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Spherical interpolation method of emitter localisation using weighted least squares

机译：加权最小二乘法的辐射源定位球面插值方法

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摘要

In this study, a new noise model is presented to address the issue of finding an emitting target using time difference of arrival measurements, based on the range between the emitter and a known sensor. To improve the performance of the estimator under the proposed noise model, a weighted version of the spherical interpolation method is proposed and then two weighting matrices required in the method are derived in two different conditions. A detailed theoretical error analysis associated with this algorithm is presented and the Cramer-Rao lower bound is also derived. Simulation studies verify the validity of the proposed error analysis. In addition, in a two-dimensional space and in the case of a minimal number of sensors, the authors analytically determine the sensors layout in which the location solution is not unique. Via simulations, several placements in a covered region are studied to select the appropriate placement in which the root mean square error of the target position estimation is minimised. Furthermore, simulation results show that they can do this work by the derived expression of the error analysis, which leads to the same outcome.
机译：在这项研究中，提出了一种新的噪声模型，以解决基于发射器和已知传感器之间的距离，使用到达时间差来找到发射目标的问题。为了在所提出的噪声模型下提高估计器的性能，提出了球面插值方法的加权形式，然后在两种不同条件下推导了该方法所需的两个加权矩阵。提出了与此算法相关的详细理论误差分析，并导出了Cramer-Rao下界。仿真研究验证了所提出的误差分析的有效性。此外，在二维空间中，在传感器数量最少的情况下，作者分析性地确定了位置解决方案并非唯一的传感器布局。通过模拟，研究了覆盖区域中的几个放置，以选择适当的放置，在该放置中目标位置估计的均方根误差最小。此外，仿真结果表明，他们可以通过误差分析的派生表达式来完成这项工作，从而得出相同的结果。

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