Two-Dimensional DOA Estimation of Underwater Acoustic Signals With Gain-Phase Errors

The intrinsic qualities of the underwater acoustic channel (UAC), such as multipath propagation and motion-induced Doppler shift, may result in large direction of arrival (DOA) estimation bias. In this paper, we propose a two-dimensional DOA estimation method for the underwater acoustic signals with gain-phase errors, coined as ML-ANM (Maximum Likelihood-Atomic Norm Minimization). We assume that the number of received signals satisfies the parameter identifiability condition. First, we propose a bimodal atomic norm involving noncoherent and coherent signals under the maximum likelihood estimation (MLE) framework, which allows simultaneous processing of noncoherent and coherent signals without decorrelation. To avoid the direct calculation of gain-phase errors, we transform the primal MLE optimization model into an ML-ANM optimization problem with two positive semidefinite constraints. Second, we utilize oblique projection to divide the optimal problem into two optimal subproblems involving noncoherent and coherent signals, and prove the equivalence of the problems and their solutions. Then, we obtain the global optimal solutions for the two optimal subproblems. Third but not the least, we provide the Cramér-Rao lower bound (CRB) and prove that the asymptotic error covariance matrix of ML-ANM achieves the CRB. Extensive experiments through realistic ocean simulations demonstrate the effectiveness of the ML-ANM method.