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 coordinates. 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 maximum 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 confirm the superiority on the convergence of the proposed solution.