This paper studies a new type of filtering problem, where the diffusion coefficient of the observation noise is strictly positive only in the interior of the bounded interval where observation takes its values. We derive a Zakai and a Kushner–Stratonovich equation, and prove uniqueness of the measure–valued solution of the Zakai equation.
"Nonlinear filtering with degenerate noise." Electron. Commun. Probab. 22 1 - 14, 2017. https://doi.org/10.1214/17-ECP74