3D DoA-based Localization with Phase Jump Corrections

Localizing a source based on the directions of its signals is an attractive approach because no synchronization among clocks is required. In this paper, we propose a Maximum Likelihood (ML) estimator to solve the location problem in 3D schemes, where a signal's direction is mathematically expressed by an elevation angle and an azimuth angle which applies iterative procedures for position estimation. This estimator applies iterative procedures for position estimations. To avoid confusions, the value of each angle must be predefined in an interval of 2 pi-length. However, the convergence of iterative procedures will be really challenging if there are angle estimation errors caused by noisy measurements with values near the boundaries of this interval. In our proposed procedure, the elevation angle is defined with the arctan function and the azimuth angle is defined with the atan2 function, whose codomain is 2 pi-long, to map the DoA. Furthermore, to robustify the estimations near the boundaries, phase jump corrections are proposed to rectify the final estimates. Simulation results show significant performance improvements.