A gradual-trust-mechanism-directed TOA localization under impulsive noise environment

Conventional time-of-arrival (TOA) localization methods often depend on fixed thresholds to distinguish inliers and outliers, which is an unreliable strategy in the presence of impulsive noise. Inappropriate thresholds introduce a high risk of measurement misclassification, where valid measurements may be treated as outliers while corrupted ones may be mistakenly retained, leading to further degradation in localization accuracy. To address this problem, we propose a robust cost function (RCF) directed by a gradual trust mechanism (GTM). This RCF enhances tolerance to large deviations, which reduces the risk of discarding valid measurements. Meanwhile, the proposed GTM preserves inlier contributions and suppresses contaminated measurements through an annealing competition mechanism. Furthermore, a fixed-point approach (FPA) is formulated to efficiently minimize residual errors under impulsive noise environment. Error analysis demonstrates that the iterative FPA process asymptotically reduces the sum of spatial error vectors toward zero. Simulation results demonstrate that the proposed FPA outperforms several state-of-the-art algorithms in scenarios with strong and multiple impulsive interference sources.