This paper investigates the problem of source localization using signal time-difference-of-arrival (TDOA) measurements in the presence of clock synchronization bias and sensor position errors. Our existing work has developed a unified solution for TDOA localization in the presence of sensor position errors but clock synchronization bias was not considered. Clock synchronization bias is a more complex problem often encountered in practical localization networks. This paper further generalizes this framework to include clock synchronization bias. The proposed technique employs multiple calibration emitters to simultaneously alleviate both the sensor position errors and clock synchronization bias. The maximum likelihood estimator (MLE) for this problem is optimal, but too complex to be applied in practice. We develop a semidefinite programming (SDP) based localization algorithm to effectively solve the MLE problem. This SDP algorithm can reach the Cram$\acute{\text{e}}$r-Rao lower bound when sensor position errors are not unrealistically large.

中文翻译：

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缓解TDOA定位中时钟同步偏差和传感器位置误差的半定规划方法

本文研究了在存在时钟同步偏差和传感器位置误差的情况下使用信号到达时间差 (TDOA) 测量进行源定位的问题。我们现有的工作已经为存在传感器位置误差的 TDOA 定位开发了一个统一的解决方案，但没有考虑时钟同步偏差。时钟同步偏差是实际定位网络中经常遇到的一个更复杂的问题。本文进一步概括了该框架以包含时钟同步偏差。所提出的技术采用多个校准发射器来同时减轻传感器位置误差和时钟同步偏差。此问题的最大似然估计器 (MLE) 是最佳的，但太复杂而无法在实践中应用。我们开发了一种基于半定规划 (SDP) 的定位算法来有效解决 MLE 问题。当传感器位置误差不是不切实际的大时，这种 SDP 算法可以达到 Cram$\acute{\text{e}}$r-Rao 下限。