2D DoA-based Positioning with Phase Jump Corrections and An Approximate Maximum Likelihood Estimator

Direction of arrival (DoA) estimation is crucial to improve communications systems' performance, leading to much more accurate results in localization, one of the most vital applications in the Internet of Things (IoT). Unlike the range-based ones, the direction-based positioning algorithms estimate the unknown position by the measured angles whose values must be predefined in an interval of 2 pi-length. Noisy measurements with values near the edges of this interval can lead to drastic estimation errors, making the convergence of iterative procedures much more challenging. In this paper, we propose a Maximum Likelihood (ML) estimator, which applies iterative procedures for position estimation. Our procedure is based on the atan2 function, which has the 2 pi-long codomain to map the DoA. Moreover, a novel mechanism to make the estimation near the edges much more robust, phase jump corrections are proposed to rectify the final estimates. In addition, a new approximate ML estimator, where the effects of approximately normal distributed DoA estimation errors are limited to first-order perturbations, is also introduced. Outputs of this approximate estimator help to enhance the accuracy of the true ML estimator. Simulation results show significant performance improvements.