Sample matrix inversion

Sample matrix inversion (or direct matrix inversion) is an algorithm that estimates weights of an array (adaptive filter) by replacing the correlation matrix R_u with its estimate. Using K samples $x(k), k=1,2,\dots,K-1$, an unbiased estimate of R_u, 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 R_u, and the inverse of the estimates matrix is then used for finding estimated optimal weights.