  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.
