Near-Field Source Localization by Using Focusing Technique

Abstract

We discuss two fast algorithms to localize multiple sources in near field. The symmetry-based method proposed by Zhi and Chia ( 2007) is first improved by implementing a search-free procedure for the reduction of computation cost. We present then a focusing-based method which does not require symmetric array configuration. By using focusing technique, the near-field signal model is transformed into a model possessing the same structure as in the far-field situation, which allows the bearing estimation with the well-studied far-field methods. With the estimated bearing, the range estimation of each source is consequently obtained by using 1D MUSIC method without parameter pairing. The performance of the improved symmetry-based method and the proposed focusing-based method is compared by Monte Carlo simulations and with Crammer-Rao bound as well. Unlike other near-field algorithms, these two approaches require neither high-computation cost nor high-order statistics.

Focusing-based approach for wide-band source localization in near-field

“…The results from the proposed method are compared with the narrow band focusing-based algorithm presented in [2] and the corresponding Crammer Rao Bounds (CRBs) given in [1]. Figs.…”

“…The focusing-based estimator has been proposed in [2] for the position estimation of narrow-band sources, in which a focusing matrix is employed to compensate the distorted wavefront due to the near-field propagation. For high frequency wide-band sources formulated in the previous section, we propose here a frequency-dependent focusing matrix B (f ) ∈ C M ×M .…”

“…The principle of these algorithms [1,6] is to separate the estimation of DOA and range by using appropriate approximations. Based on this idea, a narrow-band focusing-based estimator has been proposed in [2], where the near-field wavefront distortion (with respect to far-field wavefront) is compensated via focusing in order to enable the application of far-field DOA algorithms for near-field bearing estimation.…”

“…Based on the focusing technique proposed in [2], the wide-band near-field focusing matrix is able to compensate the wavefront distortion due to near-field propagation and the phase change caused by frequency shift within one time focusing calculation. The snapshots sampled in different frequencies are coherently summed and focused on a pre-estimated point.…”

Mixed-Field Source Localization Based on the Non-Hermitian Matrix

“…where s k (t) stands for the signal from the kth source, n m (t) represents the additive Gaussian noise (colored or white) at the mth sensor. Generally, the phase difference between the 0th and mth elements ϕ mk can be expressed as [19]…”