Reference-free time-based localization for an asynchronous target

Low-complexity least-squares (LS) estimators based on time-of-arrival (TOA) or time-difference-of-arrival (TDOA) measurements have been developed to locate a target node with the help of anchors (nodes with known positions). They require to select a reference anchor in order to cancel nuisance parameters or relax stringent synchronization requirements. Thus, their localization performance relies heavily on the reference selection. In this article, we propose several reference-free localization estimators based on TOA measurements for a scenario, where anchor nodes are synchronized, and the clock of the target node runs freely. The reference-free LS estimators that are different from the reference-based ones do not suffer from a poor reference selection. Furthermore, we generalize existing reference-based localization estimators using TOA or TDOA measurements, which are scattered over different research areas, and we shed new light on their relations. We justify that the optimal weighting matrix can compensate the influence of the reference selection for reference-based weighted LS (WLS) estimators using TOA measurements, and make all those estimators identical. However, the optimal weighting matrix cannot decouple the reference dependency for reference-based WLS estimators using a nonredundant set of TDOA measurements, but can make the estimators using the same set identical as well. Moreover, the Cramér-Rao bounds are derived as benchmarks. Simulation results corroborate our analysis.