Robust Iterative Solution for Linear Array-Based 3-D Localization by Message Passing

Recent research has shown that using the 1-D signal arrival angles observed by linear arrays can locate a 3-D source in unique co-ordinates. Current methods to solve this localization problem are based on semidefinite programming (SDP) or gradient-based iteration, which are either computationally demanding or facing divergence or local convergence issues. This paper reformulates the maxi-mum likelihood (ML) estimation of the 3-D localization problem using the factor graph model, where an effective algorithm is designed through message passing. Although iterative, the proposed solution is more robust to measurement noise than the Gauss-Newton (GN) iterative solution, and the complexity is lower than the SDP solution without the need to introduce semidefinite relaxation error. Simulations validate the analytical performance and complexity, and con-firm the superiority on the convergence of the proposed solution.