I am currently working on a problem on filtering. In fact, let's suppose a signal that is expressed as : $r(t) = z(t) + x_i(t)$, where $z(t)$ is a smooth function and $x_i(t)$ is white Gaussian noise.
The question is to find the optimal filter for eliminating the Gaussian noise $x_i(t)$ if nothing is known about the smooth signal $z(t)$?".
Sure thing, Kalman Filter has been lately solicited faced to problems that ask for optimal filters. However,in this situation, that Kalman filter is the best candidate since we do not know anything about z.
Thus, I think they are better candidates for this problem.