Recursive Linear Estimation for Doubly Stochastic Poisson Processes

The problem of estimating the inten- sity process of a doubly stochastic Poisson process is analyzed. Using covariance information, a re- cursive linear minimum mean-square error estimate is designed. Moreover, an e-cient procedure for the computation of its associated error covariance is shown. The proposed solution becomes an alternative approach to the Kalman fllter which is applicable un- der the only structural assumption that the intensity process to be estimated has a flnite-dimensional co- variance function.