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.

Introduction

At present, there is an increasing number of studies focusing on wireless sensor networks (WSNs), mainly due to their rich applications in environmental monitoring, internet of things (IoT), military purposes and so on [1]–[۶]. Localization plays one of the most important roles in WSNs. This is because a large number of operations of WSNs require the accurate localization of the individual nodes as a priori information to know where the metrics were measured [7]–[۱۲]. Although global positioning systems (GPSs) are well-known methods for source localization, the accuracy provided by GPS is not always sufficient in harsh environments (e.g., urban canyons and indoor scenes). Moreover, the terminals in GPS-based localization systems require GPS receivers, which are uneconomical and unrealistic [13], [14]. For this reason, many source node localization algorithms applied to wireless sensor networks have recently been proposed in the literature. Wireless sensor networks commonly contain two types of sensor nodes, referred to as anchor nodes and tag nodes. Anchors have perfectly known locations and are regarded as the referent nodes to locate tags. Tags have unknown locations and need to be located. The purpose of localization is to estimate the locations of tags via measurements among the sensor nodes [15]–[۱۸]. In general, localization algorithms can be classified as rangebased methods and range-free methods. This paper pays attention to the range-based methods because they tend to provide better performances.