let's start with smoothing what's the main idea behind smoothing let's go back to filtering which we've been doing in filtering what you have is you try to find a distribution over variable XT after you have observed some sensor measurements Z 0 through ZT and ideally over time I keep track of this when you go to the next time you again find a distribution for XT plus 1 given all observations up to time T plus 1 and repeat now if you look at this very symmetric you only use information from the past and often that's indeed the