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Synchronization and ranging in internet of things (IoT) networks arechallenging due to the narrowband nature of signals used for communicationbetween IoT nodes. Recently, several estimators for range estimation usingphase difference of arrival (PDoA) measurements of narrowband signals have beenproposed. However, these estimators are based on data models which do notconsider the impact of clock-skew on the range estimation. In this paper,clock-skew and range estimation are studied under a unified framework. Wederive a novel and precise data model for PDoA measurements which incorporatesthe unknown clock-skew effects. We then formulate joint estimation of theclock-skew and range as a two-dimensional (2-D) frequency estimation problem ofa single complex sinusoid. Furthermore, we propose: (i) a two-way communicationprotocol for collecting PDoA measurements and (ii) a weighted least squares(WLS) algorithm for joint estimation of clock-skew and range leveraging theshift invariance property of the measurement data. Finally, through numericalexperiments, the performance of the proposed protocol and estimator is comparedagainst the Cramer Rao lower bound demonstrating that the proposed estimator isasymptotically efficient.

Joint Ranging and Clock Synchronization for Dense Heterogeneous IoT Networks