Sample matrix inversion

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Sample matrix inversion (or direct matrix inversion) is an algorithm that estimates weights of an array (adaptive filter) by replacing the correlation matrix Ru with its estimate. Using K samples x(k), k=1,2,\dots,K-1, an unbiased estimate of Ru, the correlation matrix of the array signals, may be obtained by means of a simple averaging scheme:

\hat{R}_u (k) = (1/k) \sum(x(k) x^H(k)).

The expression of the theoretically optimal weights requires the inverse of Ru, and the inverse of the estimates matrix is then used for finding estimated optimal weights.