Reduced-order Kalman filtering for state constrained linear systems  

作　　者：Chaoyang Jiang Yongan Zhang 

机构地区：[1]Center for Control Theory and Guidance Technology, Harbin Institute of Technology

出　　处：《Journal of Systems Engineering and Electronics》2013年第4期674-682,共9页系统工程与电子技术（英文版）

基　　金：supported by the National Key Basic Research Development Project (973 Program) (2012CB821205);the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology(HIT.NSRIF.2009004)

摘　　要：This paper aims at solving the state filtering problem for linear systems with state constraints. Three classes of typical state constraints, i.e., linear equality, quadratic equality and inequality, are discussed. By using the linear relationships among different state variables, a reduced-order Kalman filter is derived for the system with linear equality constraints. Afterwards, such a solution is applied to the cases of the quadratic equality constraint and inequality constraints and the two constrained state filtering problems are transformed into two relative constrained optimization problems. Then they are solved by the Lagrangian multiplier and linear matrix inequality techniques, respectively. Finally, two simple tracking examples are provided to illustrate the effectiveness of the reduced-order filters.This paper aims at solving the state filtering problem for linear systems with state constraints. Three classes of typical state constraints, i.e., linear equality, quadratic equality and inequality, are discussed. By using the linear relationships among different state variables, a reduced-order Kalman filter is derived for the system with linear equality constraints. Afterwards, such a solution is applied to the cases of the quadratic equality constraint and inequality constraints and the two constrained state filtering problems are transformed into two relative constrained optimization problems. Then they are solved by the Lagrangian multiplier and linear matrix inequality techniques, respectively. Finally, two simple tracking examples are provided to illustrate the effectiveness of the reduced-order filters.

关 键 词：state constraint state filtering reduced-order Kalman filter linear matrix inequality （LMI）. 

分 类 号：TN713[电子电信—电路与系统]