Statistical Stability of Correlation Based Imaging Algorithms

Abstract

We consider imaging of an airborne target and study the stability of correlation based imaging methods to random fluctuations in the target's motion. The imaging system consists of a ground based emitter, and several passive receivers. By migrating the cross correlations of the received signals the two-point interference matrix is obtained. An image is then formed either by taking the diagonal of this matrix or by computing the eigenvector corresponding to the largest eigenvalue of the matrix. We call the latter the rank-1 imaging method. We show that the rank-1 image exhibits exceptional stability with respect to fluctuations in the platform's motion. We relate that to the stability of the first eigenvector of a matrix perturbed by multiplicative random phase noise. We provide simulations as well as an analytical model that demonstrates the robustness of the rank-1 imaging method to random fluctuations in the target's motion.