Synchronization Parameter Estimation Algorithm of Silent Node in Wireless Sensor Networks With Timestamp-free Exchange
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摘要: 能效是无线传感网(Wireless sensor networks, WSNs)时间同步机制设计时需考虑的一个关键因素. 近年来, 隐含同步和免时间戳同步两种低功耗同步机制备受关注. 前者利用监听方式节省了发送同步信息所带来的能耗; 后者则通过接收端的定时响应, 无需在交互过程中传递时间戳, 减少了能量开销. 将免时间戳同步与隐含同步相结合, 能够进一步降低无线传感网同步功能实施所导致的额外能耗. 但目前免时间戳交互下的隐含节点只能估计时钟漂移, 无法估计时钟偏移. 针对该问题, 提出了一种基于最大似然估计(Maximum likelihood estimation, MLE)的免时间戳同步参数估计算法, 实现对隐含节点时钟漂移和偏移参数的联合估计, 并推导获得了对应估计器的性能界限. 仿真结果验证了所提估计器的有效性.Abstract: Energy efficiency is a key issue for designing time synchronization mechanism in wireless sensor networks (WSNs). Recently, implicit synchronization and timestamp-free synchronization have attracted much attention. The former uses the monitoring method to save the energy consumption caused by sending synchronization information. The latter reduces the energy overhead by the timing response of receiver without transmitting the timestamp in the exchange process. The combination of timestamp-free synchronization and implicit synchronization can further reduce additional energy consumption caused by the implementation of synchronization function in wireless sensor networks. However, at present, the silent node in timestamp-free exchange can only estimate the clock skew and not the clock offset. To solve this issue, a timestamp-free synchronization parameter estimation algorithm based on maximum likelihood estimation (MLE) is proposed, which can achieve the joint estimation of clock skew and offset for silent node. Then, the corresponding lower bounds of estimation are derived. Finally, simulation results verify the effectiveness of the proposed estimators.
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图 2 节点
$Q$ 监听节点$O$ 与节点$P$ 之间的$N$ 轮免时间戳交互Fig. 2 The
$N$ rounds of timestamp-free exchange between node$O$ and$P$ with node$Q$ overhearing them
图 3 隐含节点
$Q$ 时钟漂移估计${{\hat{\alpha }}^{\left(QO \right)}}$ 的MSE与CRLBFig. 3 MSE and CRLB of estimated clock skew
${{\hat{\alpha }}^{\left(QO \right)}}$ for silent node$Q$ 
图 4 隐含节点
$Q$ 时钟偏移估计${{\hat{\vartheta }}^{\left(QO \right)}}$ 的MSE与CRLBFig. 4 MSE and CRLB of estimated clock offset
${{\hat{\vartheta }}^{\left(QO \right)}}$ for silent node$Q$ 
图 5 不同系数
$\xi $ 下时钟漂移估计器性能对比结果Fig. 5 The performance comparison results of clock skew estimator under different coefficient
$\xi $ 表 1 本文算法与隐含同步算法、免时间戳同步算法以及免时间戳和隐含同步结合算法的计算数量对比结果
Table 1 The comparison results of the number of calculations among proposed algorithm, implicit synchronization algorithm, timestamp-free synchronization algorithm and combination algorithm of timestamp-free and implicit synchronization
算法 参数 加减法数量 乘除法数量 本文算法 时钟漂移 $2{N^2} + 14N - 3$ ${N^2} + 11N + 3$ 时钟偏移 $5{N^2} + 13N - 2$ $4{N^2} + 11N + 4$ 隐含同步算法 时钟漂移 $2{N^2} + 12N - 3$ $3N + 3$ 时钟偏移 $5{N^2} + 11N - 3$ ${N^2} + 3N + 3$ 免时间戳同步算法 时钟漂移 ${N^2} + 6N - 2$ $4N + 3$ 免时间戳与隐含同步结合算法 时钟漂移 $4{N^2} + 10N - 1$ $4{N^2} + 12N + 1$ 
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