Sensor array signal processing via a procrustes rotations based eigenanalysis of the ESPRIT data pencil

The authors propose the procrustes-rotation-based ESPRIT algorithm, PRO-ESPRIT, for estimating characteristic parameters associated with a scene of radiating sources, given data derived from two identical sensor arrays, the X and Y arrays, which are displaced relative to one another. PRO-ESPRIT uses the inherent redundancy built into the ESPRIT array system to compensate for deviations from the ideal array model. This redundancy is manifested by two fundamental properties of the noiseless X and Y data matrices comprising the ESPRIT data pencil: (a) they have the same row space, the signal subspace; and (2) they have the same column space, the source subspace. These properties are utilized by invoking two primary tools: (1) the solution to the procrustes problem for optimally approximating an invariant subspace rotation; and (2) the total-least-squares method for perturbing each of two estimates of a common subspace in a minimal fashion until the two perturbed spaces are the same.>