Direct approach to diffusion filtering equations

The model consists of a system of two diffusion equations one of which is called a signal and another is an observation process. The task is for any moment of time to compute the best in square mean estimator of the signal given observations to this time, which is called filter and for which linearized SPDE equations have been derived (long ago). In the talk it will be shown how to derive these equations "by hands" without any big theory. If time allows, approximation issues will be also discussed.