Multi-rate optimal state estimation

Abstract

This article formulates a multi-rate linear minimum mean squared error (LMMSE) state estimation problem, which includes four rates as follows: the state updating rate in the model, the measurement sampling rate, the estimate updating rate and the estimate output rate. This formulation is unique in two ways. First, the rate ratio between state measurement and state estimate is more general (a rational number), instead of just an integer or its reciprocal as considered in the existing literature. Second, state estimates are produced in blocks, which have never been considered before in the multi-rate estimator design. The multi-rate LMMSE estimation problem is solved by examining several distinctive cases for single-rate state estimation, obtained through the lifting technique. Also, sufficient conditions are given for asymptotic stability of the proposed multi-rate LMMSE estimators. An example in tracking a manoeuvering target is given to illustrate the proposed multi-rate state estimators.

Keywords:

• multi-rate systems
• state estimation
• filter stability
• optimal filtering
• information fusion
• wireless sensor networks

Acknowledgements

The authors would like to express their appreciation to the anonymous reviewers for their constructive comments and suggestions, which helped a great deal in improving the article. The authors also express sincere thanks to the editor for the efficient review management. This research was supported in part by NSERC, the National Natural Science Foundation of China (Grant No. 60634030), the 111 Project (B08015), the Scientific and Technological Innovation Foundation of NPU and the Program for New Century Excellent Talents of University, China.

Additional information

Notes on contributors

Yan Liang

†Dr Liang was a visiting scholar at the University of Alberta in 2008.