Approximate Subspace-Based Iterative Adaptive Approach for Fast Two-Dimensional Spectral Estimation

In this paper, we devise a new approach for fast implementation of two-dimensional (2-D) iterative adaptive approach (IAA) using single or multiple snapshots. Our underlying idea is to apply the subspace methodology in this nonparametric technique by performing the IAA on the dominant singular vectors extracted from the singular value decomposition (SVD) or higher-order SVD of the multidimensional observations. In doing so, 2-D IAA is approximately realized by multiple steps of 1-D IAA, implying that computational attractiveness is achieved particularly for large data size, number of grid points and/or snapshot number. Algorithms based on matrix and tensor operations are developed, and their implementation complexities are analyzed. Computer simulations are also included to compare the proposed approach with the state-of-the-art techniques in terms of resolution probability, spectral estimation performance and computational requirement.