State estimation from space-time point process observations with an application in optical beam tracking

A stochastic model is considered which involves a linear system driven by Wiener process and the observations of a space-time point process whose intensity depends on the state of this linear system. It is shown that the problem of estimating the state of this continuous-time system can be reduced to estimating the state of a discrete-time linear stochastic system with a Gaussian process noise and a generally non-Gaussian measurement noise. Two types of estimators are developed for this discrete-time system: a linear minimum mean squared estimator and a nonlinear estimator based on the successive projection of the posterior density of the state vector on a Gaussian family of density functions. These discrete-time estimators are employed to determine two classes of estimators for the original continuous-time system. An application to optical beam tracking is presented.