Cooperative Localization in Wireless Sensor Networks With AOA Measurements
Shengchu Wang, Xianbo Jiang, Henk Wymeersch
Abstract
This paper researches the cooperative localization in wireless sensor networks (WSNs) with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\pi /\pi $ </tex-math></inline-formula> -periodic angle-of-arrival (AOA) measurements. Two types of localizers are developed from the perspectives of Bayesian inference and convex optimization. When the orientation angles are known, the positioning problem is resolved by a phase-only generalized approximate message passing (POG-AMP) algorithm with importance sampling mechanism. From the perspective of convex optimization, the positioning problem under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\pi /\pi $ </tex-math></inline-formula> -periodic AOAs is converted as a least square (LS) problem and then resolved by the gradient-descent/projected gradient-descent method named as Type-I LS localizer. When the orientations are unknown, expectation-maximization (EM) mechanism is introduced into the POG-AMP localizer, where node positions and orientations are alternatively updated through exchanging their statistical confidences. Type-II LS localizer is constructed by alternatively executing Type-I LS and a maximum-likelihood (ML) estimator of orientation. Cramér-Rao lower bounds (CRLBs) are derived for the proposed localizers. Simulation results validate that the proposed AMP-type and LS-type localizers outperform existing localizers, AMP-type localizers successfully handle nonlinear quantization losses, and EM-framework and ML estimator handle unknown orientation problem. AMP-type localizers outperform LS-type ones, and can approach to the CRLBs even under high noise contaminations.