Filtering and detection for doubly stochastic Poisson processes
Filtering and detection for doubly stochastic Poisson processes
复制标题
双随机泊松过程的过滤和检测
DOI：
10.1109/tit.1972.1054756
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发表时间：
1972
期刊：
影响因子：
--
通讯作者：
D. Snyder
中科院分区：
文献类型：
--
作者：
D. Snyder
推导了描述一般马尔可夫过程后验统计量的时间演化方程，该过程调节观测到的非齐次泊松计数过程的强度函数。基本方程是马尔可夫过程条件特征函数的随机微分方程。建立了检测具有随机强度函数的泊松过程的分离定理。具体地说，随机强度的因果最小均方误差估计以相同的方式被纳入最优Reiffen-Sherman检测器，就好像它是已知的一样。当一组随机变量调节强度时，得到专门的结果。其中包括变量的最大后验概率估计方程和基于Cramer-Rao不等式的一些精度方程。给出了马尔可夫过程精确估计的近似方法。通过对精确估计和近似估计的仿真比较表明，所提出的近似估计即使在低计数率条件下也能很好地工作。
Equations are derived that describe the time evolution of the posterior statistics of a general Markov process that modulates the intensity function of an observed inhomogeneous Poisson counting process. The basic equation is a stochastic differential equation for the conditional characteristic function of the Markov process. A separation theorem is established for the detection of a Poisson process having a stochastic intensity function. Specifically, it is shown that the causal minimum-mean-square-error estimate of the stochastic intensity is incorporated in the optimum Reiffen-Sherman detector in the same way as if it were known. Specialized results are obtained when a set of random variables modulate the intensity. These include equations for maximum a posteriori probability estimates of the variables and some accuracy equations based on the Cramer-Rao inequality. Procedures for approximating exact estimates of the Markov process are given. A comparison by simulation of exact and approximate estimates indicates that the approximations suggested can work well even under low count rate conditions.