Robust 3-D AOA Localization Against Malicious Attacks in Non-Gaussian Noise

This article addresses the robust angle-of-arrival (AOA) localization problem for 3-D sensor networks in adversarial environment. The problem becomes more challenging in practical scenarios where attack information is unknown and background noise has heavy-tailed property. With reasonable assumptions on the attack model and non-Gaussian noise, we propose a robust sparse regularization formulation by adopting the
${l}_{{1}}$
-norm as loss function to meet the need for heavy-tailed noise and nonconvex Cauchy function as penalty due to the sparsity of attack perturbations. To solve this nonconvex and nonsmoothed source localization problem, we develop a new smoothed Cauchy-regularized least absolution (SCLA) estimator based on the alternating direction of multipliers method (ADMM) and provide the sufficient convergence condition for SCLA. Unfortunately, the solution of SCLA is biased due to the correlation between noise vector and measurement matrix in the pseudolinear measurement equations. To handle this bias problem, an instrumental-variable (IV)-based Cauchy-regularized least absolution (IVSCLA) estimator is finally proposed by introducing the IV estimator into SCLA. Extensive simulation experiments demonstrate that the performance of IVSCLA has advantages over state-of-the-art algorithms in robustness and effectiveness for different noise distributions.