摘要
The input uk and output yk of the multivariate ARMAX system A（x）yk = B（z）uk ＋ C（z）wk are observed with noises： uk^ob△=uk ＋ εk^u and yk^ob △=yk＋ εk^y, where εk^u and εk^y denote the observation noises. Such kind of systems are called errors-in-variables （EIV） systems. In the paper, recursive algorithms based on observations are proposed for estimating coefficients of A（z）, B（z）, C（z）, and the covariance matrix Rw of wk without requiring higher than the second order statistics. The algorithms are convenient for computation and are proved to converge to the system coefficients under reasonable conditions. An illustrative example is provided, and the simulation results are shown to be consistent with the theoretical analysis.
The input uk and output yk of the multivariate ARMAX system A（x）yk = B（z）uk ＋ C（z）wk are observed with noises： uk^ob△=uk ＋ εk^u and yk^ob △=yk＋ εk^y, where εk^u and εk^y denote the observation noises. Such kind of systems are called errors-in-variables （EIV） systems. In the paper, recursive algorithms based on observations are proposed for estimating coefficients of A（z）, B（z）, C（z）, and the covariance matrix Rw of wk without requiring higher than the second order statistics. The algorithms are convenient for computation and are proved to converge to the system coefficients under reasonable conditions. An illustrative example is provided, and the simulation results are shown to be consistent with the theoretical analysis.
基金
Supported by the National Natural Science Foundation of China (Grant Nos. 60821091, 60874001)
the National Laboratory of Space Intelligent Control
