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 Ru with its estimate. Using K samples x ( k ) , k = 1 , 2 , … , K − 1 {displaystyle 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: 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 , … , K − 1 {displaystyle 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: 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.