Two-Stage Localization Scheme with TDOA Measurements Using the Multidimensional Scaling Model

In railway transportation and smart stations, it is important to locate an object through wireless communication signals. In urban terrestrial scenarios, subterranean scenarios, and indoor scenarios, localization scheme using the time-difference-of-arrival (TDOA) measurements provides a useful positioning technique. One of the localization techniques with TDOA measurements is to define a cost function using the multidimensional scaling (MDS) model, where the minimize of the cost function is defined as the estimate of the emitting source position. However, the existing cost function has not taken the noise distribution into consideration, so the estimate of the source position will not be accurate enough. In this paper, a two-stage localization scheme is proposed. The first-stage estimate is calculated by subspace analysis. It is used for refining the cost function by taking the noise distribution into account. The second-stage estimate is the minimize of the refined cost function, which is calculated literately using Newton’s method with the first-stage estimate as its initial point. Simulation results show that the proposed method achieves higher localization accuracy than the traditional method that uses the minimize of the original MDS-based cost function as the estimate of the source position.