Multidimensional Scaling-Based TDOA Localization in Modified Polar Representation

Multidimensional scaling (MDS) is an attractive method for location-related applications due to its robustness against noise. This paper applies MDS to time difference of arrival (TDOA) localization in the modified polar representation (MPR) for integrating near-field and far-field localizations. The new MDS formulation yields a constrained optimization problem in terms of the source position. We then propose a computationally efficient and noise robust solution to solve this problem. The solution is closed-form and asymptotically unbiased. It can achieve better mean-square error (MSE) in the large noise region and possibly lower bias than the closed-form solutions from the literature, and also has attractive complexity.