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 timeof-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.INDEX TERMS Source localization, wireless sensor network (WSN), time-of-flight (TOF), symmetric double-sided two-way ranging (SDS-TWR), relative clock skew.

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Accuracy and energy consumption are two crucial assessment standards for localization systems. The positioning algorithm used in a single technique may not balance the accuracy and power problem due to its limitations. Moreover, the performance of the existing combined localization method is unsatisfactory. In this paper, taking the relative clock skew into account, we investigate the biased time-of-flight (TOF) compensation problem in the symmetric double-sided two-way ranging (SDS-TWR) method. We first estimate the relative clock skew among sensor nodes to improve the accuracy of the ranging result. We then combine with the time-difference-of-arrival (TDOA) algorithm and reduce the number of transmissions and receptions on the tag (a node that needs to be located) side. Finally, the tag location is determined by Newton's iteration method. A simulation is implemented to validate our theoretical analysis and the results show that our proposed hybrid localization algorithm improves the locating accuracy significantly, compared with that of the C-TDOA method. Furthermore, the proposed hybrid localization algorithm can overcome the shortcoming of high power cost in the conventional TOF-based algorithm. INDEX TERMS Wireless sensor network, hybrid localization algorithm, time-difference-of-arrival (TDOA), time-of-flight (TOF), clock skew estimation.

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