A Compensated Multi-Anchors TOF-Based Localization Algorithm for Asynchronous Wireless Sensor Networks

Tag localization for asynchronous wireless sensor networks requires the development of a scheme for clock synchronization. This remains a difficult and open problem since the performance of tag localization can be adversely affected by complications such as reply time and relative clock skew. Joint clock synchronization and a tag localization algorithm that implements a multi-anchor compensated time-of-flight (TOF) to the asynchronous wireless sensor network is a possible and viable solution. Although previous methods that leverage TOF measurements are effective and easily conducted, their performance is not always superior due to the relative clock skew. In this paper, we propose to extend the joint clock/tag synchronization/localization algorithm by introducing a compensation factor that can cancel relative clock skews from multi-tag anchor pairs. We apply a least squares estimation (LSE) algorithm to both the time of emission (TOE) and time of arrival (TOA) for the clock synchronization step. Under the assumption of a Gaussian measurement noise model, the tag localization problem is approximately solved by maximum likelihood estimation (MLE). To assess the performance of our algorithm, we derive the mean square error (MSE) of both relative clock skew and tag location and numerically evaluate the Cramér-Rao lower bound (CRLB) as a benchmark. The simulation results show that the accuracy of the relative clock skew-based estimation and tag localization are significantly improved over traditional algorithms when the appropriate reply time is selected. This is what our proposed algorithm focuses on: it is robust to tag mobility to some extent. We test the performance of proposed algorithm using a well-designed experiment. Based on the experiment results, the localization algorithm can achieve high accuracy without an additional restriction on the reply time and the clock skew.