constraint information into the state equation to ensure that the estimates naturally satisfy the constraints, the constrained filtering problem can be transformed into an unconstrained one. Second, according to a linear transformation of the state vector and the linear relationship between different new state components, a reduced-order Kalman filter is developed. Third, adding a projection step after the one-step state prediction in the Kalman filtering algorithm, we present a state prediction projection method. These approaches are mutually equivalent, and the existing null space method proves to be a special case of them. Most of current methods and the proposed approaches can be summed up in a unified framework and boil down to three forms of the projection method. Finally, a vehicle tracking example is provided to compare the performance of the discussed constrained filters.

Keywords:

• Kalman filtering
• linear equality constraints
• state prediction projection
• reduced-order Kalman filter

Acknowledgements

The authors would like to thank the anonymous reviewers for their suggestions on improving this manuscript.

This research is supported by Natural Scientific Research Innovation Foundation in Harbin Institute of Technology under grant number HIT.NSRIF.2009004.