Recursive linear estimation for doubly stochastic Poisson processes

The problem of estimating the intensity process of a doubly stochastic Poisson process is analyzed. Using covariance information, a recursive linear minimum mean-square error estimate is designed. Moreover, an efficient procedure for the computation of its associated error covariance is shown. The proposed solution becomes an alternative approach to the Kalman filter which is applicable under the only structural assumption that the intensity process to be estimated has a finite-dimensional covariance function.