On Martingales and Least Squares Linear System Identification

نویسندگان

  • John B. Moore
  • Brian D.O. Anderson
چکیده

In this paper, a nontrivial generalization of a scalar martingale convergence theorem to the vector case is derived. In particular, a theorem is derived concerning the almxat sure convergence to zero of a (vector) martingale normalized by its (ntatrix) process vaziance. This theorem allows a derivation of almost a~n-e convergence results for least squarea identification algorithms applicable to cases when nonstationary processes and unstable signal models are involved. The various convergence results and also a novel matrix Kronecker lemma are derived by means of the Toeplitz lemma and standard martingale convergence theorems.

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تاریخ انتشار 1975