Closed Form Solution for 3D Localization Based on Joint RSS and AOA Measurements for Mobile Communications

To address three-dimensional (3D) localization problems in the wireless sensor networks (WSNs) of mobile communications, a closed-form algorithm by utilizing hybrid information extracted from the received-signal-strength (RSS) with unknown signal powers and the angle-of-arrival (AOA) is proposed in this paper. Firstly, the distance of the target is expressed as the linear equation with respect to coordinates of target and trigonometric functions of angles. Then, the RSS measurement is rewritten as the ratios of distances between the target and different receiving sensors. Furthermore, the set of pseudo-linear equations for the location of target is derived with respect to the AOA and nonlinear RSS measurements. Under the condition of the small variance of measurements, the first-order Taylor expansion around the value of measurement is taken to the set of pseudo-linear equations and the first-order perturbation errors is also obtained. Finally, the solution of the target localization is derived utilizing the weighted least square (WLS). Theoretical analysis and simulation results show that the performance of proposed algorithm converge to the CRLB in the situation of the moderate measurement errors.