超宽带传感器网络中的时钟刚性及位置-时钟联合估计
Clock Rigidity and Joint Position-Clock Estimation in Ultra-Wideband Sensor Networks
摘要：
在无线传感器网络的许多应用中，位置和时钟联合估计是至关重要的，特别是在基于距离的估计与到达时间（TOA）测量。在这项工作中，我们考虑了一个基于TOA的超宽带（UWB）传感器网络，提出了一种新的时钟刚性理论，并研究网络图的属性和TOA时间戳测量的时钟估计的可行性之间的关系。它表明，一个时钟框架可以唯一地确定到一个翻译的时钟偏移和缩放的所有时钟参数，当且仅当它是无限小时钟刚性。我们进一步证明了一个时钟框架是无穷小时钟刚性的，如果它的基础图是一般轴承刚性在2维空间中，至少有一个冗余的边缘。结合距离刚性，时钟刚性提供了一个图形化的方法来分析关节的位置和时钟的问题。它表明，一个位置时钟框架可以唯一地确定到一些微不足道的变化对应的位置和时钟当且仅当它是无穷小关节刚性。仿真结果表明，时钟估计和联合位置时钟估计。
英文摘要：
Joint position and clock estimation is crucial in many wireless sensor network applications, especially in distance-based estimation with time-of-arrival (TOA) measurement. In this work, we consider a TOA-based ultra-wideband (UWB) sensor network, propose a novel clock rigidity theory and investigate the relation between the network graph properties and the feasibility of clock estimation with TOA timestamp measurements. It is shown that a clock framework can be uniquely determined up to a translation of clock offset and a scaling of all clock parameters if and only if it is infinitesimally clock rigid. We further prove that a clock framework is infinitesimally clock rigid if its underlying graph is generically bearing rigid in 2-dimensional space with at least one redundant edge. Combined with distance rigidity, clock rigidity provides a graphical approach for analyzing the joint position and clock problem. It is shown that a position-clock framework can be uniquely determined up to some trivial variations corresponding to both position and clock if and only if it is infinitesimally joint rigid. Simulation results are presented to demonstrate the clock estimation and joint position-clock estimation.
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