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Robust Centralized and Weighted Measurement Fusion Kalman Predictors with Multiplicative Noises, Uncertain Noise Variances, and Missing Measurements

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Abstract

For multisensor uncertain systems with mixed uncertainties, including multiplicative noises in state and process noise transition matrices, uncertain-variance multiplicative and additive white noises, and missing measurements, this paper addresses the problem of designing robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman predictors. By introducing fictitious noises, the system under study is converted into a system with only uncertain noise variances. According to the minimax robust estimation principle, which is based on the worst-case system with conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman predictors are presented in a unified framework. Using the Lyapunov equation, the robustness of these predictors is proven in the sense that the actual prediction error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using an information filter, they are proven to have the same robust and actual accuracies. The complexity analysis shows that when the number of sensors is larger, the WMF algorithm more significantly reduces the computational burden than the CF algorithm. The corresponding robust fused steady-state Kalman predictors are also presented. The three modes of convergence in a realization among the time-varying and steady-state robust fused Kalman predictors are proposed and proven using the dynamic error system analysis method. Two simulation examples, autoregressive moving average signal processing and an uninterruptible power system, demonstrate the effectiveness of the proposed methods.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants NSFC-60874063 and NSFC-60374026 and the Science and Technology Research Foundation of Heilongjiang Education Department under Grant 12541698. The authors thank the reviewers and editors for their helpful and constructive comments, which have been very valuable in improving the quality of the paper.

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Authors and Affiliations

  1. Department of Automation, Electronic Engineering College, Heilongjiang University, Harbin, 150080, People’s Republic of China

    Wen-Qiang Liu, Xue-Mei Wang & Zi-Li Deng

  2. Computer and Information Engineering College, Heilongjiang University of Science and Technology, Harbin, 150022, People’s Republic of China

    Wen-Qiang Liu

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  1. Wen-Qiang Liu
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  3. Zi-Li Deng
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Correspondence to Zi-Li Deng.

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Liu, WQ., Wang, XM. & Deng, ZL. Robust Centralized and Weighted Measurement Fusion Kalman Predictors with Multiplicative Noises, Uncertain Noise Variances, and Missing Measurements. Circuits Syst Signal Process 37, 770–809 (2018). https://doi.org/10.1007/s00034-017-0578-6

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