An analysis of the error characteristics of two time of arrival localization techniques

Accurate local positioning systems usually use a network of anchor nodes at known locations to track mobile nodes based on the measurement of the time of arrival (TOA) at anchor nodes of beacon signals transmitted by the mobile nodes. To localize the mobile node either TOA processing, where the unknown transmit time is estimated along with the node location, or time difference of arrival (TDOA) processing, where the transmit time is eliminated before estimating the node location, can be used. We show that the position error bound of both these formulations are the same by analyzing the Cramér-Rao lower bound. When processing data collected in field trials, however, we observed that the TOA processing yields better localization accuracy, and explain this behavior using differential geometry-based curvature measures that show that the TDOA cost function has greater degree of non-linearity.