Localization using time-difference of arrival (TDOA) has myriad applications, e.g., in passive surveillance systems and marine mammal research. In this paper, we present a Bayesian estimation method that can localize an unknown number of static sources in 3-D based on TDOA measurements. The proposed localization algorithm based on particle flow (PFL) can overcome the challenges related to the highly nonlinear TDOA measurement model, the data association (DA) uncertainty, and the uncertainty in the number of sources to be localized. Different PFL strategies are compared within a unified belief propagation (BP) framework in a challenging multisensor source localization problem. In particular, we consider PFL-based approximation of beliefs based on one or multiple Gaussian kernels with parameters computed using deterministic and stochastic flow processes. Our numerical results demonstrate that the proposed method can correctly determine the number of sources and provide accurate location estimates. The stochastic flow demonstrates greater accuracy compared to the deterministic flow when using the same number of particles.

翻译：利用到达时间差（TDOA）进行定位具有广泛的应用，例如在无源监视系统和海洋哺乳动物研究中。本文提出一种贝叶斯估计方法，能够基于TDOA测量在三维空间中定位未知数量的静态声源。所提出的基于粒子流（PFL）的定位算法能够克服以下挑战：高度非线性的TDOA测量模型、数据关联（DA）不确定性以及待定位声源数量的不确定性。在具有挑战性的多传感器声源定位问题中，我们在统一的置信传播（BP）框架内比较了不同的PFL策略。具体而言，我们考虑了基于一个或多个高斯核的置信度PFL近似方法，其参数通过确定性和随机性流过程计算。数值结果表明，所提方法能够正确确定声源数量并提供精确的位置估计。在使用相同粒子数的情况下，随机流方法相比确定性流方法展现出更高的精度。