Stable matrix inverse method for array DF using trapezoidal factorisation
Abstract
A trapezoidaldiagonal (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 triangulardiagonal (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.
 Publication:

Electronics Letters
 Pub Date:
 February 1986
 DOI:
 10.1049/el:19860123
 Bibcode:
 1986ElL....22..177B
 Keywords:

 Adaptive Filters;
 Digital Filters;
 Factorization;
 Matrices (Mathematics);
 Maximum Likelihood Estimates;
 Signal Processing;
 Covariance;
 Hermitian Polynomial;
 Numerical Stability;
 Signal Measurement;
 Communications and Radar