A novel algorithm for two-dimensional frequency estimation

This paper addresses the two-dimensional (2-D) frequency estimation embedded in additive Gaussian noise. By use of the biorthogonality of matrices and rotational invariance property, we construct an interesting cost function and propose a novel iterative algorithm for 2-D frequency estimation, which obtains one column of the Vandermonde matrix containing 1-D frequencies and the corresponding column of the Vandermonde matrix containing the other 1-D frequencies at each stage. Therefore, the proposed algorithm can pair the 2-D frequencies automatically. The convergence of the proposed iterative algorithm is also proven. Moreover, all the columns of the frequency matrices can be obtained by systematically multistage decomposition and multistage reconstruction. Simulation results are provided to show the good performance of the proposed algorithm.