Semidefinite Programming Methods for Alleviating Sensor Position Error in TDOA Localization

This paper develops a unified solution for time-difference-of-arrival (TDOA) localization in the presence of sensor position errors. This technique starts with maximum likelihood estimation (MLE), which is known to be nonconvex. A semidefinite programming technique to effectively transform the MLE problem into a convex optimization is proposed, together with a unified solution for four scenarios: 1) without a calibration emitter; 2) with a single calibration emitter, whose position is subject to measurement errors; 3) with a single calibration emitter, whose position is perfectly known; and 4) with a single calibration emitter, whose position is completely unknown. The results are finally extended to the case of multiple calibration emitters, whose positions are also subject to errors. Similar to the existing schemes that are known to have good performances, the proposed solution also reaches the Cramér–Rao lower bound when sensor position errors and TDOA measurement noise are sufficiently small. However, as TDOA measurement noise or sensor position errors increase, comparison with the existing state-of-the-art methods for each scenario shows that the proposed solution performs significantly better.