well a Kalman filter could work but then you could also sending for the smoother you could say oh let me also run the smoother and what would you hope for you'd hope for the smoother let's move your estimate to have a mean that is closer to the real state than the filter it doesn't always have to be closer but an expectation it should be closer because it brings in more information by bringing more information it should be able to do better where might this would be most pronounced at time 0 because at time 0 the filter will have no