Improved localization of near-field sources using a realistic signal propagation model and optimally-placed sensors

Abstract

In this paper we analyze the estimation of the angle and the range of a narrow-band source located in the near-field of an arbitrary centro-symmetric linear array (CSLA). This analysis deals with the Cramer Rao bound (CRB) on both angle and range, obtained thanks to an exact expression of the source-to-sensor delay and a realistic (range-dependent) model of source-to-sensor attenuation, ultimately achieving two objectives. On the first hand, closed-form approximate expressions of the CRB are developed and compared to those obtained assuming (unrealistically) that sensors perceive the same power despite being at different distances from the source. While the impact on angle estimation is negligible, range CRB significantly decreases if one incorporates the more appropriate range-dependent power model (except for sources at broadsides). An important consequence is that localization algorithms taking this range-dependent modelization of the apparent source power into account in their signal modeling should have much better range performance. On the second hand, the obtained CRBs are used to design nonuniform CSLA taking into account the ambiguities, with improved angle and range estimation, comparatively to uniform linear arrays (ULA). Finally, we show that our optimized CSLA for a single source also brings some benefits for two closely-spaced sources.