Abstract
The input u k and output y k of the multivariate ARMAX system A(z)y k = B(z)u k + C(z)w k are observed with noises: u ≜ u k + e and y ≜ y k + e , where e and e 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 w k 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.
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