Estimating Electrically Small Targets Using Equivalent Dipoles and Sparse Processing

Abstract

We develop an algorithm for localizing and estimating electrically small targets using sparse processing framework and vector electric-field measurements. To model the sources of electromagnetic field, we use equivalent electric and magnetic dipoles, assuming that only a few of them are sufficient for accurate source representation. To find the locations and complex amplitudes of the equivalent dipoles, we apply the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization, which mitigates the inherent ill-posedness of the inverse problem. The method includes a normalization scheme which harmonizes imbalances in the system matrix and, consequently, improves the numerical stability of the method. In addition, we develop an algorithm for finding the optimal value of the regularization coefficient, based on the L-curve approach. The performance of the algorithm has been extensively tested using experimental data collected over a wide frequency bandwidth.