Interval Hyperbolic Localization Based on Iterative Contraction for Cellular Networks

Time difference of arrival (TDOA) positioning results obtained using commonly adopted algebraic methods lack uncertainty information. In this letter, we propose to incorporate interval computation into TDOA-based hyperbolic localization and employ an iterative contraction strategy to generate interval positioning results that guarantee to enclose the true solution. With the newly developed algorithm, interval TDOA measurements are considered as interval hyperbolas and partitioned into non-overlapping sets of rectangles using the dichotomy method. The intersection of these rectangles is determined and applied to update the target location interval through an iterative contraction process to shrink the location interval until convergence. Simulations are conducted to evaluate the accuracy, uncertainty and validity of the proposed interval hyperbolic localization algorithm. It is shown that the new algorithm can attain the Cramér-Rao lower bound under high level Gaussian noise and produce, with a probability close to one, positioning intervals enclosing the true target location.