We consider the positioning problem in non line-of-sight (NLoS) situations, where several base stations (BS) try to locate a user equipment (UE) based on uplink angle of arrival (AoA) measurements and a digital twin of the environment. Ray launching in a Monte Carlo manner according to the AoA statistics enables to produce a map of points for each BS. These points represent the intersections of the rays with a xy plane at a given user equipment (UE) elevation. We propose to fit a parametric probability density function (pdf), such as a Gaussian mixture model (GMM), to each map of points. Multiplying the obtained pdfs for each BS enables to compute the position probability of the UE. This approach yields an algorithm robust to a reduced number of launched rays. Moreover, these parametric pdfs may be fitted and stored in an offline phase such that ray tracing can be avoided in the online phase. This significantly reduces the computational complexity of the positioning method.

翻译：针对非视距(NLoS)场景下的定位问题，我们研究了多基站(BS)基于上行到达角(AoA)测量值与数字环境孪生体对用户设备(UE)进行定位的方法。根据到达角统计特性采用蒙特卡洛方式进行射线发射，可为每个基站生成二维平面上的交点分布图（这些交点为射线与给定用户设备高度处xy平面的交点）。我们提出为每幅交点分布图拟合参数化概率密度函数（如高斯混合模型），将各基站所得概率密度函数相乘即可计算用户设备的位置概率。该算法对射线发射数量较少的情况具有鲁棒性。同时，这些参数化概率密度函数可在离线阶段完成拟合与存储，从而在线阶段避免射线追踪，显著降低定位方法的计算复杂度。