3D-Localization of A Stationary Random Acoustic Source in Near-Field by Using 3 Point-Detectors

Abstract

For the purpose of developing refined devices for environmental recognition in robotics, a practical method for 3D-localization of a stationary random acoustical source in near-field is proposed by newly introducing 3 fixed-detectors. By using two pairs of estimated auto-and cross-spectra of signals detected simultaneously at 3 fixed detectors, two sets of information about difference in propagation distances and the amplitude attenuation of wave propagation are derived in such a manner that the derivation is independent of the shape of power spectra of detected random signals so as to be applicable to any stationary random acoustical source and additive corrupting noises at detectors are cancelled out as completely as possible. Then, by combining these information with the geometric relation of signal detection, the source position in 3D-space is estimated. After the principle of the proposed 3D-localization and the required conditions being made clear, 3D-distribution area of the position estimate is theoretically evaluated as concentration ellipsoid, based on the sampling variations of estimated spectra, and a simple method of evaluating the 3D-distribution or localizable area with prescribed relative errors is derived from the maximum length of major axes of the ellipsoid. To show the effectiveness of the theoretical results and make clear the influence of the source range, SNR, at detection and spatial distance between detectors on the final source distribution or localizable area, numerical analyses are carried out by changing them parametrically, the result of which illustrate the effectiveness as well as fundamental characteristics of the proposed method under practical circumstances.