## 2016/10/26

### A primer on filtering

Say that you have a dynamical process of interest $X_1,\ldots,X_n$ and you can only observe the process with some noise, i.e., you get an observation sequence $Y_1,\ldots,Y_n$. What is the optimal way to estimate $X_n$ conditioned on the whole sequence of observations $Y_{1:n}$?