SCIENCE CHINA Information Sciences, Volume 61, Issue 4: 042201(2018) https://doi.org/10.1007/s11432-017-9242-8

## On extended state based Kalman filter design for a class of nonlinear time-varying uncertain systems

• AcceptedSep 22, 2017
• PublishedMar 5, 2018
Share
Rating

### Abstract

This paper considers the filtering problem for a class of multi-input multi-output systems with nonlinear time-varying uncertain dynamics, random process andmeasurement noise. An extended state based Kalman filter, with the idea of timely estimating the unknown dynamics, is proposed for better robustness and higher estimation precision. The stability of the proposed filter is rigorously proved for nonlinear time-varying uncertain system with weaker stability condition than the extended Kalman filter, i.e., the initial estimation error, the uncertain dynamics and the noises are only required to be bounded rather than small enough. Moreover, quantitative precision of the proposed filter is theoretically evaluated. The proposed algorithm is proved to be the asymptotic unbiased minimum variance filter for constant uncertainty. The simulation results of some benchmark examples demonstrate the feasibility and effectiveness of the method.

### Acknowledgment

This work was supported by National Natural Science Foundation of China (NSFC) (Grant Nos. 61603380, 61633003-3), and National Basic Research Program of China (Grant No. 2014CB845301). The authors would like to thank professer Lei GUO with Chinese Academy of Sciences for his helpful suggestions.

• Figure 1

(Color online) The estimation error of ESKF and EKF (Example 1).

• Figure 2

(Color online) The MSE of ESKF and SVF for C1 (Example 2).

• Figure 3

(Color online) The estimate error of ESKF and SVF for C2 (Example 2).

• Figure 4

(Color online) The MSE of ESKF and SVF for C3 (Example 2).

• Figure 5

(Color online) The estimation of ESKF and the state value for C3 (Example 2).

• Figure 6

(Color online) The mean square error of ESKF and the diagonal elements of $P_k$ in ESKF for C3protect łinebreak (Example 2).

Citations

• #### 0

Altmetric

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有