Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 65, Issue 6, Pages 2654-2661Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2019.2942826
Keywords
Kalman filters; Time-varying systems; Robot sensing systems; Covariance matrices; Noise measurement; Stability analysis; Collectively uniform detectability (CUD); Kalman consensus filters (KCFs); sensor networks; time-varying systems; uniform bounds
Funding
- National Natural Science Foundation of China [61873148, 61873169, 61933007]
- Research Grants Council of the Hong Kong Special Administrative Region of China [CityU 11200717]
- CityU Strategic Research Grant [7005029]
- Alexander von Humboldt Foundation of Germany
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In this paper, the uniform bounds of error covariances for several types of Kalman consensus filters (KCFs) are investigated for a class of linear time-varying systems over sensor networks with given topologies. Rather than the traditional detectability assumption, a new concept called collectively uniform detectability (CUD) is proposed to address the detectability issues over sensor networks with relaxed restrictions. By using matrix inequality analysis techniques, the conditions for the newly proposed CUD concept are established, and then, the explicit expressions of the uniform upper/lower bounds are derived for error covariances of several commonly used KCF algorithms. Consequently, a comparison is conducted between the obtained bounds so as to reveal their relationships. Finally, a numerical example is provided to calculate and further compare the bounds of interest in order to demonstrate the practical usefulness of the developed theory.
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