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Sensors 2018, 18(9), 2976; https://doi.org/10.3390/s18092976

Globally Optimal Distributed Kalman Filtering for Multisensor Systems with Unknown Inputs

College of Mathematics, Sichuan University, Chengdu 610064, Sichuan, China
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Received: 10 July 2018 / Revised: 30 August 2018 / Accepted: 3 September 2018 / Published: 6 September 2018
(This article belongs to the Collection Multi-Sensor Information Fusion)
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Abstract

In this paper, the state estimation for dynamic system with unknown inputs modeled as an autoregressive AR (1) process is considered. We propose an optimal algorithm in mean square error sense by using difference method to eliminate the unknown inputs. Moreover, we consider the state estimation for multisensor dynamic systems with unknown inputs. It is proved that the distributed fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurement; therefore, it achieves the best performance. The computation complexity of the traditional augmented state algorithm increases with the augmented state dimension. While, the new algorithm shows good performance with much less computations compared to that of the traditional augmented state algorithms. Moreover, numerical examples show that the performances of the traditional algorithms greatly depend on the initial value of the unknown inputs, if the estimation of initial value of the unknown input is largely biased, the performances of the traditional algorithms become quite worse. However, the new algorithm still works well because it is independent of the initial value of the unknown input. View Full-Text
Keywords: optimal estimate; unknown inputs; distributed fusion; augmented state Kalman filtering (ASKF) optimal estimate; unknown inputs; distributed fusion; augmented state Kalman filtering (ASKF)
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Ruan, Y.; Luo, Y.; Zhu, Y. Globally Optimal Distributed Kalman Filtering for Multisensor Systems with Unknown Inputs. Sensors 2018, 18, 2976.

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