Time synchronization is one of the key technologies of wireless sensor networks. At present, most studies assume that the transmission delay is a fixed value, and there is no effective processing of historical clock data. Therefore, this paper proposes a clock frequency drift and phase offset estimation scheme which is considering variable transmission delay and historical clock data. This paper has clarified the effectiveness of the Gaussian delay model in the calculation of time synchronization error. On this basis, this paper calculated the maximum likelihood estimations of frequency drift and phase offset and the corresponding Cramer-Rao lower bound. Meanwhile, the transmission delay is optimized by comparing the chi-square distance between measured and standard data. Also, this paper conducts autonomous training on historical data to provide services for improving the accuracy of fitting estimation. Simulation results validate the performance of the proposed scheme.

中文翻译：

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基于双向消息交换的WSN时间同步有效频移和相位偏移估计

时间同步是无线传感器网络的关键技术之一。目前，大多数研究假设传输延迟是一个固定值，没有对历史时钟数据进行有效处理。因此，本文提出了一种考虑可变传输延迟和历史时钟数据的时钟频率漂移和相位偏移估计方案。本文阐明了高斯延迟模型在时间同步误差计算中的有效性。在此基础上，本文计算了频率漂移和相位偏移的最大似然估计值以及相应的Cramer-Rao下界。同时，通过比较测量数据和标准数据之间的卡方距离来优化传输延迟。还，本文对历史数据进行自主训练，为提高拟合估计的准确性提供服务。仿真结果验证了所提方案的性能。