Stochastic stability of the derivative unscented Kalman filter

作     者：胡高歌 高社生 种永民 高兵兵 

作者机构：School of AutomaticsNorthwestern Polytechnical University School of AerospaceMechanical and Manufacturing EngineeringRMIT University 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2015年第24卷第7期

页      面：64-73页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 080902[工学-电路与系统] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0714[理学-统计学（可授理学、经济学学位）] 0704[理学-天文学] 070103[理学-概率论与数理统计] 0701[理学-数学] 

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) 

主　　题：nonlinear stochastic system stochastic process unscented Kalman filter stochastic stability 

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.