Fast Calculation Method for Time Difference of Arrival-based Localization

Time difference of arrival-based localization systems successfully utilized the consensus functions, which provide robust location estimates even in extremely hostile environments, when a large number of measurements are outliers. The naive calculation of the consensus function, however, is computationally expensive, thus various acceleration methods are utilized. In this paper a special property of the consensus function is experimentally studied and validated. The property allows the construction of an upper bound of the consensus function in a spherical region in space. Based on this property a fast search algorithm is constructed, which requires an order of magnitude less computation than earlier acceleration methods.