中国物理B ›› 2015, Vol. 24 ›› Issue (7): 70202-070202.doi: 10.1088/1674-1056/24/7/070202

• GENERAL • 上一篇    下一篇

Stochastic stability of the derivative unscented Kalman filter

胡高歌a, 高社生a, 种永民b, 高兵兵a   

  1. a School of Automatics, Northwestern Polytechnical University, Xi'an 710072, China;
    b School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Australia
  • 收稿日期:2014-10-28 修回日期:2015-01-15 出版日期:2015-07-05 发布日期:2015-07-05
  • 基金资助:
    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).

Stochastic stability of the derivative unscented Kalman filter

Hu Gao-Ge (胡高歌)a, Gao She-Sheng (高社生)a, Zhong Yong-Min (种永民)b, Gao Bing-Bing (高兵兵)a   

  1. a School of Automatics, Northwestern Polytechnical University, Xi'an 710072, China;
    b School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Australia
  • Received:2014-10-28 Revised:2015-01-15 Online:2015-07-05 Published:2015-07-05
  • Contact: Hu Gao-Ge E-mail:hugaoge1111@126.com
  • Supported by:
    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).

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摘要： 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.

关键词: nonlinear stochastic system, stochastic process, unscented Kalman filter, stochastic stability

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.

Key words: nonlinear stochastic system, stochastic process, unscented Kalman filter, stochastic stability

中图分类号:  (Control theory)

  • 02.30.Yy
02.50.Ey (Stochastic processes) 02.50.Fz (Stochastic analysis)