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The theoretical and practical performance limits of a 2D ultrawideband impulse-radio localization system operating in the far field are studied under the assumption that estimates of location are based on time-difference-of-arrival (TDOA) measurements. Performance is evaluated in the presence of errors in both the TDOA measurements and the sensor locations. The performance of both optimal (maximum-likelihood) and suboptimal location estimation algorithms is studied and compared with the theoretical performance limit defined by the Cramér-Rao lower bound on the variance of unbiased TDOA location estimates. A novel weighted total-least-squares algorithm is introduced that compensates somewhat for errors in sensor positions and reduces the bias in location estimation compared with a widely used weighted least-squares approach. In addition, although target tracking per se is not considered in this paper, performance is evaluated both under the assumption that sequential location estimates are not aggregated as well as under the assumption that some sort of tracker is available to aggregate a sequence of estimates.