Speaker
Description
Most studies on acoustical source localization focus on estimating directions of arrival (DOAs) of far-field source, or localization of sources in a plane parallel to the array. Nevertheless, in several applications, an estimate of the source-array distance is desirable, such as the localization of drones. Numerical and experimental studies on source localization have evidenced that distance estimation fails for distant sources. The critical distance above which the distance estimation fails is generally considered to be the Rayleigh distance. This study provides a theoretical analysis of the Cramer-Rao bound (CRB) for the distance estimation problem using planar microphone arrays. The CRB provides a lower bound for the variance of the estimation of the parameters of the sources (e.g. position, power), for any unbiased estimator. Asymptotic approximations of the CRB under the conditional (time-harmonic source signal) and unconditional (random source signal) hypotheses are derived. In both cases, a high increase rate of the CRB in function of the distance is found. It is also shown that the Rayleigh distance does not predict the distance at which source localization fails. The results of numerical simulations and of an experiment strongly support the theoretical analysis.