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Least squares range difference location

机译:最小二乘范围差异位置

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摘要

An array of n sensors at known locations receives the signal from an emitter whose location is desired. By measuring the time differences of arrival (TDOAs) between pairs of sensors, the range differences (RDs) are available and it becomes possible to compute the emitter location. Traditionally geometric solutions have been based on intersections of hyperbolic lines of position (LOPs). Each measured TDOA provides one hyperbolic LOP. In the absence of measurement noise, the RDs taken around any closed circuit of sensors add to zero. A bivector is introduced from exterior algebra such that when noise is present, the measured bivector of RDs is generally infeasible in that there does not correspond any actual emitter position exhibiting them. A circuital sum trivector is also introduced to represent the infeasibility; a null trivector implies a feasible RD bivector. A 2-step RD Emitter Location algorithm is proposed which exploits this implicit structure. Given the observed noisy RD bivector Δ, (1) calculate the nearest feasible RD bivector Δ?, and (2) calculate the nearest point to the ( 3n) planes of position, one for each of the triads of elements of Δ?. Both algorithmic steps are least squares (LS) and finite. Numerical comparisons in simulation show a substantial improvement in location error variances
机译:在已知位置的n个传感器的阵列从需要其位置的发射器接收信号。通过测量传感器对之间的到达时间差(TDOA),可以得到距离差(RD),并且有可能计算发射器位置。传统上,几何解决方案基于双曲线位置线(LOP)的交集。每个测量的TDOA提供一个双曲LOP。在没有测量噪声的情况下,在传感器的任何闭合电路周围采集的RD都为零。从外部代数引入双矢量,使得当存在噪声时,测得的RD双矢量通常是不可行的,因为不存在任何实际的显示它们的发射器位置。还引入了回路和三矢量来表示不可行。空三向量表示可行的RD双向量。提出了一种利用此隐式结构的两步RD发射器定位算法。给定观察到的有噪声的RD双矢量Δ,(1)计算最接近的可行RD双矢量Δβ,(2)计算到位置(3n)平面的最接近点,每个Δα元素三单元组之一。这两个算法步骤都是最小二乘(LS)和有限的。仿真中的数值比较显示位置误差方差的显着改善

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