How to track a swarm of fireflies by observing their flashes (Corresp.)

In this correspondence, we examine the problem of estimating the centroid of a normally shaped intensity function of a time-space point process in terms of an observed realization of the point process. The centroid is assumed to move randomly as a projection of a Gauss-Markov process. We find that the centroid is conditionally normal given the observations. Dynamical equations are given for the conditional mean and covariance of the centroid. The resulting filter is nonlinear, but closely related to the continuous-discrete Kalman-Bucy filter. An application to optical position sensing is given.