Reducing bias for closed-form TDOA localization in unified near- and far-field model

Bias is a key metric to evaluate the average error of an estimator. Lower bias implies that the mean is closer to the true value. Recent research about time difference of arrival (TDOA) localization unifies near- and far-field by using modified polar representation (MPR), where the new position estimator is robust to the source range. However, the existing closedform solutions suffer relatively high bias. This paper first overviews the current work of MPR-based localization. Then, it is dedicated to improving the bias performance of TDOA-based localization in MPR. A new method, called direct deviation refinement (DDR), is proposed. The DDR is implemented by a weighted spherical intersection with a refinement. Simulation results show the new method lowers the bias level remarkably compared to successive unconstrained minimization (SUM) and generalized trust region subproblem (GTRS) solutions, while the degradation of the meansquared error (MSE) is insignificant.