Stochastic stability of the derivative unscented Kalman filter  

作　　者：胡高歌 高社生 种永民 高兵兵 

机构地区：[1]School of Automatics,Northwestern Polytechnical University [2]School of Aerospace,Mechanical and Manufacturing Engineering,RMIT University

出　　处：《Chinese Physics B》2015年第7期64-73,共10页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.61174193);the Doctorate Foundation of Northwestern Polytechnical University,China(Grant No.CX201409)

摘　　要：This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discretetime 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.This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discretetime 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 

分 类 号：O211.63[理学—概率论与数理统计] TN713.1[理学—数学]