Array shape calibration using sources in known locations

Most sensor array processing methods for multiple source localization require knowledge of the sensor array pattern characteristics or the array manifold. In particular, they assume a precise knowledge of the relative positions of the sensors which may not represent the true sensor positions. An iterative Newton-type array shape calibration algorithm to estimate the array sensor positions is proposed. This technique is based on the asymptotically efficient weighted subspace fitting (WSF) estimator using known calibration sources. A closed form expression for the asymptotic Cramer-Rao bound (CRB) for the sensor positions is also presented. Numerical examples are presented to illustrate the improved performance in resolution and accuracy for multiple source localization problems using this technique as well as the asymptotic optimality of the WSF array shape calibration algorithm in approaching the CRB