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.

References

• B.Widrow , P.E Mantey, L.J Griffiths and B.B.Goode. (1967) "Adaptive Antenne systems". Proceedings of the IEEE, 55(12), 2143–2159
• S.Haykin (2002) Adaptive Filter Theory. Prentice Hall , pages 165–168 ISBN 0-13-048434-2