Stochastic stability of the derivative unscented Kalman filter

doi:10.1088/1674-1056/24/7/070202

Abstract This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discrete-time system with linear system state equation. The first paper established a derivative unscented Kalman filter (DUKF) to eliminate the redundant computational load of the unscented Kalman filter (UKF) due to the use of unscented transformation (UT) in the prediction process. The present paper studies the error behavior of the DUKF using the boundedness property of stochastic processes. It is proved that the estimation error of the DUKF remains bounded if the system satisfies certain conditions. Furthermore, it is shown that the design of the measurement noise covariance matrix plays an important role in improvement of the algorithm stability. The DUKF can be significantly stabilized by adding small quantities to the measurement noise covariance matrix in the presence of large initial error. Simulation results demonstrate the effectiveness of the proposed technique.

Keywords: nonlinear stochastic system stochastic process unscented Kalman filter stochastic stability

Received: 28 October 2014
Revised: 15 January 2015
Accepted manuscript online:

PACS:	02.30.Yy	(Control theory)
	02.50.Ey	(Stochastic processes)
	02.50.Fz	(Stochastic analysis)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61174193) and the Doctorate Foundation of Northwestern Polytechnical University, China (Grant No. CX201409).

Corresponding Authors: Hu Gao-Ge
E-mail: hugaoge1111@126.com

Cite this article:

Hu Gao-Ge (胡高歌), Gao She-Sheng (高社生), Zhong Yong-Min (种永民), Gao Bing-Bing (高兵兵) Stochastic stability of the derivative unscented Kalman filter 2015 Chin. Phys. B 24 070202

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