Wideband Joint Elevation-Azimuth Angle Estimation Based on Multiple Frequency Model and Atomic Norm Minimizaion

The estimation of the Direction of Arrival (DOA) plays a critical role in sonar, radar, and acoustic source localization. However, current research predominantly concentrates on narrowband, one-dimensional signals, which can’t be directly applied to practical scenarios where the signals are usually wideband and multi-dimensional. In this paper, we propose a two-dimensional multi-frequency atomic norm minimization (2DMFANM) algorithm for the estimation of elevation and azimuth angles for wideband signals. A multi-frequency signal representation is adopted to accurately model wideband signals. The technique of atomic norm minimization (ANM) is leveraged to extract DOA information from the received signals in a gridless fashion. To transform the intractable ANM formulation into a solvable semi-definite programming (SDP) problem, we conduct a thorough analysis of the corresponding dual problem. Subsequently, we introduce a novel two-dimensional mapping operator, which aids in the construction of a multivariate trigonometric polynomial representation. This formulation is specifically designed to facilitate the application of the bounded lemma, thereby enabling the transformation of the ANM problem into the SDP framework. Compared with narrowband ANM methods, 2DMFANM takes advantage of additional data from multiple frequencies and remarkably improves the accuracy of estimation. Numerical simulations are executed and demonstrate the superior performance of our proposed method than existing algorithms.