Now, the really interesting mapping problem is "close the loop". This is a difficult problem since the odometry error---despite my incremental correction algorithms---can grow without a bound. When closing the loop, I have to revise past beliefs backwards in time!
Notice our new statistical techniques tha allow me to track my
position on-line, build the maximum likelihood map, but also maintain
a probabilistic belief (green samples) that allows me to realign my
map when "closing the loop".