Computationally attractive and statistically efficient estimator for noise resilient TOA localization

Localization technologies have received considerable attentions and been well-studied in past few decades. However, the performance under limited number of sensors and large noise/error environments still needs to be improved for balancing the performance and complexity. Taking these factors into consideration, this paper focuses on the time of arrival (TOA) localization problem where the measurement noise level can be high, the sensor position errors are present and the number of sensors is limited. We propose a location estimator that consists of a coarse solution and a refined estimate to enhance the quality of the coarse solution. The proposed estimator is closed-form and simple to compute. It is asymptotically unbiased, and having the estimation covariance matrix analytically matching the Cramér–Rao lower bound (CRLB). Simulations validate the theoretical results and illustrate the proposed algorithm works well with small number of sensors, has more noise resilient behavior in the large error region than the existing methods, and performs close to the Maximum Likelihood Estimator with ideal initialization.