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Reference broadcast-based time synchronisation protocols are appreciated by the wireless sensor network community for their low-power demands. The underlying time relation characteristics of the broadcast-based time synchronisation schemes are prone to the effects resulting from the time record correlations. The recursive equivalents of the existing time synchronisation methods have large clock skew estimation error variance since these methods ignore the effect of correlation. In this study, the authors propose a novel recursive clock synchronisation algorithm based on a time relation model that reflects the effect of correlation. The authors utilise the maximum likelihood estimator to reach an asymptotically consistent and efficient clock skew estimator. The authors theoretically evaluate the performance of the developed estimator and compare it with the existing ones. Of the methods studied, the proposed estimator achieved the smallest estimation error variance. Experimental validation suggests an accuracy of less than one tick at synchronisation instants for a 6 h experiment.