We consider the problem of estimating the rate of a doubly- stochastic, time-space Poisson process when the observations are restricted to a region D subset of R^2. In the general case, we obtain a representation of the minimum mean-square-error (MMSE) estimate in terms of the conditional characteristic function of an underlying state process. In the case D=R^2, we extend a known result to compute the MMSE estimate explicitly. For a special form of the rate process, a well-defined integral equation is presented which defines the linear MMSE estimate of the rate.
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机译：当观察仅限于R ^ 2的D区域子集时，我们考虑估计双随机时空泊松过程的速率的问题。在一般情况下，我们根据基本状态过程的条件特征函数获得最小均方误差（MMSE）估计的表示。在D = R ^ 2的情况下，我们扩展已知结果以显式计算MMSE估计。对于速率过程的一种特殊形式，提出了定义明确的积分方程，该方程定义了速率的线性MMSE估计。
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