Optimal State Estimation of Linear Discrete-time Systems with Correlated Random Parameter Matrices
In this paper,dynamic systems with correlated random parameter matrices are considered.Firstly,we consider dynamic systems with deterministic transition matrices and temporally one-step correlated measurement matrices.The optimal recursive estimation of the state is derived by converting the problem to the optimal Kalman lter with one-step correlated measurement noises.Then,we consider a class of speci c dynamic systems where both state transition matrices and measurement matrices are one-step moving average matrix sequences driven by a common independent zero-mean parameter sequence.The optimal recursive estimation of the state can be obtained by using the rst order through the sixth order moments of the driving parameter sequence,which implies that when both transition matrices and measurement matrices are correlated,in general,it is impossible to obtain an optimal lter by only using the variance and covariance information of the transition matrices and the measurement matrices.Moreover,if only the state transition matrices in the dynamic system are temporally correlated,optimal lters can be given by using lower order moments of the driving parameters.Numerical examples support the theoretical analysis and show that the optimal estimation is better than the random Kalman lter with the correlation of parameter matrices ignored, especially for the case of both the transition matrices and the measurement matrices being correlated.
SHEN Xiaojing ZHU Yunmin LUO Yingting
Department of Mathematics Sichuan University Chengdu,Sichuan 610064,P.R.China Department of Computer Department of Mathematics Sichuan University Chengdu,Sichuan 610064,P.R.China
国际会议
The 30th Chinese Control Conference(第三十届中国控制会议)
烟台
英文
1-6
2011-07-01（万方平台首次上网日期，不代表论文的发表时间）