A closed-form solution for 3-D mm-Wave localization

Millimeter wave (mm-Wave) multiple-input-multiple-output systems have the unique characteristics of high temporal resolution and high directivity, enabling very accurate localization. By utilizing the time delay, angle of departure, and angle of arrival measurements from both line-of-sight and non-line-of-sight paths, provided by the mm-Wave system, we propose a two-stage solution method to jointly estimate the user equipment (UE) position and orientation as well as the scatterer positions. Specifically, based on the geometric relations between the UE and scatterer positions, a coarse estimate is obtained by solving a set of equations, which is then refined by a linear weighted least squares estimator. The computational complexity of the proposed method is pretty low in that both solutions in the two stages are in closed form. Simulation results show that the proposed method is able to reach the Cramér-Rao lower bound performance at low noise levels.