A Novel 3-D Localization Scheme Using 1-D Angle Measurements

The traditional 3-D localization methods based on angle of arrival (AOA) using 2-D arrays has been well studied over the past few decades. However, in some situations, the sensors are only allowed to equip linear arrays for the space limitation. In those cases, the traditional methods could not locate the unknown source precisely in the 3-D space. This letter proposes a novel 3-D localization technique using 1-D AOAs of the source. This technique gives the measurement model between the 3-D location of the source where the 1-D AOAs measured by the linear array at each sensor. The localization problem is formulated as a constrained weighted least-squares optimization problem. The semidefinite programming method is applied to solve this problem after relaxing the nonconvex constraints by semidefinite relaxing technology. To improve the performance further, a Gaussian-Newton iteration is implemented for the maximum likelihood estimator. The Cramér-Rao lower bound (CRLB) is analyzed for evaluating the performance. Simulation results show that the performance of the proposed method reaches the CRLB.