Nonlinear Filtering with Optimal MTLL
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., $[-π,π]$. 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.
math.OC↗