The linear array's one-dimensional spatial geometry is simple but suffices for univariate direction finding, i.e., is adequate for the estimation of an incident source's direction-of-arrival relative to the linear array axis. However, this nominal one-dimensional ideality could be often physically compromised in the real world, as the constituent sensors may dislocate three-dimensionally from their nominal positions. For example, a towed array is subject to ocean-surface waves and to oceanic currents [Tichavsky and Wong (2004). IEEE Trans. Sign. Process. 52(1), 36–47]. This paper analyzes how a nominally linear array's one-dimensional direction-finding accuracy would be degraded by the three-dimensional random dislocation of the constituent sensors. This analysis derives the hybrid Cramér-Rao bound (HCRB) of the arrival-angle estimate in a closed form expressed in terms of the sensors' dislocation statistics. Surprisingly, the sensors' dislocation could improve and not necessarily degrade the HCRB, depending on the dislocation variances but also on the incident source's arrival angle and the signal-to-noise power ratio.

中文翻译：

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均匀线性阵列的各向同性传感器-方向发现的混合Cramér-Rao界中的三维位错。

线性阵列的一维空间几何结构很简单，但足以用于单变量方向查找，即，足以估计入射源相对于线性阵列轴的到达方向。然而，这种标称一个维理想可以经常身体在现实世界中受到损害，作为构成传感器可以打乱3从其标称位置加以-dimensionally。例如，被拖曳的阵列会受到海面波和洋流的影响[Tichavsky and Wong（2004）。IEEE Trans。标志。处理。52（1），36–47]。本文分析标称线性阵列的如何一个维向精度将由降解3个构成传感器的维随机错位。该分析以传感器的位错统计数据表示的闭合形式，得出了到达角估计值的混合Cramér-Rao界（HCRB）。出乎意料的是，传感器的位错可以改善HCRB，而不必降低HCRB，这取决于位错变化，还取决于入射源的到达角和信噪比。