Maximum likelihood sensor array calibration using non-approximate hession matrix

Unknown array non-ideal characteristics, including mutual coupling between array elements, channel gain/phase errors, and sensor position errors, will degrade the array performance of direction finding and beamforming. In this letter, we propose an improved maximum likelihood (ML) calibration algorithm to estimate all such non-ideal characteristics with lower computational complexity and faster convergence rate. First a modified formulation of the ML function is developed to avoid matrix inversion in each iteration. Then, a damped Newton formula with non-approximate Hession matrix is derived, which greatly improves the convergence rate. The numerical results demonstrate the effectiveness and efficiency of the proposed algorithm.