Estimation of sensor gain and phase using known field covariance

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. The Cramer-Rao (CR) lower bounds on the variances of gain and phase estimates are given. The Newton algorithm is proposed for maximizing the log-likelihood, and a simple estimator for generating initial conditions is also proposed. Comparisons of the maximum likelihood estimator and CR bounds are given for a simple two-sensor example