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Decomposition method for solving kalman filter gains in singularly perturbed systems
Author(s) -
Shen Xuemin,
Rao Ming,
Ying Yiqun
Publication year - 1993
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660140106
Subject(s) - kalman filter , decoupling (probability) , mathematics , control theory (sociology) , invariant extended kalman filter , transformation (genetics) , alpha beta filter , fast kalman filter , decomposition , singularity , extended kalman filter , moving horizon estimation , computer science , mathematical analysis , engineering , ecology , biochemistry , statistics , chemistry , control (management) , control engineering , artificial intelligence , biology , gene
In this paper a decomposition method is introduced for the solution of the optimal Kalman filter gains in singularly perturbed systems by solving two reduced‐order linear equations. The decomposition is achieved via the use of the Chang transformation, which is applied to the Hamiltonian matrix of the singularity perturbed Kalman filter. Since the decoupling transformation can be obtained up to an arbitrary degree of accuracy at very low cost, this approach produces an efficient numerical method for obtaining the Kalman filter gains. A numerical example is given to demonstrate the efficiency of the method.