Synchronization and ranging in internet of things (IoT) networks are challenging due to the narrowband nature of signals used for communication between IoT nodes. Recently, several estimators for range estimation using phase difference of arrival (PDoA) measurements of narrowband signals have been proposed. However, these estimators are based on data models which do not consider the impact of clock-skew on the range estimation. In this paper, clock-skew and range estimation are studied under a unified framework. We derive a novel and precise data model for PDoA measurements which incorporates the unknown clock-skew effects. We then formulate joint estimation of the clock-skew and range as a two-dimensional (2-D) frequency estimation problem of a single complex sinusoid. Furthermore, we propose: (i) a two-way communication protocol for collecting PDoA measurements and (ii) a weighted least squares (WLS) algorithm for joint estimation of clock-skew and range leveraging the shift invariance property of the measurement data. Finally, through numerical experiments, the performance of the proposed protocol and estimator is compared against the Cramer Rao lower bound demonstrating that the proposed estimator is asymptotically efficient.
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