Properties of optimal linear smoothing
Brian D. O. Anderson · IEEE Transactions on Automatic Control · 1969
The problem is considered of characterizing the improvement in estimating the state of a linear system when filtering is replaced by smoothing. It is found that when the optimal filter is exponentially asymptotically stable, a smoothing lag equal to several time constants associated with this filter yields practically all the possible improvement. The extent of improvement, as measured by an error variance matrix, is also found.