Stable matrix inverse method for array DF using trapezoidal factorisation

A trapezoidal-diagonal (TD) factorization method is defined for finding the inverse of the covariance matrix employed in digital filtering by maximum likelihood techniques. The application of the TD method, rather than the normally used lower triangular-diagonal (LD) technique, is shown to require only the same number of elimination steps as the number of signals in the environment. The LD method requires calculations equal to the number of elements in the matrix, and thereby introduces the possibility of instability, a condition which is exacerbated by a small number of signals. The TD method permits accurate signal measurements with digital filters working with only one sample for each channel.