2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125935We 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., $[-π,π]$. 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.Optimization and ControlProbability60G35text