Stable and Fast Fixed-Point Algorithm for Time-of-Arrival-Based Location with Suppression of Outliers

Conventional time-of-arrival (TOA) localization methods often suffer from performance degradation in the presence of outliers. To address this issue, a robust framework is proposed to mitigate the effects of impulsive noise, including both Gaussian noise and outliers. This framework introduces a soft-decision criterion (SDC) designed to suppress impulsive noise by satisfying three essential conditions. Building on SDC, a robust cost function (RCF) is formulated to reduce the impact of outliers on position estimation, enhancing the tolerance to large biases and false detections while utilizing all candidate inliers as much as possible. Furthermore, a stable and fast fixed-point algorithm (FPA) is derived from the maximum likelihood estimator (MLE) by forcing an approximation of the RCF gradient to zero. Simulation results confirm that the FPA outperforms several state-of-the-art convex relaxation algorithms, especially in the presence of strong and numerous outliers.