Rank reduction direction-of-arrival estimators with an improved robustness against subarray orientation errors

The problem of signal direction-of-arrival (DOA) estimation in partly calibrated arrays composed of multiple subarrays with unknown intersubarray parameters and imperfectly known subarray orientations is studied. The recently developed spectral and root versions of the rank reduction estimator (RARE) are applicable to scenarios where no intersubarray calibration is available, but unfortunately, these algorithms are very sensitive to subarray orientation errors. Therefore, the conventional RARE algorithms can be applied to partly calibrated arrays with subarray orientation errors only if these errors are negligibly small. In this correspondence, a new robust modification of the RARE algorithm with a reduced sensitivity to subarray misorientations is proposed, and expressions for the corresponding stochastic Crame´r-Rao bound (CRB) are derived. The performance of our robust RARE algorithm is demonstrated to be close to this bound in the case of moderate subarray orientation errors.