Enhancing Performance for Wireless Location: Leveraging Linear Trend and Uncertainty Inherent in NLOS Error

Wireless localization with ultra-wideband technology or 5G/6G cellular networks is a major contributor to addressing satellite signal-denied positioning. The accuracy of localization, however, suffers from non-line-of-sight (NLOS) propagation. Literature has highlighted several approaches to improve precision, such as channel-based, map-based, and statistical feature-based. More attention has focused on the linear growth trend of NLOS error with distance at lower prior information acquisition costs. However, no previous study explores the uncertainty in the trend arising from a dynamic NLOS environment. Accordingly, this article intends to comprehensively utilize the linear trend and uncertainty to find the optimal location solution. First, we propose a distance-dependent uncertain model for NLOS error and construct an uncertain second-order cone programming. We then convert the nonconvex problem into a solvable positive semidefinite programming by Schur complement, Cauchy–Schwarz inequality, S-lemma, and constraint relaxation/tightening techniques. Simulations and experiments show that the resulting optimal and robust solution can obtain remarkable positioning accuracy in densely cluttered environments. The importance and originality of this study are that it fully uses the linear growth trend of NLOS error while incorporating the uncertainty for the trend.