  We consider the problem of nonlinear filtering of one-dimensional diffusions
from noisy measurements. The filter is said to lose lock if the estimation
error exits a prescribed region. In the case of phase estimation this region is
one period of the phase measurement function, e.g., $[-\pi,\pi]$. We show that
in the limit of small noise the causal filter that maximizes the mean time to
loose lock is Bellman's minimum noise energy filter.
