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 with its estimate. Using -dimensional samples , an unbiased estimate of , the correlation matrix of the array signals, may be obtained by means of a simple averaging scheme:
where is the conjugate transpose. The expression of the theoretically optimal weights requires the inverse of , and the inverse of the estimates matrix is then used for finding estimated optimal weights.
References[]
- Widrow, B.; Mantey, P. E.; Griffiths, L. J.; Goode, B. B. (1967). "Adaptive antenna systems" (PDF). Proceedings of the IEEE. 55 (12): 2143–2159. doi:10.1109/proc.1967.6092.
- Haykin, S. (2002). Adaptive Filter Theory. Prentice Hall. pp. 165–168. ISBN 0-13-048434-2.
Categories:
- Covariance and correlation
- Filter theory