3-D near field source localization using second order statistics

Passive localization of narrowband sources in the spherical coordinates (azimuth, elevation, and range) is considered. A new method which proceeds in two steps and uses only the second order statistics (SOS) of the observations collected from a centro-symmetric cross-array is introduced. The first step is a signal pre-processing which consists in the computation of some properly chosen spatial correlation sequences of the observed signal. The correlation coefficients are shown to be superimposed exponential sequences and their frequencies are nonlinear functions of azimuths, elevations and the ranges of the source signals. The second step consists in the estimation of the frequency components using the subspace rotation invariance (also known as ESPRIT and matrix pencils) technique. This method, however requires a correct parameter pairing (or eigenvalue association) to achieve a consistent estimation of the signal parameters. Several pairing techniques are considered. The source azimuths, elevations, and ranges are then calculated from the estimated frequency components. The effectiveness of the proposed method is illustrated by some numerical simulations.