Abstract
Let the observed sequence {y k } be generated by the multivariate ARMAX system A(z)y k = B(z)u k−1 +C(z)w k , where {w k } is the system noise with unknown covariance matrix R w ≫ 0, and {u k } is a sequence of mutually independent and identically distributed (iid) random vectors. Based on {y k } and {u k }, identification algorithms are proposed to simultaneously estimate the orders (p,q,r), the covariance matrix R w , and the coefficients of A(z), B(z), and C(z). Under reasonable conditions the estimates are proved to converge to the true values with probability one. The advantage of the proposed algorithms is that the estimates can be easily updated for online identification.
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