Gridless DOA Estimation Under the Multi-frequency Model

Direction of Arrival (DOA) estimation is widely applied in acoustic source localization. A multi-frequency model is suitable for characterizing the broadband structure in acoustic signals. In this work, we solve the continuous (gridless) line spectrum estimation problem by incorporating the multi-frequency model into an atomic norm minimization (ANM) framework. We show that our ANM problem is equivalent to a semi-definite program (SDP) which can be solved by an off-the-shelf SDP solver. We also provide the dual certificate that can certify the optimality of the SDP solution, and we localize the sources by finding the peaks of the norm of the dual polynomial. Numerical results support our theoretical findings and demonstrate the effectiveness of the method.