Eigenvector-based signal subspace estimation

Abstract

In this work, we explore the performance of a new algorithm for the estimation of signal and noise subspaces from limited data collected by a large-aperture sonar array. Based on statistical properties of scalar products between deterministic and complex random vectors, the proposed algorithm defines a statistically justified threshold to identify target-related features (i.e., wavefronts) embedded in the sample eigenvectors. This leads to an improved estimator for the signal-bearing eigenspace that can be applied to known eigenspace beamforming processors. It is shown that data projection into the improved subspace allows better detection of closely spaced targets compared to current subspace beamformers, which utilize a subset of the unaltered sample eigenvectors for subspace estimation. In addition, the proposed threshold gives the user control over the maximum number of false detections by the beamformer. Simulated data are used to quantify the performance of the signal subspace estimator according to a normalized metric that compares estimated and true signal subspaces. Improvement on beamforming resolution using the proposed method is illustrated with simulated data corresponding to a horizontal line array, as well as experimental data from the Shallow Water Array Performance experiment.