A robust TDOA localization method for researching upper bound on NLOS ranging error

In time-difference-of-arrival (TDOA) localization, the accuracy of the robust convex optimization algorithm is significantly affected by the upper bound of non-line-of-sight (NLOS) ranging error. Some algorithms estimate NLOS ranging error and source coordinates together, which makes the NLOS upper bound seem unnecessary, but this often leads to lower localization accuracy. Therefore, it is crucial to establish a reasonable upper bound for the NLOS ranging error. However, existing robust optimization algorithms suffer a significant drawback when introducing upper bounds on NLOS ranging error: The assignment of the upper bound of the NLOS ranging error does not match the actual environment, leading to poor algorithm accuracy. To solve the rationality problem of the NLOS ranging error upper bound assignment, this paper innovatively proposes the NLOS error upper bound as an uncertain variable arising from NLOS variability. We then develop a robust optimization formulation using matrix transformations to optimize the upper bound. By applying techniques such as linearization and perturbation decomposition, we derive an optimal solution that adjusts the NLOS error upper bound. Simulations and experiments show that the proposed approach outperforms existing algorithms in terms of localization accuracy in NLOS environments.