Discrete time nonlinear filtering with marked point process observations

This work discusses the problem of estimating a nonlinear signal process with nonadditive non-Gaussian noise via a marked point process observation. We begin by introducing a modeling of discrete-time marked point processes. In order to derive the exact filter, namely the conditional density of the signal given the observation history, a reference probability is introduced; this probability measure renders the signal and the observation processes independent, as needed. We present a discrete-time version of Zakai equation corresponding to our model. By specializing the signal to be linear, we moreover show, under suitable assumptions, that the filter is finite dimensional.