Cooperative Localization in Wireless Sensor Networks with AOA Ranging Measurements

This paper researches the cooperative localization in wireless sensor networks (WSNs) with $2\pi/\pi$-periodic angle-of-arrival (AOA) ranging measurements. When the orientation angles of the antenna arrays at WSN nodes are known, a ranging link loss is defined based on the tan-relationships between AOA observations and xy-minus coordinates of two neighboring nodes. Subsequently, the positioning problem under $2\pi$-periodic AOAs is converted as a convex optimization problem about minimizing total ranging-link loss through optimizing agent positions, which is resolved by the gradient-descent (GD) method. Under $\pi$-periodic AOAs, additional 0/1 integers are introduced to indicate the front-or-back impinging directions. By relaxing 0/1 integers as continuous variables within $[0,1]$, the positioning problem is relaxed as a nonconvex optimization one about minimizing total link loss over the agent positions and indicating variables, which is solved by the projected GD (PGD) method. Finally, Type-I least-square (LS) localizer is developed for WSNs with both $2\pi$ and $\pi$-periodic AOAs. When the orientation angles are unknown, Type-II LS localizer is developed by combining Type-I LS localizer with a maximum-likelihood (ML) orientation estimator, which alternatively updates agent positions and orientation angles. Simulation results validate that the proposed LS-type localizers outperform existing localizers.