Analysis of the Kalman filter based estimation algorithm: an orthogonal decomposition approach

作     者：Cao, LY Schwartz, HM 

作者机构：Carleton Univ Dept Syst & Comp Engn Ottawa ON K1S 5B6 Canada Micro Opt Design Corp Moncton NB E1E 4M3 Canada 

出 版 物：《AUTOMATICA》 (自动学)

年 卷 期：2004年第40卷第1期

页      面：5-19页

核心收录：

学科分类：0711[理学-系统科学] 0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 071101[理学-系统理论] 

主　　题：Kalman filter recursive parameter estimation least squares algorithm windup directional tracking 

摘      要：In this paper we shall provide new analysis on some fundamental properties of the Kalman filter based parameter estimation algorithms using an orthogonal decomposition approach based on the excited subspace. A theoretical analytical framework is established based on the decomposition of the covariance matrix, which appears to be very useful and effective in the analysis of a parameter estimation algorithm with the existence of an unexcited subspace. The sufficient and necessary condition for the boundedness of the covariance matrix in the Kalman filter is established. The idea of directional tracking is proposed to develop a new class of algorithms to overcome the windup problem. Based on the orthogonal decomposition approach two kinds of directional tracking algorithms are proposed. These algorithms utilize a time-varying covariance matrix and can keep stable even in the case of unsufficient and/or unbounded excitation. (C) 2003 Elsevier Ltd. All rights reserved.