For a positioning system with $L$ sensors, a maximum of $L(L-1)/2$ distinct time-difference-of-arrival (TDOA) measurements, which are referred to as the full TDOA set, can be obtained. In this paper, closed-form expressions regarding optimum conversion of the full TDOA set to the nonredundant TDOA set, which corresponds to $(L-1)$ TDOA measurements with respect to a common reference receiver, in the case of white signal source and noise, are derived. The most interesting finding is that optimum conversion can be achieved via the standard least squares estimation procedure. Furthermore, the CramÉr-Rao lower bound for TDOA-based positioning is produced in closed-form, which will be useful for optimum sensor array design.
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机译：对于带有$ L $传感器的定位系统，最多可以获得$ L（L-1）/ 2 $个独特的到达时间差（TDOA）测量值，称为完整的TDOA集。在本文中，关于在白色信号源和白色信号源的情况下，将完整TDOA集最佳转换为非冗余TDOA集的闭式表达式，这对应于相对于公共参考接收器的$（L-1）$ TDOA测量。噪音。最有趣的发现是可以通过标准的最小二乘估计程序实现最佳转换。此外，用于基于TDOA的定位的CramÉr-Rao下限以封闭形式生成，这对于优化传感器阵列设计很有用。
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