本文實現麥克風隨機排列陣列的遠場聲源定位和分離的兩個階段。麥克風的位置以模擬退火(simulated annealing, SA) 法優化設計,麥克風各點的位置以高斯分佈的方式隨機取點,繪製遠場波束圖(Beam-pattern)並尋求最大旁瓣(maximum side-lobe) 的最小化。兩階段的演算法皆以球面波模型的基礎進行推導。在定位階段,先以延遲相加方法(delay and sum, DAS) 定出大致的聲源位置區,接著使用參數估測方法使定位更加精確。在分離階段中,聲源振幅可以藉由麥克風接收到的聲壓與聲源傳遞至麥克風的傳遞矩陣之間的反矩陣問題求得。而當聲源的數量小於麥克風時則形成超定問題,可以透過提可諾夫法 (Tikhonov, TIKR)和最大可能性估測法(maximum likelihood estimation, MLE)求解。
A far-field random array is implemented for localization and separation of noise sources. Microphone positions are optimized, with the aid of the simulated annealing (SA) method. Random samples of sensor position are drawn from Gaussian distribution to minimize the side-lobe maximum of the far-field beampattern. A two-stage algorithm is devised on the basis of the spherical-wave model on the image plane. In the localization stage, the active source regions are located by using the delay-and-sum (DAS) method, followed by parametric array localization with improved resolution. In the separation stage, source amplitude extraction can be achieved by formulating an inverse problem based on the steering matrix relating the sound pressures received by the microphones and the source amplitudes. The number of sources is selected to be less than the number of microphones to render an overdetermined problem which can be solved by using the Tikhonov regularization (TIKR) and Maximum Likelihood Estimation (MLE).