2D DDoA-based Self-Positioning for Mobile Devices

Multi-antenna techniques enable Direction of Arrival (DoA) estimation and lead to highly accurate results. In DoA-based positioning, the angles values must be predefined in an interval of $2\pi$-length, and the prior knowledge of x-direction is required. However, this prerequisite is impractical for a self-positioning task at a mobile device because its orientation is unknown. In this paper, we propose an algorithm using the differences among the DoAs to overcome such a difficulty. The algorithm relies on the estimation of the Direction Difference of Arrival (DDoA), which is linked to the DoAs. In our procedure, the definition of DoA utilizes the atan2 function, which has the $2{\pi}$-long codomain to map the DoA. An iterative Maximum Likelihood (ML) estimator for position estimation is presented. Noisy measurements with values near the edges of this codomain can lead to drastic position estimation errors, making the convergence of iterative procedures more challenging. Therefore, a phase correction scheme is proposed to robustify the estimation considerably. Simulation results show substantial improvement in performances compared to the methods without correction.