Interpretation of the Multi-Stage Nested Wiener Filter in the Krylov Subspace Framework

In this paper, we show that the Multi-Stage Nested Wiener Filter (MSNWF) can be identified to be the solution of the Wiener-Hopf equation in the Krylov subspace of the covariance matrix of the observation and the crosscorrelation vector of the observation and the desired signal. This understanding leads to the conclusion that the Arnoldi algorithm which arises from the MSNWF development can be replaced by the Lanczos algorithm. Thus, the computation of the underlying basis of the Krylov subspace can be simplified. Moreover, the settlement of the MSNWF in the Krylov subspace framework helps to derive an alternative formulation of the already presented MSNWF composition.

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