Solving the semi-definite generalized eigenvalue problem with application to ESPRIT

Two methods are developed for computing the generalized eigenvalues and eigenvectors associated with the matrix pair , where A and B are singular hermitian matrices with the range space of A a subset of the range space of B. Conventional methods of solution break down for this case. An application is described based on the recently reported Estimation of Signal Parameters by Rotational Invariance Techniques (ESPRIT) algorithm. ESPRIT possesses remarkable advantages over other high-resolution direction-of-arrival estimation algorithms in terms of speed, storage, and indifference to array calibration.