We give an approximation for optimal filtering estimates of a diffusion type signal and its observation under contamination affecting their drifts. The method of analysis is based on the averaging principle and convergence in total variation for distributions of signal and observation.
"Nonlinear filtering problem with contamination." Ann. Appl. Probab. 7 (4) 917 - 934, November 1997. https://doi.org/10.1214/aoap/1043862418