Estimation of sensor gain and phase

The problem of estimating the direction-independent gain and phase characteristics of an array of sensors, using knowledge of the true field covariance at the sensor locations, is considered. A concise expression for the log-likelihood function is derived and several mathematical properties of this objective function are given. The Cramer-Rao (C-R) lower bounds on the variances of gain and phase estimates are derived, with the plane wave in isotropic noise considered as a special case. The maximum-likelihood estimates are shown to be consistent, asymptotically efficient and asymptotically normal. A simple estimator is proposed which is consistent and which gives good initial estimates for a Newton algorithm for finding the maximum-likelihood solution. Comparison of the maximum-likelihood estimates and the C-R bounds is given for the plane-wave-in-isotropic-noise example