Rapprochement between discrete and continuous nonlinear filtering

In this paper we explore the connection between discrete and continuous nonlinear filtering. In particular, we develop a novel incremental form of the discrete nonlinear filtering equations that holds for arbitrary sampling period. We also show that this form of the discrete nonlinear filter has the same spirit as the continuous filter and embeds the continuous filter as a special case when only certain terms are retained in the equations. Finally, we use these results to gain insights into the choice of sample period in nonlinear filtering. The paper is part review and part novel.