Changepoint detection using nonlinear filters

In this paper we study the optimal nonlinear filter for a jump process arising in changepoint detection problems. We formulate an suboptimal approximation to this filter which uses the Zakai equation to define projection operators in a suitably chosen probability density space. This is an extension of the powerful approach introduced in [4], where such operators where used to filter diffusion processes. We compare this Projection Filter with the optimal one in a simulation study, and indicate how its excellent performance may be exploited in detection and estimation problems.