We present a detection problem where several spatially distributed sensors observe Poisson signals emitted from a single radioactive source of unknown position. The measurements at each sensor are modeled by independent inhomogeneous Poisson processes. A method based on Bayesian change-point estimation is proposed to identify the location of the source’s coordinates. The asymptotic behavior of the Bayesian estimator is studied. In particular, the consistency and the asymptotic efficiency of the estimator are analyzed. The limit distribution and the convergence of the moments are also described. The similar statistical model could be used in GPS localization problems.

中文翻译：

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平面上的泊松源定位：变点情况

我们提出了一个检测问题，其中几个空间分布的传感器观察从未知位置的单个放射源发出的泊松信号。每个传感器的测量都由独立的非齐次泊松过程建模。提出了一种基于贝叶斯变化点估计的方法来识别源坐标的位置。研究了贝叶斯估计量的渐近行为。特别地，分析了估计量的一致性和渐近效率。还描述了极限分布和矩的收敛性。类似的统计模型可用于 GPS 定位问题。