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Estimation of a Low-Intensity Filtered Poisson Process in Additive White Gaussian Noise

机译:加性高斯白噪声中低强度滤波泊松过程的估计

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A Poisson–Gauss process is defined as the sum of a filtered Poisson process (a Poisson process passed through a linear filter) and a white Gaussian noise. This model describes the electrical signal at the output of an optical measuring unit consisted of a photodetector and its following amplifying circuits. The intensity of the Poisson process in this model is proportional to the received optical power. With the observations of a Poisson–Gauss process, three estimation problems are considered: minimum mean squared error estimation of the Poisson process at every fixed but arbitrary time, minimum mean squared error estimation of the Poisson intensity, and the maximum likelihood estimation of the intensity. The solutions to these problems are presented in terms of a complicated functional of the observed Poisson–Gauss process which is hard to compute for an arbitrary value of the Poisson intensity; however, under a low-intensity regime, nonlinear filtering schemes are developed to efficiently compute this functional. This special case provides a signal processing framework for single photon detection, a technology dedicated to measurement of low optical powers.
机译:泊松-高斯过程定义为经过滤波的泊松过程(通过线性滤波器的泊松过程)和高斯白噪声的总和。该模型描述了由光电检测器及其后续放大电路组成的光学测量单元输出端的电信号。此模型中的泊松过程的强度与接收的光功率成正比。通过对泊松-高斯过程的观察,考虑了三个估计问题:每个固定但任意时间的泊松过程的最小均方误差估计,泊松强度的最小均方误差估计以及强度的最大似然估计。这些问题的解决方案是根据观察到的泊松-高斯过程的复杂功能提出的,很难对泊松强度的任意值进行计算。然而,在低强度状态下,开发了非线性滤波方案以有效地计算该函数。这种特殊情况为单光子检测提供了一种信号处理框架,该技术专门用于测量低光功率。

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