An attractive and challenging problem in source localisation is to locate a target in three-dimensional (3D) space using a single station. To satisfy the observability requirements and achieve higher accuracy, the authors draw on the idea of the inverse synthetic aperture radar for single-station localisation, which leverages the mobility of target and a time serial measurements of angle of arrival (AoA) and time difference of arrival (TDoA). A closed-form pseudo-linear estimator (PLE) is developed to estimate both 3D position and velocity of mobile target through the linearisation of AoA–TDoA measurement equations. Furthermore, to suppress the large bias of PLE caused by the correlation of measurement noise, the authors propose a superior bias-reduced estimator (BRE), which imposes a quadratic constraint to minimise the noise correlation term. They prove that BRE is asymptotically efficient, attaining the Cramér-Rao lower bound (CRLB) over the moderate noise region. Extensive simulations show that both bias and mean square error of BRE are well predicted by theoretical analysis. Most importantly, in comparison with both PLE and two traditional bias reduction methods, namely weighted total least squares and weighted instrumental variables, BRE can approach the CRLB over a wider noise region and maintain a lower bias.

中文翻译：

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使用具有AoA–TDoA测量值的单站对移动目标进行精确的3D定位

源定位中一个有吸引力且具有挑战性的问题是使用单个工作站在三维（3D）空间中定位目标。为了满足可观测性要求并获得更高的精度，作者借鉴了用于单站定位的逆向合成孔径雷达的思想，该思想利用了目标的移动性以及到达角（AoA）和时间差的时间序列测量到达（TDoA）。开发了一种封闭形式的伪线性估计器（PLE），以通过AoA–TDoA测量方程的线性化来估计移动目标的3D位置和速度。此外，为了抑制由测量噪声的相关性引起的PLE的较大偏差，作者提出了一种优越的减小偏差的估计器（BRE），该估计器施加了二次约束以最小化噪声相关项。他们证明了BRE是渐近有效的，在中等噪声范围内达到了Cramér-Rao下界（CRLB）。大量的仿真表明，通过理论分析可以很好地预测BRE的偏差和均方误差。最重要的是，与PLE和两种传统的偏差减少方法（即加权总最小二乘法和加权工具变量）相比，BRE可以在更宽的噪声范围内接近CRLB并保持较低的偏差。