Underdetermined DOA estimation of quasi-stationary signals using a partly-calibrated array

Quasi-stationary signals have been widely found in practical applications, which have time-varying second-order statistics while staying static within local time frames. In this paper, we develop a robust direction-of-arrival (DOA) estimation algorithm for quasi-stationary signals based on the Khatri–Rao (KR) subspace approach. A partly-calibrated array is considered, in which some of the sensors have an inaccurate knowledge of the gain and phase. In detail, we first develop a closed-form solution to estimate the unknown sensor gains and phases. The array is then calibrated using the estimated sensor gains and phases which enables the improved DOA estimation. To reduce the computational complexity, we also proposed a reduced-dimensional method for DOA estimation. The exploitation of the KR subspace approach enables the proposed method to achieve a larger number of degrees-of-freedom, i.e., more sources than sensors can be estimated. The unique identification condition for the proposed method is also derived. Simulation results demonstrate the effectiveness of the proposed underdetermined DOA estimation algorithm for quasi-stationary signals.