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 $$R$$ with its estimate. Using $$K$$ $$N$$-dimensional samples $$X_1, X_2,\dots,X_K$$, an unbiased estimate of $$R_{X}$$, the $$N \times N$$ correlation matrix of the array signals, may be obtained by means of a simple averaging scheme:
 * $$\hat{R}_{X} = \frac{1}{K} \sum\limits_{k=1}^K X_k X^H_k,$$

where $$H$$ is the conjugate transpose. The expression of the theoretically optimal weights requires the inverse of $$R_{X}$$, and the inverse of the estimates matrix is then used for finding estimated optimal weights.