Novel techniques for estimation of array signal parameters based on matrix pencils, subspace rotations, and total least squares

A novel algorithm for sensor array signal processing and spatial source parameter estimation, referred to as the method of simultaneous rotations, is introduced. The algorithm is in the same genre as the recently proposed ESPRIT algorithm, which works with two identical arrays, an X array and a Y array. A major tenet of the originality of the new approach is that it treats the X and Y data matrices as a rectangular matrix pencil and uses the fact that they have the same row space, the source subspace, as well as the same column space, the signal subspace. A novel technique for reducing the problem to that of solving the eigensystem of a square matrix pencil of dimension equal to the number of sources is developed, based on the solution to the Procrustes problem for optimally performing an invariant subspace rotation. Refinements to the algorithm invoking the total-least-squares concept are also presented for the purpose of further exploiting the similarity in structure between the X and Y data matrices