Accession Number : ADA313748

Title :   Determining the Rank of a Noisy Square Matrix Using the Characteristic Coefficients.

Descriptive Note : Final rept. Jun 95-Jul 96,

Corporate Author : NAVAL AIR WARFARE CENTER AIRCRAFT DIV WARMINSTER PA

Personal Author(s) : Gleeson, Ronald F. ; Stiller, Peter F. ; Williams, Robert M.

PDF Url : ADA313748

Report Date : 15 JUL 1996

Pagination or Media Count : 37

Abstract : Determining the rank of a matrix has several important applications. In modern array processing, the rank can be used to determine the number of targets detected. Radar normally performs this operation prior to determining the direction and velocity of each air platform. Also, sonar performs this operation before it attempts to classify submarines. It is therefore essential that the rank of the signal matrix be determined efficiently and accurately. It is assumed that the signal matrix is square and free of a nilpotent part. Unfortunately, there is usually noise added to the elements of the signal matrix due to such factors as the background in which the signal is embedded or instrument uncertainty. This paper describes a method for predicting the rank of a signal matrix by analyzing the coefficients of the characteristic polynomial of the noisy version of this matrix. These coefficients can be computed from algebraic sums of products of the elements. Time consuming iterations, which take place in methods involving singular values, are avoided. Furthermore, the results are shown to compare favorably to those produced by a singular value approach.

Descriptors :   *SIGNAL PROCESSING, *MATRIX THEORY, UNCERTAINTY, ARRAYS, RADAR, COEFFICIENTS, POLYNOMIALS, NOISE REDUCTION, SONAR.

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE