Improved TOA Localization Using Modified Polar Representation

Existing communication systems are required to provide highly precise locations of users or terminals to support diverse applications. This study enhances the performance of time of arrival localization by utilizing modified polar representation, regardless of the range of users or terminals. We propose two solutions: 1) the two-stage semidefinite relaxation (2S-SDR), enhancing accuracy by refining the weighting matrix after initial SDR; 2) the maximum likelihood estimator (MLE), using Gauss-Newton iteration to minimize its cost function. Both solutions achieve the Cramér-Rao lower bound (CRLB) under moderate noise levels. Particularly, the MLE demonstrates CRLB accuracy and lower bias in the low noise region. Simulation results validate the effectiveness of the proposed solutions.