DOA and steering vector estimation using a partially calibrated array

We consider the problem of estimating directions of arrival (DOAs) using an array of sensors, where some of the sensors are perfectly calibrated, while others are uncalibrated. We identify a cost function whose minimizer is a statistically consistent and efficient estimator of the unknown parameters-the DOAs and the gains and phases of the uncalibrated sensors. Next we present an iterative algorithm for finding the minimum of that cost function The proposed algorithm is guaranteed to converge. The performance of the estimation algorithm is compared with the Cramer Rao bound (CRB). The derivation of the bound is also included. It is shown that DOA accuracy can be improved by adding uncalibrated sensors to a precisely calibrated array. Moreover, the number of sources that can be resolved may be larger than the number that can be resolved by the calibrated portion of the array.