Rotated Eigenstructure Analysis for Source Localization without Energy-decay Models

Herein, the problem of simultaneous localization of two sources given a modest number of samples is examined. In particular, the strategy does not require knowledge of the target signatures of the sources a priori, nor does it exploit classical methods based on a particular decay rate of the energy emitted from the sources as a function of range. General structural properties of the signatures such as unimodality are exploited. The algorithm localizes targets based on the rotated eigenstructure of a reconstructed observation matrix. In particular, the optimal rotation can be found by maximizing the ratio of the dominant singular value of the observation matrix over the nuclear norm of the optimally rotated observation matrix. It is shown that this ratio has a unique local maximum leading to computationally efficient search algorithms. Moreover, analytical results are developed to show that the squared localization error decreases at a rate faster than the baseline scheme.