Variable step size predictor design for a class of linear discrete-time censored system

Zhifang Li; Huihong Zhao; Hailong Meng; Yong Chen; Zhifang Li; Huihong Zhao; Hailong Meng; Yong Chen

doi:10.3934/math.2021614

AIMS Mathematics

2021, Volume 6, Issue 10: 10581-10595. doi: 10.3934/math.2021614

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Research article

Variable step size predictor design for a class of linear discrete-time censored system

1.
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
2.
North Automatic Control Technology Institute, Taiyuan, China

Received: 05 March 2021 Accepted: 15 July 2021 Published: 21 July 2021
MSC : 93E11, 93C55

We propose a novel variable step size predictor design method for a class of linear discrete-time censored system. We divide the censored system into two parts. The system measurement equation in one part doesn't contain the censored data, and the system measurement equation in the other part is the censored signal. For the normal one, we use the Kalman filtering technology to design one-step predictor. For the one that the measurement equation is censored, we determine the predictor step size according to the censored data length and give the gain compensation parameter matrix $β(\mathfrak{s})$ for the case predictor with obvious errors applying the minimum error variance trace, projection formula, and empirical analysis, respectively. Finally, a simulation example shows that the variable step size predictor based on empirical analysis has better estimation performance.
- censored system,
- Kalman filtering,
- variable step size predictor,
- minimum error variance trace,
- projection formula
Citation: Zhifang Li, Huihong Zhao, Hailong Meng, Yong Chen. Variable step size predictor design for a class of linear discrete-time censored system[J]. AIMS Mathematics, 2021, 6(10): 10581-10595. doi: 10.3934/math.2021614

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Abstract

We propose a novel variable step size predictor design method for a class of linear discrete-time censored system. We divide the censored system into two parts. The system measurement equation in one part doesn't contain the censored data, and the system measurement equation in the other part is the censored signal. For the normal one, we use the Kalman filtering technology to design one-step predictor. For the one that the measurement equation is censored, we determine the predictor step size according to the censored data length and give the gain compensation parameter matrix $β(\mathfrak{s})$ for the case predictor with obvious errors applying the minimum error variance trace, projection formula, and empirical analysis, respectively. Finally, a simulation example shows that the variable step size predictor based on empirical analysis has better estimation performance.

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