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Robust Kalman Filtering for Discrete-Time Time-Varying Systems With Stochastic and Norm-Bounded Uncertainties

[+] Author and Article Information
Mahdi Abolhasani

Department of Electrical Engineering,
Imam-Khomeini International University,
Qazvin 3414896818, Iran

Mehdi Rahmani

Department of Electrical Engineering,
Imam-Khomeini International University,
Qazvin 3414896818, Iran
e-mail: mrahmani@eng.ikiu.ac.ir

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 12, 2017; final manuscript received July 10, 2017; published online November 8, 2017. Assoc. Editor: Puneet Singla.

J. Dyn. Sys., Meas., Control 140(3), 030901 (Nov 08, 2017) (8 pages) Paper No: DS-17-1022; doi: 10.1115/1.4037777 History: Received January 12, 2017; Revised July 10, 2017

In this paper, a new robust Kalman filter is proposed for discrete-time time-varying linear stochastic systems. The system under consideration is subject to stochastic and norm-bounded uncertainties in all matrices of the system model. In the proposed approach, the filter is first achieved by solving a stochastic min–max optimization problem. Next, we find an upper bound on the estimation error covariance, and then, by using a linear matrix inequality (LMI) optimization problem, unknown parameters of the filter are determined such that the obtained upper bound is minimized. Finally, two numerical examples are given to demonstrate the effectiveness and performance of the proposed filtering approach compared to the existing robust filters.

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Figures

Grahic Jump Location
Fig. 1

MSE of state 1 for the stochastic uncertainty (first scenario)

Grahic Jump Location
Fig. 2

MSE of state 2 for the stochastic uncertainty (first scenario)

Grahic Jump Location
Fig. 3

MSE of state 3 for the stochastic uncertainty (first scenario)

Grahic Jump Location
Fig. 4

MSE of state 1 for the bounded uncertainty (second scenario)

Grahic Jump Location
Fig. 5

MSE of state 2 for the bounded uncertainty (second scenario)

Grahic Jump Location
Fig. 6

MSE of state 3 for the bounded uncertainty (second scenario)

Grahic Jump Location
Fig. 7

MSE of state 1 for the stochastic and bounded uncertainty (third scenario)

Grahic Jump Location
Fig. 8

MSE of state 2 for the stochastic and bounded uncertainty (third scenario)

Grahic Jump Location
Fig. 9

MSE of state 3 for the stochastic and bounded uncertainty (third scenario)

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